Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE)

The Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE) is an online archive aimed at collecting, preserving, and disseminating digital copies of scientific papers published by researchers of the International Center for Numerical Methods in Engineering (CIMNE).

The goal of the repository is to widely disseminate the results of the research performed at CIMNE, by sharing the preprints or postprints -depending on the article sharing policies of the original ... show more

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Numerical simulation and visualization of material flow in friction stir welding via particle tracing
N. Dialami, M. Chiumenti, M. Cervera, C. Agelet de Saracibar, J. Ponthot, P. Bussetta

(2014). S. Idelsohn (Ed.), Numerical Simulations of Coupled Problems in Engineering, Part III, Chapter 7 Computational Methods, Vol. 33, Springer, pp. 157-169

Abstract
This work deals with the numerical simulation and material flow visualization of Friction Stir Welding (FSW) processes. The 4-th order Runge-Kutta (RK4) integration method is used for the computation of particle trajectories. The particle tracing method is used to study the effect of input process parameters and pin shapes on the weld quality. The results show that the proposed method is suitable for the optimization of the FSW process.
Abstract
This work deals with the numerical simulation and material flow visualization of Friction Stir Welding (FSW) processes. The 4-th order Runge-Kutta (RK4) integration method [...]
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Challenges to be tackled in the computational modeling and numerical simulation of FSW processes
C. Agelet de Saracibar

Metals (2019). Vol. 9 (5), pp. 573

Abstract
The computational modeling and numerical simulation of Friction Stir Welding (FSW) processes is an extremely challenging task due to the highly nonlinear and coupled nature of the physical problem and the complex computational issues that need to be properly tackled in the numerical model.
Abstract
The computational modeling and numerical simulation of Friction Stir Welding (FSW) processes is an extremely challenging task due to the highly nonlinear and coupled nature [...]
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Conserving algorithms for frictionless and full stick friction contact dynamic problems using the direct elimination method
C. Agelet de Saracibar, D. Di Capua

Int. J. Numer. Meth. Engng. (2017). (preprint) Vol. 113 (6), pp. 910-937

Abstract
In this paper, conserving time‐stepping algorithms for frictionless and full stick friction dynamic contact problems are presented. Time integration algorithms for frictionless and full stick friction dynamic contact problems have been designed to preserve the conservation of key discrete properties satisfied at the continuum level. Energy and energy‐momentum–preserving algorithms for frictionless and full stick friction dynamic contact problems, respectively, have been designed and implemented within the framework of the direct elimination method, avoiding the drawbacks linked to the use of penalty‐based or Lagrange multipliers methods. An assessment of the performance of the resulting formulation is shown in a number of selected and representative numerical examples, under full stick friction and slip frictionless contact conditions. Conservation of key discrete properties exhibited by the time‐stepping algorithm is shown.
Abstract
In this paper, conserving time‐stepping algorithms for frictionless and full stick friction dynamic contact problems are presented. Time integration algorithms for frictionless [...]
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Software Solutions for ICME
G. Schmitz, A. Engstrom, R. Bernhardt, U. Prahl, L. Adam, J. Seyfarth, M. Apel, C. Agelet de Saracibar, P. Korzhavyi, J. Agren, B. Patzak

Journal of The Minerals, Metals & Materials Society (2016). Vol. 68 (1), pp. 70-76

Abstract
The Integrated Computational Materials Engineering expert group (ICMEg), a coordination activity of the European Commission, aims at developing a global and open standard for information exchange between the heterogeneous varieties of numerous simulation tools. The ICMEg consortium coordinates respective developments by a strategy of networking stakeholders in the first International Workshop on Software Solutions for ICME, compiling identified and relevant software tools into the Handbook of Software Solutions for ICME, discussing strategies for interoperability between different software tools during a second (planned) international workshop, and eventually proposing a scheme for standardized information exchange in a future book or document. The present article summarizes these respective actions to provide the ICME community with some additional insights and resources from which to help move this field forward.
Abstract
The Integrated Computational Materials Engineering expert group (ICMEg), a coordination activity of the European Commission, aims at developing a global and open standard [...]
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A direct elimination algorithm for quasi-static and dynamic contact problems
D. Di Capua, C. Agelet de Saracibar

Finite Elements in Analysis and Design (2015). (preprint) Vol. 93 (1), pp. 107-125

Abstract
This paper deals with the computational modeling and numerical simulation of contact problems at finite deformations using the finite element method. Quasi-static and dynamic problems are considered and two particular frictional conditions, full stick friction and frictionless cases, are addressed. Lagrange multipliers and regularized formulations of the contact problem, such as penalty or augmented Lagrangian methods, are avoided and a new direct elimination method is proposed. Conserving algorithms are also introduced for the proposed formulation for dynamic contact problems. An assessment of the performance of the resulting formulation is shown in a number of selected benchmark tests and numerical examples, including both quasi-static and dynamic contact problems under full stick friction and frictionless contact conditions. Conservation of key discrete properties exhibited by the time stepping algorithm used for dynamic contact problems is also shown in an example
Abstract
This paper deals with the computational modeling and numerical simulation of contact problems at finite deformations using the finite element method. Quasi-static and dynamic [...]
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Discrete element modelling and simulation of sand mould manufacture for the lost foam process
J. Rojek, F. Zárate, C. Agelet de Saracibar, C. Gilbourne, P. Verdot

Int. J. Numer. Meth. Engng. (2004). Vol. 62 (11), pp. 1241-1441

Abstract
This paper presents a numerical model of mould manufacture for the lost foam casting process. The process of mould filling with sand and sand compaction by vibration are modelled using spherical (in 3D) or cylindrical (in 2D) discrete elements. The motion of discrete elements is described by means of equations of rigid body dynamics. Rigid particles interact among one another with contact forces, both in normal and tangential directions. Numerical simulation predicts defects of the mould due to insufficient sand compaction around the pattern. Combining the discrete element model of sand with the finite element model of the pattern allows us to detect possible distortion of the pattern during mould filling and compaction. Results of numerical simulation are validated by comparison with experimental data.
Abstract
This paper presents a numerical model of mould manufacture for the lost foam casting process. The process of mould filling with sand and sand compaction by vibration are modelled [...]
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Numerical analysis of coupled thermomechanical frictional contact problems. Computational model and applications
C. Agelet de Saracibar

Archives of Comp. Meths. Engng. (1998). Vol. 5 (3), pp. 243-301

Abstract
In this paper a numerical model for the analysis of coupled thermomechanical multi-body frictional contact problems at finite deformations is presented. The multi-body frictional contact formulation is fully developed on the continuum setting and then a spatial (Galerkin projection) and temporal (time-stepping algorithm) discretization is applied. A contact pressure and temperature dependent thermal contact model has been used. A fractional step method arising from an operator split of the governing equations has been used to solve the coupled nonlinear system of equations, leading to a staggered solution algorithm. The numerical model has been implemented into an enhanced version of the computational finite element program FEAP. Numerical examples and simulation of industrial metal forming processes show the performance of the numerical model in the analysis of coupled thermomechanical frictional contact problems.
Abstract
In this paper a numerical model for the analysis of coupled thermomechanical multi-body frictional contact problems at finite deformations is presented. The multi-body frictional [...]
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Modeling the effect of storage temperature on the respiration rate and texture of fresh cut pineapple
S. Benítez, M. Chiumenti, F. Sepulcre, I. Achaerandio, M. Pujolá

Journal of Food Engineering (2012). Vol. 113 (4), pp. 527-533

Abstract
The effect of temperature on the respiration rate and texture of fresh cut pineapple was studied over the course of 10 days of storage. The thermal exchange between the pineapple trays and the cooling environment was simulated using the finite element method and tested at 6 °C. The temperatures on pineapple wedges differed between the cold point and points near the surface, indicating that the respiration rate may be affected in pineapple subjected to temperature abuse. The experimental respiration rates obtained were used to develop a model relating respiration to O2 and CO2concentrations at different temperatures using the closed system method. The O2 consumption and CO2 production of pineapple wedges was accurately modeled using Michaelis–Menten kinetics. The texture degradation of pineapple wedges follows a zero-order kinetic reaction at different temperatures and the thermal dependence of the model’s parameters for both respiration rate and texture degradation was described by Arrhenius-type equations.
Abstract
The effect of temperature on the respiration rate and texture of fresh cut pineapple was studied over the course of 10 days of storage. The thermal exchange between the [...]
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Shear band localization via local J2 continuum damage mechanics
M. Cervera, M. Chiumenti, C. Agelet de Saracibar

Comput. Methods Appl. Mech. Engrg., (2004). Vol. 193 (9-11), pp. 849-880

Abstract
This paper describes a novel formulation for the solution of problems involving shear band localization using a local isotropic J2 continuum damage model and mixed linear simplex (triangles and tetrahedra). Stabilization methods are used to ensure existence and uniqueness of the solution, attaining global and local stability of the corresponding discrete finite element formulation. Consistent residual viscosity is used to enhance robustness and convergence of the formulation. Implementation and computational aspects are also discussed. A simple isotropic local J2 damage constitutive model is considered, either with linear or exponential softening. The softening modulus is regularized according to the material mode II fracture energy and the element size. Numerical examples show that the formulation derived is fully stable and remarkably robust, totally free of volumetric locking and spurious oscillations of the pressure. As a consequence, the results obtained do not suffer from spurious mesh-size or mesh-bias dependence, comparing very favourably with those obtained with the ill-posed standard approaches.
Abstract
This paper describes a novel formulation for the solution of problems involving shear band localization using a local isotropic J2 continuum damage model and mixed linear [...]
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On the numerical modeling of frictional wear phenomena
C. Agelet de Saracibar, M. Chiumenti

Comput. Methods Appl. Mech. Engrg., (1999). Vol. 177 (3-4), pp. 401-426

Abstract
The evolution of the contact surfaces wear may become particularly important in the definition of the frictional behavior, in particular for frictional contact problems involving large slips, typically in sheet metal forming and bulk forming operations. Despite this fact, most of the current applications reported in the literature are restricted to a standard Coulomb law, using a constant friction coefficient. Such simple models may represent only a limited range of tribological situations and it appears to be necessary to develop a class of models which incorporate the state conditions and their evolution at the contact surfaces, taking into account the influence of complex phenomena such as wear, lubrication and chemical reactions, among others, see Oden and Martins [1]. In this paper a simple numerical model for the simulation of frictional wear behavior, within a fully nonlinear setting, including large slip and finite deformation, is presented. The model relies on the introduction of an internal variable related to the state conditions at the contact surface. Here, two possible definitions of this internal variable have been considered. The fully nonlinear frictional contact formulation, entirely derived first on a continuum setting by Laursen and Simo [2–6], has been extended here to accomodate the characterization of the wear frictional behavior. Within the computational aspects, two families of robust time stepping algorithms, arising from an operator split of the constrained frictional evolution equations, are discussed. Finally, following current approaches, see Lassen [9], Lassen and Bay [10], Owen et al. [11], de Souza et al. [12], Stromberg et al. [13] and Stromberg [14], a long-term tools wear prediction is given by introducing an a priori wear estimate derived from Archard's law, Archard [15]. The numerical model has been implemented into a enhanced version of the computational finite element program FEAP. Numerical examples show the suitability of the proposed model to capture the essential features of the frictional behavior at the contact interfaces and to provide a prediction of tool wear in forming operations.
Abstract
The evolution of the contact surfaces wear may become particularly important in the definition of the frictional behavior, in particular for frictional contact problems involving [...]
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An accurate non-local bonded discrete element method for non linear analysis of solids. Application to concrete fracture tests
M. Celigueta, S. Latorre, F. Arrufat, E. Oñate

Computational Particle Mechanics (2019). (prepint)

Abstract
We present a numerical procedure for elastic and non linear analysis (including fracture situations) of solid materials and structures using the Discrete Element Method (DEM). It can be applied to strongly cohesive frictional materials such as concrete and rocks. The method consists on defining the non-local constitutive equations at the contact interfaces between discrete particles using the information provided by the stress tensor over the neighbour particles. The method can be used with different yield surfaces and in the paper it is applied to the analysis of fracture of concrete samples. Good comparison with experimental results is obtained.
Abstract
We present a numerical procedure for elastic and non linear analysis (including fracture situations) of solid materials and structures using the Discrete Element Method (DEM). [...]
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Combination of a non-local damage model for quasi-brittle materials with a mesh-adaptive finite element technique
I. de-Pouplana, E. Oñate

Finite Elements in Analysis and Design (2016). Vol. 112, pp. 26-39

Abstract
Progressive fracture in quasi-brittle materials is often treated via strain softening models in continuum damage mechanics. Such constitutive relations favour spurious strain localization and ill-posedness of boundary value problems. The introduction of non-local damage models together with a characteristic length parameter controlling the size of the fracture process zone is known to regularize the problem. In order to account for the non-locality of these models, it is crucial to work with fine spatial discretizations at the damage progress zone. In this paper we present a non-local damage model in combination with a mesh-adaptive finite element technique that can help automatize the analysis of progressive fracture problems in an efficient manner. Classical two-dimensional examples are given to illustrate the presented approach.
Abstract
Progressive fracture in quasi-brittle materials is often treated via strain softening models in continuum damage mechanics. Such constitutive relations favour spurious strain [...]
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El valor del cálculo en los sistemas de ayuda a la toma de decisiones en ingeniería
E. Oñate

Revista de Obras Públicas (2004). Vol. 151 (3449), pp. 41-48

Abstract
El artículo revindica el valor de los métodos de cálculo que se enseñan en las Escuelas de Ingeniería, como herramientas indispensables en los nuevos sistemas de ayuda a la toma de decisiones (SAD). Los SAD integran base de datos, métodos de cálculo y módulos de inteligencia artificial, y su utilización se extiende cada día más para ayuda al diseño y gestión de infraestructuras y servicios de ingeniería. En el texto se describen varios desarrollos y aplicaciones recientes de SAD en ingeniería civil. El artículo acaba con una reflexión sobre los límites de los SAD. The paper stresses the value of the computational methods taught in engineering faculties as indispensable tools within the new decision support systems (DSS). The DSS integrate data bases, computational methods and artificial intelligence modules. They are increasingly used for supporting the design and management of civil constructions and services in engineering. The paper describes recent developments and applications of DSS in civil engineering. The text ends up with a discussion on the limits of the DSS.
Abstract
El artículo revindica el valor de los métodos de cálculo que se enseñan en las Escuelas de Ingeniería, como herramientas indispensables [...]
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An implicit unsteady hydraulic solver for suspended cuttings transport in managed pressure wells
R. Flores, R. Ortega, A. Ilin, D. Simpkins, E. Oñate

Computational Particle Mechanics (2019). Vol. 6 (2), pp 163–175

Abstract
We present a simulation tool for transient events in complex hydraulic networks. The code includes modelling of the transport of suspended cuttings in near-vertical wells. An unstructured finite volume formulation with implicit time integration has been chosen. The unconditional stability of the integrator makes the method suitable for the simulation of transient events over a wide range of characteristic timescales. It handles both very fast transients (e.g. fluid hammer events) and the long-term evolution of the well (e.g. hole cleaning operations). The software has been developed to address the need of the oil industry for a robust and efficient predictive tool allowing effective well control in managed pressure drilling operations. The physical modelling follows the standard practices accepted by the industry (e.g. mud rheology computations). The mathematical foundation of the algorithm is described followed by validation cases that illustrate its capabilities and accuracy. Finally, a practical industrial application example is provided to demonstrate the real-world performance of the software.
Abstract
We present a simulation tool for transient events in complex hydraulic networks. The code includes modelling of the transport of suspended cuttings in near-vertical wells. [...]
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Effect of the integration scheme on the rotation of non-spherical particles with the discrete element method
J. Irazábal González, F. Salazar, M. Santasusana, E. Oñate

Computational Particle Mechanics (2019). pp. 1-15

Abstract
The discrete element method (DEM) is an emerging tool for the calculation of the behaviour of bulk materials. One of the key features of this method is the explicit integration of the motion equations. Explicit methods are rapid, at the cost of a limited time step to achieve numerical stability. First- or second-order integration schemes based on a Taylor series are frequently used in this framework and shown to be accurate for the translational and rotational motion of spherical particles. However, they may lead to relevant inaccuracies when non-spherical particles are used since the orientation implies a modification in the second-order inertia tensor in the inertial reference frame. Specific integration schemes for non-spherical particles have been proposed in the literature, such as the fourth-order Runge–Kutta scheme presented by Munjiza et al. and the predictor–corrector scheme developed by Zhao and van Wachem which applies the direct multiplication algorithm for integrating the orientation. In this work, both methods are adapted to be used together with a velocity Verlet scheme for the translational integration. The performance of the resulting schemes, as well as that of the direct integration method, is assessed, both in benchmark tests with analytical solution and in real-scale problems. The results suggest that the fourth-order Runge–Kutta and the Zhao and van Wachem schemes are clearly more accurate than the direct integration method without increasing the computational time.
Abstract
The discrete element method (DEM) is an emerging tool for the calculation of the behaviour of bulk materials. One of the key features of this method is the explicit integration [...]
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A unified Lagrangian formulation for solid and fluid dynamics and its possibility for modelling submarine landslides and their consequences
X. Zhang, E. Oñate, S. Galindo, J. Bleyer, K. Krabbenhoft

Comput. Methods Appl. Mech. Engrg., (2019). Vol. 343, pp. 314-338

Abstract
Consequences of submarine landslides include both their direct impact on offshore infrastructure, such as subsea electric cables and gas/oil pipelines, and their indirect impact via the generated tsunami. The simulation of submarine landslides and their consequences has been a long-standing challenge majorly due to the strong coupling among sliding sediments, seawater and infrastructure as well as the induced extreme material deformation during the complete process. In this paper, we propose a unified finite element formulation for solid and fluid dynamics based on a generalised Hellinger–Reissner variational principle so that the coupling of fluid and solid can be achieved naturally in a monolithic fashion. In order to tackle extreme deformation problems, the resulting formulation is implemented within the framework of the particle finite element method. The correctness and robustness of the proposed unified formulation for single-phase problems (e.g. fluid dynamics problems involving Newtonian/Non-Newtonian flows and solid dynamics problems) as well as for multi-phase problems (e.g. two-phase flows) are verified against benchmarks. Comparisons are carried out against numerical and analytical solutions or experimental data that are available in the literature. Last but not least, the possibility of the proposed approach for modelling submarine landslides and their consequences is demonstrated via a numerical experiment of an underwater slope stability problem. It is shown that the failure and post-failure processes of the underwater slope can be predicted in a single simulation with its direct threat to a nearby pipeline and indirect threat by generating tsunami being estimated as well.
Abstract
Consequences of submarine landslides include both their direct impact on offshore infrastructure, such as subsea electric cables and gas/oil pipelines, [...]
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Modeling polycrystalline materials with elongated grains
I. Pérez, M. Farias, M. Castro, R. Roselló, C. Morfa, L. Medina, E. Oñate

Int J Numer Methods Eng. (2019). Vol. 118 (3), pp. 121-131

Abstract
A novel algorithm to reproduce the arrangement of grains in polycrystalline materials was recently published by the authors. In this original approach, a dense package of circles (or spheres) with the same distribution as the grains is generated to produce a set of Voronoi cells that are later modified to Laguerre cells representing the original structure. This algorithm was successfully applied to materials with somewhat equidimensional grains; however, it fails for long‐shaped grains. In this paper, modifications are provided in order to overcome these drawbacks. This is accomplished by moving each vertex of the Voronoi cells in such a way that the vertex should be equidistant from the particles with respect to the Euclidean distance. The algorithm is applied to packages of ellipses and spherocylinders in 2D. An example for a package of spheres is also provided to illustrate the application for a simple 3D case. The adherence between the generated packages and the corresponding tessellations is verified by means of the Jaccard coefficient (J). Several packages are generated randomly and the distribution of J coefficients is investigated. The obtained values satisfy the theoretical restraints and the quality of the proposed algorithm is statistically validated.
Abstract
A novel algorithm to reproduce the arrangement of grains in polycrystalline materials was recently published by the authors. In this original approach, a dense package of [...]
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Advances in particle packing algorithms for generating the medium in the Discrete Element Method
C. Recarey, I. Pérez, R. Roselló, M. Muniz, E. Hernández, R. Giraldo, E. Oñate

Computer Methods in Applied Mechanics and Engineering (2019). Vol. 345, pp. 336-362

Abstract
Several theoretical contributions in order to establish a particle packing methodology are presented. In this respect, a generic formulation of a new method for packing particles based on a constructive advancing front method, which uses Monte Carlo techniques for the generation of particle dimensions, is also shown. The method can be used to obtain virtual dense packings of particles with several geometrical shapes. It employs continuous, discrete and empirical statistical distributions in order to generate the dimensions of particles. The packing algorithm is very flexible and allows alternatives for: 1- The direction of the advancing front (inwards or outwards), 2- The selection of the local advancing front, 3- The method for placing a mobile particle in contact with others and 4- The overlap checks. The algorithm also allows obtaining highly porous media when it is slightly modified. Practical applications of the formulations are presented in the end of this paper.
Abstract
Several theoretical contributions in order to establish a particle packing methodology are presented. In this respect, a generic formulation of a new method for packing [...]
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Optimizing rock cutting through computer simulation
J. Rojek, E. Oñate, C. Labra, H. Kargl, J. Akerman

(2010). Technology Innovation in Underground Construction (TUNCONSTRUCT), G. Beer (Ed.)

Abstract
This paper presents an original thermomechanical model of rock cutting with evaluation of tool wear. The model has been developed within the framework of the discrete element method, which is a suitable numerical method to study problems of multiple material fractures likes those of rock cutting. The paper presents brief overview of the theoretical formulation, calibration of the discrete element model, and a number of numerical results obtained in simulation of rock cutting processes typical for underground excavation, using both roadheaders and TBMs.
Abstract
This paper presents an original thermomechanical model of rock cutting with evaluation of tool wear. The model has been developed within the framework of the discrete element [...]
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Advances in the formulation of the rotation-free basic shell triangle
E. Oñate, F. Flores

Computer Methods in Applied Mechanics and Engineering (2005). Vol. 194 (21-24), 2406-2443

Abstract
A family of rotation-free three node triangular shell elements is presented. The simplest element of the family is based on an assumed constant curvature field expressed in terms of the nodal deflections of a patch of four elements and a constant membrane field computed from the standard linear interpolation of the displacements within each triangle. An enhanced version of the element is obtained by using a quadratic interpolation of the geometry in terms of the six patch nodes. This allows to compute an assumed linear membrane strain field which improves the in-plane behaviour of the original element. A simple and economic version of the element using a single integration point is presented. The efficiency of the different rotation-free shell triangles is demonstrated in many examples of application including linear and non linear analysis of shells under static and dynamic loads, the inflation and de-inflation of membranes and a sheet stamping problem.
Abstract
A family of rotation-free three node triangular shell elements is presented. The simplest element of the family is based on an assumed constant curvature field expressed in [...]
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Stabilized solution of the multidimensional advection-diffusion-absorption equation using linear finite elements
E. Oñate, J. Miquel, F. Zárate

Computers and Fluids (2007). Vol. 36 (1), pp. 92-112, 2007

Abstract
A stabilized finite element method (FEM) for the multidimensional steady state advection-diffusion-absorption equation is presented. The stabilized formulation is based on the modified governing differential equations derived via the Finite Calculus (FIC) method. For 1D problems the stabilization terms act as a nonlinear additional diffusion governed by a single stabilization parameter. It is shown that for multidimensional problems an orthotropic stabilizing diffusion must be added along the principal directions of curvature of the solution. A simple iterative algorithm yielding a stable and accurate solution for all the range of physical parameters and boundary conditions is described. Numerical results for 1D and 2D problems with sharp gradients are presented showing the effectiveness and accuracy of the new stabilized formulation.
Abstract
A stabilized finite element method (FEM) for the multidimensional steady state advection-diffusion-absorption equation is presented. The stabilized formulation is based on [...]
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Updated Lagrangian mixed finite element formulation for quasi and fully incompressible fluids
E. Oñate, J. Carbonell

Computational Mechanics (2014). Vol. 54 (6), pp. 1583-1596, 2014

Abstract
We present a mixed velocity-pressure finite element formulation for solving the updated Lagrangian equations for quasi and fully incompressible fluids. Details of the governing equations for the conservation of momentum and mass are given in both differential and variational form. The finite element interpolation uses an equal order approximation for the velocity and pressure unknowns. The procedure for obtaining stabilized FEM solutions is outlined. The solution in time of the discretized governing conservation equations using an incremental iterative segregated scheme is described. The linearization of these equations and the derivation of the corresponding tangent stiffness matrices is detailed. Other iterative schemes for the direct computation of the nodal velocities and pressures at the updated configuration are presented. The advantages and disadvantages of choosing the current or the updated configuration as the reference configuration in the Lagrangian formulation are discussed.
Abstract
We present a mixed velocity-pressure finite element formulation for solving the updated Lagrangian equations for quasi and fully incompressible fluids. Details of the governing [...]
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The particle finite element method. An overview
E. Oñate, S. Idelsohn, F. Del Pin, R. Aubry

International Journal of Computational Methods (2004). Vol. 1 (2), pp. 267-307

Abstract
We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use of a Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are thus viewed as particles which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations, expressed in an integral from, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility condition in the fluid is introduced via the finite calculus (FIC) method. A fractional step scheme for the transient coupled fluid-structure solution is described. Examples of application of the PFEM method to solve a number of fluid-structure interaction problems involving large motions of the free surface and splashing of waves are presented.
Abstract
We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use [...]
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Residual stress and distortion of rectangular and S-shaped Ti-6Al-4V parts by Directed Energy Deposition: Modelling and experimental calibration
X. Lu, X. Lin, M. Chiumenti, M. Cervera, Y. Hu, X. Ji, L. Ma, H. Yang, W. Huang

Additive Manufacturing (2019). (preprint) Vol. 26, pp. 166-179

Abstract
Residual stresses and distortion in Additive Manufactured (AM) parts are two key obstacles which seriously hinder the wide application of this technology. Nowadays, understanding the thermomechanical behavior induced by the AM process is still a complex task which must take into account the effects of both the process and the material parameters, the microstructure evolution as well as the pre-heating strategy. One of the challenges of this work is to increase the complexity of the geometries used to study the thermomechanical behavior induced by the AM process. The reference geometries are a rectangular and a S-shaped structures made of 44-layers each. The samples have been fabricated by Directed Energy Deposition (DED). In-situ thermal and distortion histories of the substrate are measured in order to calibrate the 3D coupled thermo-mechanical model. Once the numerical results showed a good agreement with the temperature measurements, the validated model has been used to predict the residual stresses and distortions. Different process parameters have been analyzed to study their sensitivity to the process assessment. Different preheating strategies have been also analyzed to check their effectiveness on the mitigation of both distortions and residual stresses. Finally, some simplifications of the actual scanning sequence are proposed to reduce the computational cost without loss of the accuracy of the simulation framework.
Abstract
Residual stresses and distortion in Additive Manufactured (AM) parts are two key obstacles which seriously hinder the wide application of this technology. Nowadays, understanding [...]
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In situ measurements and thermo-mechanical simulation of Ti–6Al–4V laser solid forming processes
X. Lu, X. Lin, M. Chiumenti, M. Cervera, Y. Hu, X. Ji, L. Ma, W. Huang

Int. J. Mechanical Sciences (2019). (preprint) Vol. 153-154, pp. 119-130

Abstract
Residual stresses and distortions are two technical obstacles for popularizing the additive manufacturing (AM) technology. The evolution of the stresses in AM components during the thermal cycles of the metal depositing process is not yet clear, and more accurate in situ measurements are necessary to calibrate and validate the numerical tools developed for its simulation. In this work a fully coupled thermo-mechanical analysis to simulate the laser solid forming (LSF) process is carried out. At the same time, an exhaustive experimental campaign is launched to measure the temperature evolution at different locations, as well as the distortions and both the stress and strain fields. The thermal and mechanical responses of single-wall coupons under different process parameters are recorded and compared with the numerical models. Good agreement between the numerical results and the experimental measurements is obtained. Sensitivity analysis demonstrates that the AM process is significantly affected by the laser power and the feeding rate, while poorly influenced by the scanning speed.
Abstract
Residual stresses and distortions are two technical obstacles for popularizing the additive manufacturing (AM) technology. The evolution of the stresses in AM components during [...]
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Out-of-plane seismic response and failure mechanism of masonry structures using finite elements with enhanced strain accuracy
G. Vlachakis, M. Cervera, G. Barbat, S. Salaustros

Engineering Failure Analysis (2019). (preprint) Vol. 97, pp. 534-555

Abstract
The out-of-plane response is a complex and at the same time key aspect of the seismic vulnerability of masonry structures. It depends on several factors, some of which are the material properties, the quality of the walls, the geometry of the structure, the connections between structural elements and the stiffness of the diaphragms. During the last years, a wide variety of numerical methods has been employed to assess the out-ofplane behaviour of unreinforced masonry structures. Finite element macro-modelling approaches are among the most famous as they allow modelling large structures at a reasonable computational cost. However, macro-modelling approaches may result in a non-realistic representation of localized cracks and a dependency of the numerical solution on the finite element mesh. Mixed strain/displacement finite elements have been recently proposed as a remedy to the above numerical pathologies. Due to the independent interpolation of strains and displacements these finite element formulations are characterized by an enhanced accuracy in strain localization and crack propagation problems, being at the same time practically mesh independent. For these reasons, mixed finite elements are employed in this work for the out-of-plane assessment of unreinforced masonry structures, being at the same time their first real-scale application. A full-scale experimental campaign of two masonry structures, a stone and a brick one, subjected to shaking-table tests is chosen as reference benchmark. Their structural response under seismic actions is numerically assessed through nonlinear static analysis. The proposed approach is validated through the comparison of the numerical results with the experimental ones, as well as with the results obtained using standard irreducible finite elements.
Abstract
The out-of-plane response is a complex and at the same time key aspect of the seismic vulnerability of masonry structures. It depends on several factors, some of which are [...]
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Effect of the tool tilt angle on the material flow and heat generation in Friction Stir Welding
N. Dialami, M. Cervera, M. Chiumenti

Metals (2019). Vol. 9 (1), pp. 28-45

Abstract
This work studies the effect of the tool tilt angle on the generated heat and the material flow in the work pieces joint by Friction Stir Welding (FSW). An apropos kinematic framework together with a two-stage speed-up strategy is adopted to simulate the FSW problem. The effect of tilt angle on the FSWelds is modeled through the contact condition by modifying an enhanced friction model. A rotated friction shear stress is proposed, the angle of rotation depending on the process parameters and the tilt angle. The proposed rotation angle is calibrated by the experimental data provided for a tilt angle 2.5◦ . The differences of generated heat and material flow for the cases of tool with tilt angle of 0◦ and 2.5◦ are discussed. It is concluded that due to the higher temperature, softer material and greater frictional force in the trailing side of the tool, the material flow in the rear side of the FSW tool with the title angle is considerably enhanced, which assists to prevent the generation of defect.
Abstract
This work studies the effect of the tool tilt angle on the generated heat and the material flow in the work pieces joint by Friction Stir Welding (FSW). An apropos kinematic [...]
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Prediction of joint line remnant defect in friction stir welding
N. Dialami, M. Cervera, M. Chiumenti, A. Segatori

Int. J. Mechanical Sciences (2019). Vol. 151, pp. 61-69

Abstract
This work studies computationally and experimentally the joint line remnant defects emerging in friction stir welding (FSW) due to oxide layer propagation into the weld. A finite element-based model is used for the computational simulation. To follow the evolution of the oxide layer originally placed between the butted surfaces, a material tracing technique is incorporated in the numerical model. This approach allows tracking the position of the tracers representing oxide layer particles knowing the nodal velocities. A robust and fast two-stage numerical strategy is adopted for the analysis of FSW process to solve the underlying thermo-mechanical problem. The first stage is a speed-up stage solved on a fixed mesh that allows to quickly obtain the steady state. Oxide layer evolution is traced in the second stage where the rotation of the tool is modelled. Experimentally, to produce a clearly dispersed oxide line in the weld, one of the workpieces is anodized while the other one is taken as extruded. The computationally obtained oxide layer patterns are compared to those obtained experimentally using macrograph analysis of the joint cross section. The effect of the pin features and the process parameters on the final result is studied. The results show that with appropriate modelling of the material tracers in FSW, significant agreement can be attained between the computed and measured post-FSW oxide layer evolved results.
Abstract
This work studies computationally and experimentally the joint line remnant defects emerging in friction stir welding (FSW) due to oxide layer propagation into the weld. A [...]
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Multiscale analysis using a coupled discrete/finite element model
J. Rojek, E. Oñate

Interaction and Multiscale Mechanics: An International Journal (IMMIJ) (2007). Vol. 1 (1), pp. 1-31

Abstract
The present paper presents multiscale modelling via coupling of the discrete and finite element methods. Theoretical formulation of the discrete element method using spherical or cylindrical particles has been briefly reviewed. Basic equations of the finite element method using the explicit time integration have been given. The micr-macro transition for the discrete element method has been discussed. Theoretical formulations for macroscopic stress and strain tensors have been given. Determination of macroscopic constitutive properties using dimensionless micro-macro relationships has been proposed. The formulation of the multiscale DEM/FEM model employing the DEM and FEM in different subdomains of the same body has been presented. The coupling allows the use of partially overlapping DEM and FEM subdomains. The overlap zone in the two coupling algorithms is introduced in order to provide a smooth transition from one discretization method to the other. Coupling between the DEM and FEM subdomains is provided by additional kinematic constraints imposed by means of either the Lagrange multipliers or penalty function method. The coupled DEM/FEM formulation has been implemented in the authors’ own numerical program. Good performance of the numerical algorithms has been demonstrated in a number of examples.
Abstract
The present paper presents multiscale modelling via coupling of the discrete and finite element methods. Theoretical formulation of the discrete element method using spherical [...]
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Challenges, tools and applications of tracking algorithms in the numerical modelling of cracks in concrete and masonry structures
S. Salaustros, M. Cervera, L. Pelà

Archives of Comp. Meths. Engng. (2018). (preprint) Published online, pp. 1-45

Abstract
The importance of crack propagation in the structural behaviour of concrete and masonry structures has led to the development of a wide range of finite element methods for crack simulation. A common standpoint in many of them is the use of tracking algorithms, which identify and designate the location of cracks within the analysed structure. In this way, the crack modelling techniques, smeared or discrete, are applied only to a restricted part of the discretized domain. This paper presents a review of finite element approaches to cracking focusing on the development and use of tracking algorithms. These are presented in four categories according to the information necessary for the definition and storage of the crack-path. In addition to that, the most utilised criteria for the selection of the crack propagation direction are summarized. The various algorithmic issues involved in the development of a tracking algorithm are discussed through the presentation of a local tracking algorithm based on the smeared crack approach. Challenges such as the modelling of arbitrary and multiple cracks propagating towards more than one direction, as well as multi-directional and intersecting cracking, are detailed. The presented numerical model is applied to the analysis of small- and large-scale masonry and concrete structures under monotonic and cyclic loading.
Abstract
The importance of crack propagation in the structural behaviour of concrete and masonry structures has led to the development of a wide range of finite element methods for [...]
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Modeling of microstructure evolution of Ti6Al4V for Additive Manufacturing
E. Salsi, M. Chiumenti, M. Cervera

Metals (2018). Vol. 8 (8), pp. 633-657

Abstract
AM processes are characterized by complex thermal cycles that have a deep influence on the microstructural transformations of the deposited alloy. In this work, a general model for the prediction of microstructure evolution during solid state transformations of Ti6Al4V is presented. Several formulations have been developed and employed for modeling phase transformations in other manufacturing processes and, particularly, in casting. The proposed model is mainly based on the combination and modification of some of these existing formulations, leading to a new overall model specifically dedicated to AM. The accuracy and suitability of the integrated model is enhanced, introducing new dedicated features. In fact the model is designed to deal with fast cooling and re-heating cycles typical of AM processes because: (a) it is able to consider incomplete transformations and varying initial content of phases and (b) it can take into account simultaneous transformations.The model is implemented in COMET, an in-house Finite Element (FE)-based framework for the solution of thermo-mechanical engineering problems. The validation of the microstructural model is performed by comparing the simulation results with the data available in the literature. The sensitivity of the model to the variation of material parameters is also discussed.
Abstract
AM processes are characterized by complex thermal cycles that have a deep influence on the microstructural transformations of the deposited alloy. In this work, a general [...]
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An empirical comparison of machine learning techniques for dam behaviour modelling
F. Salazar, M. Toledo, R. Morán Moya, E. Oñate

Structural Safety (2015). Vol 56, pp. 9-17

Abstract
Predictive models are essential in dam safety assessment. Both deterministic and statistical models applied in the day-to-day practice have demonstrated to be useful, although they show relevant limitations at the same time. On another note, powerful learning algorithms have been developed in the field of machine learning (ML), which have been applied to solve practical problems. The work aims at testing the prediction capability of some state-of-the-art algorithms to model dam behaviour, in terms of displacements and leakage. Models based on random forests (RF), boosted regression trees (BRT), neural networks (NN), support vector machines (SVM) and multivariate adaptive regression splines (MARS) are fitted to predict 14 target variables. Prediction accuracy is compared with the conventional statistical model, which shows poorer performance on average. BRT models stand out as the most accurate overall, followed by NN and RF. It was also verified that the model fit can be improved by removing the records of the first years of dam functioning from the training set.
Abstract
Predictive models are essential in dam safety assessment. Both deterministic and statistical models applied in the day-to-day practice have demonstrated to be useful, although [...]
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Structural shape sensitivity analysis for nonlinear material models with strain softening
G. Bugeda, L. Gil, E. Oñate

Structural Optimization (1999). Vol. 17 (2-3), pp. 162-171

Abstract
This paper describes some considerations around the analytical structural shape sensitivity analysis when the structural behaviour is computed using the finite element method with a nonlinear constitutive material model. Traditionally, the structural sensitivity analysis is computed using an incremental approach based on the incremental procedures for the solution of the structural equilibrium problem. In this work, a direct (nonincremental) formulation for computing these structural sensitivities, that is valid for some specific nonlinear material models, is proposed. The material models for which the presented approach is valid are characterized by the fact that the stresses at any timet can be expressed in terms of the strains at the timet and, in some cases, the strains at a specific past timet u (t u<t). This is the case of elasticity (linear as well as nonlinear), perfect plasticity and damage models. A special strategy is also proposed for material models with strain softening. For the cases where it is applicable, the sensitivity analysis proposed here allows us to compute the structural sensitivities around any structural equilibrium point after finishing the solution process and it is completely independent of the numerical scheme used to solve the structural equilibrium problem. This possibility is particularized for the case of a damage model considering a strain-softening behaviour. Finally, the quality and reliability of the proposed approach is assessed through its application to some example
Abstract
This paper describes some considerations around the analytical structural shape sensitivity analysis when the structural behaviour is computed using the finite element method [...]
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Wireless sensor networks for strain monitoring during steel bridges launching
R. Chacón, F. Guzmán, E. Mirabell, E. Real, E. Oñate

Structural Health Monitoring (2009). Vol. 8 (3), pp. 195-205

Abstract
n this paper, an experimental test performed on a hybrid steel plate girder was subjected to concentrated loads at the end of an unstiffened panel is presented. This load was intended to produce a typical reaction of the piers while launching steel girders in bridges. In this test, strain measurements were taken with conventional pre-wired gauges as well as with newly developed wirelessly connected strain-measuring system. Both measurements were carefully compared and the accuracy of the developed system was demonstrated. Results were also compared with numerical simulations deployed with FE models and on such a basis; the reliability of the developed wireless system was proven. Finally, suggestions of potential research trends in this area are provided
Abstract
n this paper, an experimental test performed on a hybrid steel plate girder was subjected to concentrated loads at the end of an unstiffened panel is presented. This load [...]
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Early detection of anomalies in dam performance: A methodology based on boosted regression trees
F. Salazar, M. Toledo, J. González, E. Oñate

Structural Control Health Monitoring (2017). Vol. 24 (11), Article Number: e2012

Abstract
The advances in information and communication technologies led to a general trend towards the availability of more detailed information on dam behaviour. This allows applying advanced data‐based algorithms in its analysis, which has been reflected in an increasing interest in the field. However, most of the related literature is limited to the evaluation of model prediction accuracy, whereas the ulterior objective of data analysis is dam safety assessment. In this work, a machine‐learning algorithm (boosted regression trees) is the core of a methodology for early detection of anomalies. It also includes a criterion to determine whether certain discrepancy between predictions and observations is normal, a procedure to compute a realistic estimate of the model accuracy, and an original approach to identify extraordinary load combinations. The performance of causal and noncausal models is assessed in terms of their ability to detect different types of anomalies, which were artificially introduced on reference time series generated with a numerical model of a 100‐m‐high arch dam. The final approach was implemented in an online application to visualise the results in an intuitive way to support decision making.
Abstract
The advances in information and communication technologies led to a general trend towards the availability of more detailed information on dam behaviour. This allows applying [...]
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Robust multidisciplinary unmanned aerial system design optimisation
D. Lee, J. Periaux, L. González, K. Srinivas, E. Oñate

Structural and Multidisciplinary Optimization (2012). Vol. 45 (3), pp. 433-450

Abstract
There are many applications in aeronautical/aerospace engineering where some values of the design parameters/states cannot be provided or determined accurately. These values can be related to the geometry (wingspan, length, angles) and or to operational flight conditions that vary due to the presence of uncertainty parameters (Mach, angle of attack, air density and temperature, etc.). These uncertainty design parameters cannot be ignored in engineering design and must be taken into the optimisation task to produce more realistic and reliable solutions. In this paper, a robust/uncertainty design method with statistical constraints is introduced to produce a set of reliable solutions which have high performance and low sensitivity. Robust design concept coupled with Multi-Objective Evolutionary Algorithms (MOEAs) is defined by applying two statistical sampling formulas; mean and variance/standard deviation associated with the optimisation fitness/objective functions. The methodology is based on a canonical evolution strategy and incorporates the concepts of hierarchical topology, parallel computing and asynchronous evaluation. It is implemented for two practical Unmanned Aerial System (UAS) design problems; the first case considers robust multi-objective (single-disciplinary: aerodynamics) design optimisation and the second considers a robust multidisciplinary (aero-structures) design optimisation. Numerical results show that the solutions obtained by the robust design method with statistical constraints have a more reliable performance and sensitivity in both aerodynamics and structures when compared to the baseline design. KeywordsRobust/uncertainty design–Multi-objective–Multidisciplinary–UAS–Evolutionary algorithms
Abstract
There are many applications in aeronautical/aerospace engineering where some values of the design parameters/states cannot be provided or determined accurately. These values [...]
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Discrete/finite element modelling of rock cutting with TBM disc cutter
C. Labra, J. Rojek, E. Oñate

Rock Mechanics and Rock Engineering (2017). Vol. 50 (3), pp. 621-638

Abstract
This paper presents advanced computer simulation of rock cutting process typical for excavation works in civil engineering. Theoretical formulation of the hybrid discrete/finite element model has been presented. The discrete and finite element methods have been used in different subdomains of a rock sample according to expected material behaviour, the part which is fractured and damaged during cutting is discretized with the discrete elements while the other part is treated as a continuous body and it is modelled using the finite element method. In this way, an optimum model is created, enabling a proper representation of the physical phenomena during cutting and efficient numerical computation. The model has been applied to simulation of the laboratory test of rock cutting with a single TBM (tunnel boring machine) disc cutter. The micromechanical parameters have been determined using the dimensionless relationships between micro- and macroscopic parameters. A number of numerical simulations of the LCM test in the unrelieved and relieved cutting modes have been performed. Numerical results have been compared with available data from in-situ measurements in a real TBM as well as with the theoretical predictions showing quite a good agreement. The numerical model has provided a new insight into the cutting mechanism enabling us to investigate the stress and pressure distribution at the tool–rock interaction. Sensitivity analysis of rock cutting performed for different parameters including disc geometry, cutting velocity, disc penetration and spacing has shown that the presented numerical model is a suitable tool for the design and optimization of rock cutting process.
Abstract
This paper presents advanced computer simulation of rock cutting process typical for excavation works in civil engineering. Theoretical formulation of the hybrid discrete/finite [...]
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Possibilities of the particle finite element method for fluid-structure interaction problems with free surface waves
E. Oñate, S. Idelsohn, F. Del Pin, R. Aubry

Revue Européenne des Éléments Finis (2004). Vol. 13, pp. 637-666

Abstract
We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use of a Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are thus viewed as particles which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations, expressed in an integral from, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility condition in the fluid is introduced via the finite calculus (FIC) method. A fractional step scheme for the transient coupled fluid-structure solution is described. Examples of application of the PFEM method to solve a number of fluid-structure interaction problems involving large motions of the free surface and splashing of waves are presented.
Abstract
We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use [...]
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An Implicit Material Point Method Applied to Granular Flows
I. Iaconeta, A. Larese, R. Rossi, E. Oñate

Procedia Engineering (2017). Vol. 175, pp. 226-232

Abstract
The main objective of this work lies in the development of a variational implicit Material Point Method (MPM), implemented in the open source Kratos Multiphysics framework. The ability of the MPM technique to solve large displacement and large deformation problems is widely recognised and its use ranges over many problems in industrial and civil engineering. In the current work the continuum based implicit MPM is applied to engineering applications, where granular material flow is involved. For the resolution of the length and time scale of these particular problems, both continuum and discrete models are typically used. Even if discrete techniques predict more feasible results, nowadays, their use is limited to the investigation of element tests of particles, or to the simulation of reduced systems, not allowing to make important decisions in the analysis and design of granular processes. Some advantages of MPM over discrete methods are tested, such as, the ability to simulate granular flow at the large scale with acceptable computational cost and the capability to get information of stress and strain state in a more straightforward way. The focus of this paper is a comparative study between an irreducible and a mixed formulation, both implemented in the MPM code, to assess the improvement in accuracy and reliability of the numerical results when the latter formulation is adopted.
Abstract
The main objective of this work lies in the development of a variational implicit Material Point Method (MPM), implemented in the open source Kratos Multiphysics framework. [...]
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Modelling and simulation of the sea-landing of aerial vehicles using the Particle Finite Element Method
P. Ryzhakov, R. Rossi, A. Viña, E. Oñate

Ocean Engng. (2013). Vol. 66, pp. 92-100

Abstract
In this paper the Particle Finite Element Method (PFEM) is applied to the simulation of the sea-landing of an unmanned aerial vehicle (UAV). The problem of interest consists in modelling the impact of the vehicle against the water surface, analyzing the main kinematic and dynamic quantities (such as loads exerted upon the capsule at the moment of the impact). The PFEM, a methodology well-suited for free-surface flow simulation is used for modelling the water while a rigid body model is chosen for the vehicle. The vehicle under consideration is characterized by low weight. This leads to difficulties in modelling the fluid–structure interaction using standard Dirichlet–Neumann coupling. We apply a modified partitioned strategy introducing the interface Laplacian into the pressure Poisson's equation for obtaining a convergent FSI solution. The paper concludes with an industrial example of a vehicle sea-landing modelled using PFEM.
Abstract
In this paper the Particle Finite Element Method (PFEM) is applied to the simulation of the sea-landing of an unmanned aerial vehicle (UAV). The problem of interest consists [...]
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An extended class of multilayer perceptron
R. López, E. Oñate

Neurocomputing (2008). Vol. 71 (13-15), pp. 2538-2543

Abstract
In this work an extended class of multilayer perceptron is presented. This includes independent parameters, boundary conditions and lower and upper bounds. In some cases, such extensions contain a priori information of the problem. On some other situations they are necessary in order to define a correct representation for the solution. The use of this augmented class of neural network is illustrated through a case study in the optimal control theory. The numerical results are compared against the analytical solution.
Abstract
In this work an extended class of multilayer perceptron is presented. This includes independent parameters, boundary conditions and lower and upper bounds. In some cases, [...]
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A co-rotational 8-node assumed strain shell element for postbuckling analysis of laminated composite plates and shells
G. Lomboy, K. Kim, E. Oñate

Mechanics of Advanced Materials and Structures (2007). Vol. 14 (2), pp. 89-105

Abstract
A nonlinear resultant shell element is developed for the solution of problems of composite plates and shells undergoing nonlinear static and nonlinear dynamic behavior with progressive layer failure. The formulation of the tangent stiffness is defined on the mid-surface and is efficient for analyzing thick laminated plates and shells by incorporating bending moments and transverse shear resultant forces in the geometric stiffness. The composite element is free of both membrane and shear locking behavior by using the assumed natural strain method, such that the element also performs very well as thin laminate shells. An equilibrium approach is used to derive the improved transverse shear stiffness, instead of using a shear correction factor. The proposed formulation is computationally efficient and the test results show good agreement with references. The composite shell element is extended to determine ply failures in laminated composite structures undergoing nonlinear static or dynamic behavior. The failure analysis is done by first, computing for the inter-laminar stresses at each gauss point in an element. Having obtained the stresses in each layer, checking for failure is performed based on a chosen failure criterion. Four failure criteria are available to enable the user to adopt the appropriate criterion for the type of problem parameters present.
Abstract
A nonlinear resultant shell element is developed for the solution of problems of composite plates and shells undergoing nonlinear static and nonlinear dynamic behavior with [...]
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Analysis of segmentally constructed prestressed concrete bridges using hexahedral elements with realistic tendon profiles
P. Norachan, K. Kim, E. Oñate

Journal of Structural Engineering (2014). Vol. 140 (6), pp. 04014028/1-17

Abstract
The paper presents a systematically numerical procedure based on the finite-element method for three-dimensional analysis of segmentally constructed prestressed concrete bridges using hexahedral elements including realistic tendon profiles. The enhanced assumed strain (EAS) is used in the formulation of the hexahedral element in order to improve the element performances. Both the geometric nonlinearity and time-dependent effects due to creep, shrinkage, and aging of the concrete and relaxation of the prestress are taken into account, while variations of the structural configuration due to changes of the structural geometry and boundary conditions during the construction process are also incorporated. To include realistic tendon profiles, the idealized prestressing tendon is represented by a system of piecewise linear prestressing segments. Several numerical examples in a wide range of prestressed concrete structures are presented to demonstrate the validity and efficiency of the proposed procedure. Finally, application to the erection of a segmentally erected prestressed concrete bridge is discussed at the end of the paper.
Abstract
The paper presents a systematically numerical procedure based on the finite-element method for three-dimensional analysis of segmentally constructed prestressed concrete bridges [...]
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Numerical analysis of the manufacturing processes of a mock-up of the ITER NHF First Wall Panel
J. González, M. Chiumenti, M. Cervera, C. Agelet de Saracibar, F. Samaniego, I. Cobo

Fusion Engineering and Design (2018). (preprint) Vol. 135, Part A, pp. 65-73

Abstract
The objective of ITER is to build a new Tokamak, with the goal of demonstrating the scientific and technical feasibility of fusion power. The First Wall Panels are the inner component of the reactor, built with different materials that must support high heat flux levels inside the vacuum vessel. The manufacturing processes of the First Wall are a complex procedure including bending, hipping and cutting procedures which, in general, lead to residual stresses and distortions of the fabricated component. In this work, the analysis of the thermo-mechanical response of a simplified prototype of the ITER NHF First Wall Panel is presented from the numerical point of view. The experimental procedure within each phase of the whole manufacturing process is described. Residual stresses and distortions have been measured and analyzed. The numerical simulation of the manufacturing process includes the description of the main hypothesis, the applied loads and the boundary conditions assumed at every stage of the process. Special attention is paid to the simulation of machining and cutting by means of an ad-hoc element deactivation strategy. The numerical results are compared with the experimental evidence to show the prediction capability and the limitations of the proposed numerical model.
Abstract
The objective of ITER is to build a new Tokamak, with the goal of demonstrating the scientific and technical feasibility of fusion power. The First Wall Panels are the inner [...]
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Modeling of ground excavation with the particle finite-element method
J. Carbonell, E. Oñate, B. Suarez

Journal of Engineering Mechanics (2010). Vol. 136 (4), pp. 455-463

Abstract
An excavation process is a nonlinear dynamic problem that includes geometrical, material, and contact nonlinearities. The simulation of ground excavation has to face contact interaction in a changing geometry composed by several solid domains. The particle finite-element method (PFEM) is based on a Lagrangian description for modeling the motion of a continuum medium. The PFEM is particularly suitable for modeling a fluid motion with free surfaces. The application of the PFEM in ground excavation includes the use of the remeshing process, α-shape concepts for detecting the domain boundary, contact mechanics laws, material constitutive models, and surface wear models. Everything is correctly matched to quantify the excavation and the corresponding damage caused to the ground. The erosion and wear parameters of the soil/rock material govern the evolution of the excavation process. The preliminary results presented in this paper show that the PFEM it is a very suitable tool for the simulation of ground excavation processes.
Abstract
An excavation process is a nonlinear dynamic problem that includes geometrical, material, and contact nonlinearities. The simulation of ground excavation has to face contact [...]
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Approximating the Basset force by optimizing the method of van Hinsberg et al.
G. Casas, A. Ferrer, E. Oñate

Journal of Computational Physics (2018). Vol. 352, pp. 142-171

Abstract
In this work we put the method proposed by van Hinsberg et al. to the test, highlighting its accuracy and efficiency in a sequence of benchmarks of increasing complexity. Furthermore, we explore the possibility of systematizing the way in which the method's free parameters are determined by generalizing the optimization problem that was considered originally. Finally, we provide a list of worked-out values, ready for implementation in large-scale particle-laden flow simulations.
Abstract
In this work we put the method proposed by van Hinsberg et al. to the test, highlighting its accuracy and efficiency in a sequence of benchmarks of increasing complexity. [...]
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Volumetric constraint models for anisotropic elastic solids
C. Felippa, E. Oñate

Journal of Applied Mechanics (2004). Vol. 71 (5), pp. 731-734

Abstract
We study three “incompressibility flavors” of linearly-elastic anisotropic solids that exhibit volumetric constraints: isochoric, hydroisochoric and rigidtropic. An isochoric material deforms without volume change under any stress system. An hydroisochoric material does so under hydrostatic stress. A rigidtropic material undergoes zero deformations under a certain stress pattern. Whereas the three models coalesce for isotropic materials, important differences appear for anisotropic behavior. We find that isochoric and hydroisochoric models under certain conditions may be hampered by unstable physical behavior. Rigidtropic models can represent semistable physical materials of arbitrary anisotropy while including isochoric and hydroisochoric behavior as special cases.
Abstract
We study three “incompressibility flavors” of linearly-elastic anisotropic solids that exhibit volumetric constraints: isochoric, hydroisochoric and rigidtropic. [...]
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Active transonic aerofoil design optimization using robust multiobjective evolutionary algorithms
D. Lee, J. Periaux, L. González, E. Oñate, N. Qin

Journal of Aircraft (2011). Vol. 48 (3) pp. 1084-1094

Abstract
The use of adaptive wing/aerofoil designs is being considered, as they are promising techniques in aeronautic/ aerospace since they can reduce aircraft emissions and improve aerodynamic performance of manned or unmanned aircraft. This paper investigates the robust design and optimization for one type of adaptive techniques: active flow control bump at transonic flow conditions on a natural laminar flow aerofoil. The concept of using shock control bump is to control supersonic flow on the suction/pressure side of natural laminar flow aerofoil that leads to delaying shock occurrence (weakening its strength) or boundary-layer separation. Such an active flow control technique reduces total drag at transonic speeds due to reduction of wave drag. The location of boundary-layer transition can influence the position and structure of the supersonic shock on the suction/pressure side of aerofoil. The boundarylayer transition position is considered as an uncertainty design parameter in aerodynamic design due to the many factors, such as surface contamination or surface erosion. This paper studies the shock-control-bump shape design optimization using robust evolutionary algorithms with uncertainty in boundary-layer transition locations. The optimization method is based on a canonical evolution strategy and incorporates the concepts of hierarchical topology, parallel computing, and asynchronous evaluation. Two test cases are conducted: the first test assumes the boundary-layer transition position is at 45% of chord from the leading edge, and the second test considers robust design optimization for the shock control bump at the variability of boundary-layer transition positions. The numerical result shows that the optimization method coupled to uncertainty design techniques produces Pareto optimal shock-control-bump shapes, which have low sensitivity and high aerodynamic performance while having significant total drag reduction.
Abstract
The use of adaptive wing/aerofoil designs is being considered, as they are promising techniques in aeronautic/ aerospace since they can reduce aircraft emissions and improve [...]
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Numerical investigation of wind-tunnel model deformations caused by the twin-sting support system
F. Flores, E. Ortega, E. Oñate

Journal of Aircraft (2010). Vol. 47, pp. 708-714

Abstract
The present work is part of a broader investigation aimed at improving the understanding of the aerodynamics of the rear aircraft section. Complex flow phenomena (e.g., the thick fuselage boundary layer at the rear end) present a challenge to the accurate predictions of aerodynamic performance. Significant efficiency gains are expected from improved-fidelity computations and experimental techniques. As part of a joint effort between several research institutions and industrial partners, a series of wind-tunnel test campaigns focusing on accurate rear-end measurements was planned. To obtain accurate tail-force data, a nonstandard live-rear-end test model was adopted. This technique uses a mechanically separate rear-end section attached to the main body through internal balances, allowing direct measurement of the force acting on the tail. This mechanical setup precludes the use of a conventional tail-coneattached sting. Moreover, to minimize aerodynamic interference on the empennage caused by the support system, a wing-attached twinsting mounting was chosen
Abstract
The present work is part of a broader investigation aimed at improving the understanding of the aerodynamics of the rear aircraft section. Complex flow phenomena (e.g., [...]
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Robust design optimization in aeronautics using stochastic analysis and evolutionary algorithms
J. Pons-Prats, G. Bugeda, F. Zárate, E. Oñate

Journal of Aerospace Engineering (2011). Vol. 225, (10), pp. 1131-1151

Abstract
Uncertainties are a daily issue to deal with in aerospace engineering and applications. Robust optimization methods commonly use a random generation of the inputs and take advantage of multi-point criteria to look for robust solutions accounting with uncertainty definition. From the computational point of view, the application to coupled problems, like computational fluid dynamics (CFD) or fluid–structure interaction (FSI), can be extremely expensive. This study presents a coupling between stochastic analysis techniques and evolutionary optimization algorithms for the definition of a stochastic robust optimization procedure. At first, a stochastic procedure is proposed to be applied into optimization problems. The proposed method has been applied to both CFD and FSI problems for the reduction of drag and flutter, respectively.
Abstract
Uncertainties are a daily issue to deal with in aerospace engineering and applications. Robust optimization methods commonly use a random generation of the inputs and take [...]
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A monolithic FE formulation for the analysis of membranes in fluids
R. Rossi, P. Ryzhakov, E. Oñate

International Journal of Space Structures (2009). Vol. 24 (4), pp. 205-210

Abstract
We propose here an efficient approach for treating the interaction between membranes and fluids. Slight compressibility of the fluid is assumed. Classical total Lagrangian formulation including wrinkling is adopted for the membrane representation, whereas fluid is treated in an updated Lagrangian manner, developed in the current work. Assumption of slight compressibility of the fluid enables one to define the monolithic fluid-membrane system in a natural way. The displacements are the primary variables of both the fluid and the membrane domains. The formulation adopts the Particle Finite Element Method (PFEM) philosophy for free-surface identification and mesh regeneration. Three examples illustrate the functionality of the formulation in application to FSI problems involving motion of membranes in water
Abstract
We propose here an efficient approach for treating the interaction between membranes and fluids. Slight compressibility of the fluid is assumed. Classical total Lagrangian [...]
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Discrete element simulation of rock cutting
J. Rojek, E. Oñate, C. Labra, H. Kargl

Int. J. Rock Mechanics and Mining Sciences (2011). Vol. 48 (6), pp. 996-1010

Abstract
This paper presents numerical modelling of rock cutting processes. The model consists of a tool–rock system. The rock is modelled using the discrete element method, which is suitable to study problems of multiple material fracturing such as those involved in rock cutting. Both 2D and 3D models are considered in this work. The paper presents a brief overview of the theoretical formulation and calibration of the discrete element model by a methodology combining the dimensional analysis with simulation of the unconfined compressive strength (UCS) and indirect tension (Brazilian) tests. The rock cutting process with roadheader picks, which is typical for underground excavation, has been simulated. The results of the 2D and 3D analyses have been compared with one another, and numerical results have been compared with the available experimental data.
Abstract
This paper presents numerical modelling of rock cutting processes. The model consists of a tool–rock system. The rock is modelled using the discrete element method, [...]
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Numerical and Experimental Study of Overtopping and Failure of Rockfill Dams
A. Larese, R. Rossi, E. Oñate, M. Toledo, R. Morán Moya, H. Campos

International Journal of Geomechanics (2015). Vol. 15 (4), pp. 04014060-1 (published online)

Abstract
This paper aims to present and validate a numerical technique for the simulation of the overtopping and onset of failure in rockfill dams caused by mass sliding. This goal is achieved by coupling a fluid dynamic model for the simulation of the free surface and through-flow problems together with a numerical technique for the calculation of the rockfill response and deformation. Both the flow within the dam body and in its surroundings are taken into account. An extensive validation of the resulting computational method is performed by solving several failure problems on physical models of rockfill dams for which experimental results have been obtained by the authors.
Abstract
This paper aims to present and validate a numerical technique for the simulation of the overtopping and onset of failure in rockfill dams caused by mass sliding. This goal [...]
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A FIC‐based stabilized mixed finite element method with equal order interpolation for solid–pore fluid interaction problems
I. de-Pouplana, E. Oñate

Int. J. Numer. Anal. Meth. Geomech. (2017). Vol. 41 (1), pp. 110-134

Abstract
A new mixed displacement‐pressure element for solving solid–pore fluid interaction problems is presented. In the resulting coupled system of equations, the balance of momentum equation remains unaltered, while the mass balance equation for the pore fluid is stabilized with the inclusion of higher‐order terms multiplied by arbitrary dimensions in space, following the finite calculus (FIC) procedure. The stabilized FIC‐FEM formulation can be applied to any kind of interpolation for the displacements and the pressure, but in this work, we have used linear elements of equal order interpolation for both set of unknowns. Examples in 2D and 3D are presented to illustrate the accuracy of the stabilized formulation for solid–pore fluid interaction problems.
Abstract
A new mixed displacement‐pressure element for solving solid–pore fluid interaction problems is presented. In the resulting coupled system of equations, the balance [...]
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Numerical modelling of landslide‐generated waves with the particle finite element method (PFEM) and a non‐Newtonian flow model
F. Salazar, J. Irazábal González, A. Larese, E. Oñate

Int. J. Numer. Anal. Meth. Geomech. (2016). Vol. 40 (6), pp. 809-826

Abstract
Landslide‐generated impulse waves may have catastrophic consequences. The physical phenomenon is difficult to model because of the uncertainties in the kinematics of the mobilised material and to the intrinsic complexity of the fluid–soil interaction. The particle finite element method (PFEM) is a numerical scheme that has successfully been applied to fluid–structure interaction problems. It uses a Lagrangian description to model the motion of nodes (particles) in both the fluid and the solid domains (the latter including soil/rock and structures). A mesh connecting the particles (nodes) is re‐generated at every time step, where the governing equations are solved. Various constitutive laws are used for the sliding mass, including rigid solid and the Newtonian and non‐Newtonian fluids. Several examples of application are presented, corresponding both to experimental tests and to actual full‐scale case studies. The results show that the PFEM can be a useful tool for analysing the risks associated with landslide phenomena, providing a good estimate to the potential hazards even for full‐scale events.
Abstract
Landslide‐generated impulse waves may have catastrophic consequences. The physical phenomenon is difficult to model because of the uncertainties in the kinematics of the [...]
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Modelación del ensayo brasileño empleando modelación discreta
C. Recarey Morfa, E. Oñate, J. Rojek, J. Canet, F. Zárate, G. Cadoce, C. Labra

Ingeniería Civil (2005). Vol. 139, pp. 112-124

Abstract
Se presenta un modelo de elementos discretos o distintos (MED) en la modelizacion del ensayo de traccion indirecta o ensayo brasileno (Brazilian Test). Se realiza una comparacion entre los resultados obtenidos por el MED, con la de otros autores [26,35] que emplean el MEF. Se obtienen buenos resultados en el proceso de simulacion del ensayo brasileno, y la comparacion con el MEF (método de los elementos finitos) es muy efectiva. Se evidencia la similitud fisica que existe entre los resultados obtenidos por el MED y ensayos experimentales, lo que posibilita demostrar la fiabilidad y veracidad de la formulacion realizada. (A). English abstract: This work deals whit the use of the Distinct Element Method (DEM) to simulate an indirect traction test, also known as "the Brazilian test" A comparison is realized between results obtained with the DEM, and those obtained by other authors [26, 35] using the Finite Element Method (FEM). The Brazilian test's simulation gives good results and the comparison is very effective. There is a similarity between the results obtained using the DEM and those obtained from real experiments, similarity which proves the reliability and the veracity of this formulation.
Abstract
Se presenta un modelo de elementos discretos o distintos (MED) en la modelizacion del ensayo de traccion indirecta o ensayo brasileno (Brazilian Test). Se realiza una comparacion [...]
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Triangular prismatic solid-shell element with generalised deformation description
V. Mataix Ferrándiz, F. Flores, R. Rossi, E. Oñate

European Journal of Computational Mechanics (2018). Vol. 27 (1), pp. 1-32

Abstract
The solid-shells are an attractive kind of element for the simulation of f orming processes, due to the fact that any kind of generic 3D constitutive law can be employed without any kind of additional modification, besides the thermomechanic problem is formulated without additional assumptions. Additionally, this type of element allows the three-dimensional description of the deformable body, thus contact on both sides of the element can be treated easily. The present work consists in the development of a triangular prism element as a solid-shell, for the analysis of thin/thick shell, undergoing large deformations. The element is formulated in total Lagrangian formulation, and employs the neighbour (adjacent) elements to perform a local patch to enrich the displacement field. In the original formulation by Flores, a modified right Cauchy-Green deformation tensor () is obtained; in the present work a modified deformation gradient () is obtained, which allows to generalise the methodology and allows to employ a wide range of constitutive laws. The element is based in three modifications: (a) a classical assumed strain approach for transverse shear strains (b) an assumed strain approach for the in-plane components using information from neighbour elements and (c) an averaging of the volumetric strain over the element. The objective is to use this type of elements for the simulation of shells avoiding transverse shear locking, improving the membrane behaviour of the in-plane triangle and to handle quasi-incompressible materials or materials with isochoric plastic flow. Some examples have been evaluated to show the good performance of the element and results.
Abstract
The solid-shells are an attractive kind of element for the simulation of f orming processes, due to the fact that any kind of generic 3D constitutive law can be employed without [...]
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Interpretation of dam deformation and leakage with boosted regression trees
F. Salazar, M. Toledo, E. Oñate, B. Suarez

Engineering Structures (2016). Vol. 119, pp. 230-251

Abstract
Predictive models are essential in dam safety assessment. They have been traditionally based on simple statistical tools such as the hydrostatic-season-time (HST) model. These tools are well known to have limitations in terms of accuracy and reliability. In the recent years, the examples of application of machine learning and related techniques are becoming more frequent as an alternative to HST. While they proved to feature higher flexibility and prediction accuracy, they are also more difficult to interpret. As a consequence, the vast majority of the research is limited to prediction accuracy estimation. In this work, one of the most popular machine learning techniques (boosted regression trees), was applied to model 8 radial displacements and 4 leakage flows at La Baells Dam. The possibilities of model interpretation were explored: the relative influence of each predictor was computed, and the partial dependence plots were obtained. Both results were analysed to draw conclusions on dam response to environmental variables, and its evolution over time. The results show that this technique can efficiently identify dam performance changes with higher flexibility and reliability than simple regression models.
Abstract
Predictive models are essential in dam safety assessment. They have been traditionally based on simple statistical tools such as the hydrostatic-season-time (HST) model. These [...]
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Finite element modelling of fracture propagation in saturated media using quasi-zero-thickness interface elements
I. de-Pouplana, E. Oñate

Computers and Geotechnics (2018). Vol. 96, pp. 103-117

Abstract
A new computational technique for the simulation of 2D and 3D fracture propagation processes in saturated porous media is presented. A non-local damage model is conveniently used in conjunction with interface elements to predict the degradation pattern of the domain and insert new fractures followed by remeshing. FIC-stabilized elements of equal order interpolation in the displacement and the pore pressure have been successfully used under complex conditions near the undrained-incompressible limit. A bilinear cohesive fracture model describes the mechanical behaviour of the joints. A formulation derived from the cubic law models the fluid flow through the crack. Examples in 2D and 3D, using 3-noded triangles and 4-noded tetrahedra respectively, are presented to illustrate the accuracy and robustness of the proposed methodology.
Abstract
A new computational technique for the simulation of 2D and 3D fracture propagation processes in saturated porous media is presented. A non-local damage model [...]
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Numerical modelling of granular materials with spherical discrete particles and the bounded rolling friction model. Application to railway ballast
J. Irazábal González, F. Salazar, E. Oñate

Computers and Geotechnics (2017). Vol. 85, pp. 220-229

Abstract
The Discrete Element Method (DEM) was found to be an effective numerical method for the calculation of engineering problems involving granular materials. However, the representation of irregular particles using the DEM is a very challenging issue, leading to different geometrical approaches. This document presents a new insight in the application of one of those simplifications known as rolling friction, which avoids excessive rotation when irregular shaped materials are simulated as spheric particles. This new approach, called the Bounded Rolling Friction model, was applied to reproduce a ballast resistance test.
Abstract
The Discrete Element Method (DEM) was found to be an effective numerical method for the calculation of engineering problems involving granular materials. [...]
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Computationally optimized formulation for the simulation of composite materials and delamination failures
X. Martinez, F. Rastellini, S. Oller, F. Flores, E. Oñate

Composites Part B: Enginnering (2011). Vol. 42 (2), pp. 134-144

Abstract
The numerical simulation of complex failure modes of composite materials, such as delamination, can be computationally very demanding, as it requires special elements and/or numerical strategies to characterize damage onset and propagation. This work presents several formulations developed to optimize the computational performance of an explicit finite element code designed specifically for the simulation of large scale composite structures. The composite mechanical performance is obtained with the matrix-reinforced mixing theory, a simplified version of the serial/parallel mixing theory that does not require an iterative procedure or the calculation of the tangent stiffness matrix. The number of elements required to perform the simulation is reduced by stacking several layers inside a single finite element. This work also proposes a modification of the isotropic damage law, capable of taking into account the residual strength provided by friction in type II fracture modes. The ability of these formulations to successfully predict the mechanical performance of composite materials is assessed with the ply drop-off test. In this test a laminate with a change of thickness in its mid-span is loaded until it breaks due to a delamination process. The formulation proposed obtains a very accurate prediction of the experimental response of the test, as it provides a very good characterization of the initial laminate stiffness, the delamination onset, and its propagation along the specimen.
Abstract
The numerical simulation of complex failure modes of composite materials, such as delamination, can be computationally very demanding, as it [...]
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A hierarchical finite element for composite laminated beams using a refined zigzag theory
L. Nallim, S. Oller, E. Oñate, F. Flores

Composite Structures (2017). Vol. 163, pp. 168-184

Abstract
In this work a kinematics for laminated beams enriched with a refined formulation ZigZag (RZT), originally presented by Tessler et al. in 2007, introduced in a hierarchical one dimensional type “p” finite element is presented. The finite element employs Lagrange polynomials for the approximation of the degrees of freedom of the ends (nodes) and orthogonal Gram-Schmidt polynomials to the internal degrees of freedoms. This finite element allows a very low discretization, is free of shear locking and behaves very well when the analysis of laminated composites with accurate determination of local stresses and strains at laminar level is necessary. This element has been validated in the analysis of laminated beams with various sequences of symmetric and asymmetric stacking, studying in each case its accuracy and stability.
Abstract
In this work a kinematics for laminated beams enriched with a refined formulation ZigZag (RZT), originally presented by Tessler et al. in 2007, introduced in a hierarchical [...]
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Two-noded zigzag beam element accounting for shear effects based on an extended Euler Bernoulli theory
D. Di Capua, E. Oñate

Composite Structures (2015). Vol. 132, pp 1192-1205

Abstract
We present a new 2-noded beam element based on the refined zigzag theory and the classical Euler–Bernoulli beam theory for the static analysis of composite laminate and sandwich beams. The proposed element is able to take into account distortion effects due to shear elastic strains and can predict delamination. The element has four degrees of freedom per node. A C1 cubic Hermite interpolation is used for the vertical deflection while a C0 linear interpolation is employed for the other kinematics variables. The stiffness matrix and the load vector are calculated in explicit form using exact integration. The element is free from shear locking as confirmed with numerical tests on a wide range of the slenderness ratios. Numerical results show the ability of the EEBZ2 element to reproduce accurately the vertical deflection along the beam length and complex zigzag distributions of the axial displacement and the stresses across the thickness. Delamination effects are modeled by incorporating of an additional zigzag function corresponding to the kinematics of a zero thickness layer where delamination occurs. An example showing the capability of the new EEBZ2 element for accurately reproducing delamination effects is presented.
Abstract
We present a new 2-noded beam element based on the refined zigzag theory and the classical Euler–Bernoulli beam theory for the static analysis of composite laminate [...]
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Delamination in laminated plates using the 4-noded quadrilateral qlrz plate element based on the refined zigzag theory
A. Eijo, E. Oñate, S. Oller

Composite Structures (2014). Vol. 108, pp. 456-471

Abstract
A numerical method based on the Refined Zigzag Theory (RZT) to model delamination in composite laminated plate/shell structures is presented. The originality of this method is the use of 4-noded quadrilateral plate finite elements whit only seven variables per node to discretize the plate/shell geometry. The ability to capture the relative displacement between consecutive layers in fracture mode II and III is the more important advantage of this element, denoted QLRZ. A continuum isotropic damage model is used to model the mechanical behavior of the plies. The material non-lineal problem is solved with the modified Newton–Raphson method. The RZT plate theory, the QLRZ finite element and the isotropic damage model are described in this work. Also, the implicit integration algorithm is presented. The performance of the numerical model is analyzed by studying the delamination in a rectangular plate for two different laminates, using the 3D analysis as the reference solution
Abstract
A numerical method based on the Refined Zigzag Theory (RZT) to model delamination in composite laminated plate/shell structures is presented. The originality of this method [...]
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A numerical model of delamination in composite laminated beams using the LRZ beam element based on the refined zigzag theory
A. Eijo, E. Oñate, S. Oller

Composite Structures (2013). Vol. 104, pp. 270-280

Abstract
A method based on the Refined Zigzag Theory (RZT) to model delamination in composite laminated beam structures is presented. The novelty of this method is the use of one-dimensional finite elements to discretize the geometry of the beam. The key property of this beam element, named LRZ, is the possibility to capture the relative displacement between consecutive layers which occurs during delamination. The fracture mode that the LRZ element is capable to predict is mode II. In order to capture the relative displacement using the LRZ element it is necessary to adapt the RZT theory as presented in this paper. The mechanical properties of the layers are modeled using a continuum isotropic damage model. The modified Newton–Raphson method is used for solving the non-linear problem. The RZT theory, the LRZ finite element and the isotropic damage model are described in the paper. Also, the implicit integrations algorithm is presented. The performance of the LRZ element is analyzed by studying the delamination in a beam for two different laminates, using the plane stress solution as a reference.
Abstract
A method based on the Refined Zigzag Theory (RZT) to model delamination in composite laminated beam structures is presented. The novelty of this method is the use of one-dimensional [...]
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Robust design optimisation of advance hybrid (fiber-metal) composite structures
D. Lee, C. Morillo, S. Oller, G. Bugeda, E. Oñate

Composite Structures (2013). Vol. 99, pp. 181-192

Abstract
Hybrid Composite Structures (HCSs) are consisting of alternating layers of Fiber-Reinforced Polymer and metal sheets. Mechanical properties and responses for off-design conditions of HCSs can be improved using an innovative methodology coupling Multi-Objective Genetic Algorithm and robust design method. The concept of robust design approach ensures that a structure will be tolerant to unexpected loading and operating conditions. In this paper, two applications are considered; the first is to maximise the stiffness of the HCS while minimising its total weight through a Multi-Objective Design Optimisation. The second application considers a Robust Multi-Objective Design Optimisation (RMDO) to minimise total weight of HCS and to minimise both, the normalised mean displacement and the standard deviations of displacement, considering critical load cases. For the optimisation process, a distributed/parallel Multi-Objective Genetic Algorithm in robust multi-objective optimisation platform is used and it is coupled to a Finite Element Analysis based composite structure analysis tool to find the optimal combination of laminates sequences for HCSs. Numerical results show the advantages in mechanical properties of HCS over the metal structures, and also the use of RMDO methodology to obtain higher characteristics of HCS in terms of mechanical properties and its stability at the variability of load cases.
Abstract
Hybrid Composite Structures (HCSs) are consisting of alternating layers of Fiber-Reinforced Polymer and metal sheets. Mechanical properties and responses for off-design [...]
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Multilayered composite structure design optimisation using distributed/parallel multi-objective evolutionary algorithms
D. Lee, C. Morillo, G. Bugeda, S. Oller, E. Oñate

Composite Structures (2012). Vol. 94 (3), pp. 1087-1096

Abstract
This paper presents a research work on stacking sequence design optimisation for multilayered composite plate using a parallel/distributed evolutionary algorithm. The stacking sequence of fibres has a dramatic influence on the strength of multilayered composite plates. Multiple layers of fibre-reinforced material systems offer versatility in engineering material design due to the fact that the stacking sequence of each orthotropic layer can offer full advantage of superior mechanical properties. Numerical results show that the optimal composite structures have lower weight, higher stiffness and also affordable cost when compared to the extreme and intermediate composite structures. In addition, the benefits of using a parallel optimisation system are also presented.
Abstract
This paper presents a research work on stacking sequence design optimisation for multilayered composite plate using a parallel/distributed evolutionary algorithm. [...]
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Finite element modeling of free surface flow in variable porosity media
A. Larese, R. Rossi, E. Oñate

Archives of Comp. Meths. Engng. (2015). Vol. 22 (4), pp. 637-653

Abstract
The aim of the present work is to present an overview of some numerical procedures for the simulation of free surface flows within a porous structure. A particular algorithm developed by the authors for solving this type of problems is presented. A modified form of the classical Navier–Stokes equations is proposed, with the principal aim of simulating in a unified way the seepage flow inside rockfill-like porous material and the free surface flow in the clear fluid region. The problem is solved using a semi-explicit stabilized fractional step algorithm where velocity is calculated using a 4th order Runge–Kutta scheme. The numerical formulation is developed in an Eulerian framework using a level set technique to track the evolution of the free surface. An edge-based data structure is employed to allow an easy OpenMP parallelization of the resulting finite element code. The numerical model is validated against laboratory experiments on small scale rockfill dams and is compared with other existing methods for solving similar problems.
Abstract
The aim of the present work is to present an overview of some numerical procedures for the simulation of free surface flows within a porous structure. A particular algorithm [...]
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Data-Based Models for the Prediction of Dam Behaviour: A Review and Some Methodological Considerations
F. Salazar, R. Morán Moya, M. Toledo, E. Oñate

Archives of Comp. Meths. Engng. (2017). Vol. 24 (1), pp. 1-21

Abstract
Predictive models are an important element in dam safety analysis. They provide an estimate of the dam response faced with a given load combination, which can be compared with the actual measurements to draw conclusions about dam safety. In addition to numerical finite element models, statistical models based on monitoring data have been used for decades for this purpose. In particular, the hydrostatic-season-time method is fully implemented in engineering practice, although some limitations have been pointed out. In other fields of science, powerful tools such as neural networks and support vector machines have been developed, which make use of observed data for interpreting complex systems . This paper contains a review of statistical and machine-learning data-based predictive models, which have been applied to dam safety analysis . Some aspects to take into account when developing analysis of this kind, such as the selection of the input variables, its division into training and validation sets, and the error analysis, are discussed. Most of the papers reviewed deal with one specific output variable of a given dam typology and the majority also lack enough validation data. As a consequence, although results are promising, there is a need for further validation and assessment of generalisation capability. Future research should also focus on the development of criteria for data pre-processing and model application.
Abstract
Predictive models are an important element in dam safety analysis. They provide an estimate of the dam response faced with a given load combination, which can be compared [...]
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An Object-oriented Environment for Developing Finite Element Codes for Multi-disciplinary Applications
P. Dadvand, R. Rossi, E. Oñate

Archives of Comp. Meths. Engng. (2010). Vol. 17 (3), pp 253-297

Abstract
The objective of this work is to describe the design and implementation of a framework for building multi-disciplinary finite element programs. The main goals are generality, reusability, extendibility, good performance and memory efficiency. Another objective is preparing the code structure for team development to ensure the easy collaboration of experts in different fields in the development of multi-disciplinary applications. Kratos, the framework described in this work, contains several tools for the easy implementation of finite element applications and also provides a common platform for the natural interaction of different applications. To achieve this, an innovative variable base interface is designed and implemented. This interface is used at different levels of abstraction and showed to be very clear and extendible. A very efficient and flexible data structure and an extensible IO are created to overcome difficulties in dealing with multi-disciplinary problems. Several other concepts in existing works are also collected and adapted to coupled problems. The use of an interpreter, of different data layouts and variable number of dofs per node are examples of such approach. In order to minimize the possible conflicts arising in the development, a kernel and application approach is used. The code is structured in layers to reflect the working space of developers with different fields of expertise. Details are given on the approach chosen to increase performance and efficiency. Examples of application of Kratos to different multidisciplinary problems are presented in order to demonstrate the applicability and efficiency of the new object oriented environment.
Abstract
The objective of this work is to describe the design and implementation of a framework for building multi-disciplinary finite element programs. The main goals are generality, [...]
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Nonlinear Formulations of a Four-Node Quasi-Conforming Shell Element
G. Lomboy, S. Suthasupradit, K. Kim, E. Oñate

Archives of Comp. Meths. Engng. (2009). Vol. 16 (2), pp. 189-250

Abstract
The quasi-conforming technique was introduced in the 1980’s to meet the challenge of inter-elements conforming problems and give a unified treatment of both conforming and nonconforming elements. While the linear formulation is well established, the nonlinear formulation based on the quasi-conforming technique that includes geometric and material nonlinearity is presented in this paper. The formulation is derived in the framework of an updated Lagrangian stress resultant, co-rotational approach. The geometric nonlinear formulation provides solutions to buckling and postbuckling behaviour while the material nonlinear formulation considers the spread of plasticity within the element while maintaining an explicit construction of element matrices. Aside from the elasto-plastic constitutive relation, formulations on laminate composites and reinforced concrete are also presented. The formulations of laminate composite and reinforced concrete material are present based on the layer concept, the material properties can vary throughout the thickness and across the surface of a shell element. The various failure criteria for laminate composite are included in the formulation which makes it possible to analyses the progressive failure of fibre and matrix. For the reinforced concrete material, the nonlinearities as a result of tensile cracking, tension stiffening between cracks, the nonlinear response of concrete in compression, and the yielding of the reinforcement are considered. The steel reinforcement is modeled as a bilinear material with strain hardening.
Abstract
The quasi-conforming technique was introduced in the 1980’s to meet the challenge of inter-elements conforming problems and give a unified treatment of both conforming [...]
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Geometry optimization of the diffuser for the supersonic wind tunnel using genetic algorithm and adaptive mesh refinement technique
M. Kouhi, M. Manshadi, E. Oñate

Aerospace Science and Technology (2014). Vol. 36, pp. 64-74, 2014

Abstract
Design of two-dimensional supersonic diffusers as a part of the wind tunnel is investigated in this paper. A methodology based on the mixture of try-and-error method and optimization algorithm is developed to handle the design problem. In the first design step, using try-and-error approach, the main parameters related to the geometry of diffuser such as length, angle and area ratio between the throat and the outlet are determined assuming a diffuser with linear walls. The design criterion in this step is the fact that the shock wave should be created near the diffuser throat in order to benefit from the maximum efficiency of diffuser. In the second design step, considering the optimization methodology, it is tried to improve the optimum design obtained in the first step by modifying the wall point locations and keeping the rest of the geometry fixed. Hence, an optimization problem is defined to find the best curve for the diffuser wall instead of the a linear one used the in the first step. The objective function of this problem is to minimize the output Mach number using Genetic Algorithm (GA). The fluid flow is evaluated using the Euler equations in the conservative form where the Streamline-Upwind/Petrov–Galerkin (SUPG) finite element scheme is used to discretize the flow equations. In order to capture the flow solution around the shock waves accurately, the adaptive mesh refinement technique is coupled to the flow solution. The demonstrated results show the efficiency of the proposed method for designing supersonic diffusers
Abstract
Design of two-dimensional supersonic diffusers as a part of the wind tunnel is investigated in this paper. A methodology based on the mixture of try-and-error method [...]
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Advances in discrete element modelling of underground excavations
C. Labra, J. Rojek, E. Oñate, F. Zárate

Acta Geotechnica (2009). Vol. 3 (4), pp. 317-322

Abstract
The paper presents advances in the discrete element modelling of underground excavation processes extending modelling possibilities as well as increasing computational efficiency. Efficient numerical models have been obtained using techniques of parallel computing and coupling the discrete element method with finite element method. The discrete element algorithm has been applied to simulation of different excavation processes, using different tools, TBMs and roadheaders. Numerical examples of tunnelling process are included in the paper, showing results in the form of rock failure, damage in the material, cutting forces and tool wear. Efficiency of the code for solving large scale geomechanical problems is also shown
Abstract
The paper presents advances in the discrete element modelling of underground excavation processes extending modelling possibilities as well as increasing computational efficiency. [...]
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A two-step monolithic method for the efficient simulation of incompressible flows
P. Ryzhakov, J. Cotela, R. Rossi, E. Oñate

Int. J. Numer. Meth. Fluids (2014). Vol 74 (12), pp. 919-934

Abstract
We propose a simple technique for improving computationally the efficiency of monolithic velocity–pressure solvers for incompressible flow problems. The idea consists in solving the discrete nonlinear system of governing equations in two steps: introducing ‘artificial’ compressibility first and afterwards correcting the solution by solving the original incompressible system. The speed‐up is obtained because of a better conditioning of the modified discrete system solved at the prediction step. The formulation can be easily implemented into existing monolithic codes requiring minor modification only. The paper concludes with two examples validating the formulation and facilitating the estimation of the obtained speed‐up. For the tests chosen, an average speed‐up is approximately double, suggesting that the method is a feasible approach for incompressible flows' simulation.
Abstract
We propose a simple technique for improving computationally the efficiency of monolithic velocity–pressure solvers for incompressible flow problems. The idea consists [...]
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Multi-objective aerodynamic shape optimization using MOGA coupled to advanced adaptive mesh refinement
M. Kouhi, D. Lee, G. Bugeda, E. Oñate

Computers and Fluids (2013). Vol. 88, pp. 298-312

Abstract
This paper demonstrates the big influence of the control of the mesh quality in the final solution of aerodynamic shape optimization problems. It aims to study the trade-off between the mesh refinement during the optimization process and the improvement of the optimized solution. This subject is investigated in the transonic airfoil design optimization using an Adaptive Mesh Refinement (AMR) technique coupled to Multi-Objective Genetic Algorithm (MOGA) and an Euler aerodynamic analysis tool. The methodology is implemented to solve three practical design problems; the first test case considers a reconstruction design optimization that minimizes the pressure error between a predefined pressure curve and candidate pressure distribution. The second test considers the total drag minimization by designing airfoil shape operating at transonic speeds. For the final test case, a multi-objective design optimization is conducted to maximize both the lift to drag ratio (L/D) and lift coefficient (Cl). The solutions obtained with and without adaptive mesh refinement are compared in terms of solution improvement and computational cost. Numerical results clearly show that the use of adaptive mesh refinement can improve the solution accuracy while reducing significant computational cost in both single- and multi-objective design optimizations.
Abstract
This paper demonstrates the big influence of the control of the mesh quality in the final solution of aerodynamic shape optimization problems. It aims to study the trade-off [...]
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An efficient edge‐based level set finite element method for free surface flow problems
R. Rossi, E. Oñate, A. Larese, P. Dadvand

Int. J. Numer. Meth. Fluids (2013). Vol. 71 (6), pp. 687-716

Abstract
We present an efficient technique for the solution of free surface flow problems using level set and a parallel edge‐based finite element method. An unstructured semi‐explicit solution scheme is proposed. A custom data structure, obtained by blending node‐based and edge‐based approaches is presented so to allow a good parallel performance. In addition to standard velocity extrapolation (for the convection of the level set function), an explicit extrapolation of the pressure field is performed in order to impose both the pressure boundary condition and the volume conservation. The latter is also improved with a modification of the divergence free constrain. The method is shown to allow an efficient solution of both simple benchmark cases and complex industrial examples
Abstract
We present an efficient technique for the solution of free surface flow problems using level set and a parallel edge‐based finite element method. An unstructured semi‐explicit [...]
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Robust active shock control bump design optimisation using hybrid parallel MOGA
D. Lee, G. Bugeda, J. Périaux, E. Oñate

Computers and Fluids (2013). Vol. 80, pp. 214 - 224

Abstract
The paper investigates a robust optimisation for detail design of active shock control bump on a transonic Natural Laminar Flow (NLF) aerofoil using a Multi-Objective Evolutionary Algorithm (MOEA) coupled to Computational Fluid Dynamics (CFDs) software. For MOEA, Robust Multi-Objective Optimisation Platform (RMOP) developed at CIMNE is used. For the active shock control bump design, two different optimisation methods are considered; the first method is a Pareto-Game based Genetic Algorithm in RMOP (denoted as RMOGA). The second method uses a Hybridised RMOGA with Game-Strategies and a parallel computation for high performance computation. Numerical results show not only how the concept of Shock Control Bump (SCB) coupled to CFD can improve aerodynamic performance of classic transonic aerofoil at the variability of flight conditions but also how high performance (parallel/distributed) computation with applying Hybrid-Game increases the efficiency of optimisation in terms of computational cost and results accuracy
Abstract
The paper investigates a robust optimisation for detail design of active shock control bump on a transonic Natural Laminar Flow (NLF) aerofoil using a Multi-Objective Evolutionary [...]
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An algorithm for the simulation of thermally coupled low speed flow problems
P. Ryzhakov, E. Oñate, R. Rossi

Int. J. Numer. Meth. Fluids (2012). Vol. 70' (1), pp. 1-19

Abstract
In this paper, we propose a computational algorithm for the solution of thermally coupled flows in subsonic regime. The formulation is based upon the compressible Navier–Stokes equations, written in nonconservation form. An efficient modular implementation is obtained by solving the energy equation separately and then using the computed temperature as a known value in the momentum-continuity system. If an explicit single-step time integration scheme for the energy equation is used, the decoupling results to be natural. Integration of the momentum-continuity system is carried out using a semi-explicit method, combining Runge–Kutta and Backward Euler schemes for the momentum and continuity equations, respectively. Implicit treatment of pressure leads to favorable time step estimates even in the low Mach number (Ma ≪ 1) regimes. The numerical dissipation introduced by the Backward Euler scheme ensures absence of the spurious high frequencies in the numerical solution. The key point of the method is the assumption of linear variation of the temperature within a time step. Combined with a fractional splitting of the momentum-continuity system, it allows to solve the continuity only once per time step. Omitting the necessity of solving for the pressure at every intermediate step of the Runge–Kutta scheme minimizes the computational cost associated to the implicit step and leads to an efficiency close to that of a purely explicit scheme. The method is tested using two benchmark examples.
Abstract
In this paper, we propose a computational algorithm for the solution of thermally coupled flows in subsonic regime. The formulation is based upon the compressible Navier–Stokes [...]
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Hybrid-Game Strategies for multi-objective design optimization in engineering
D. Lee, L. González, J. Periaux, A. Srinivas, E. Oñate

Computers and Fluids (2011). Vol. 47 (1), pp. 189-204

Abstract
A number of Game Strategies (GS) have been developed in past decades. They have been used in the fields of economics, engineering, computer science and biology due to their efficiency in solving design optimization problems. In addition, research in multi-objective (MO) and multidisciplinary design optimization (MDO) has focused on developing robust and efficient optimization methods to produce a set of high quality solutions with low computational cost. In this paper, two optimization techniques are considered; the first optimization method uses multi-fidelity hierarchical Pareto optimality. The second optimization method uses the combination of two Game Strategies; Nash-equilibrium and Pareto optimality. The paper shows how Game Strategies can be hybridised and coupled to Multi-Objective Evolutionary Algorithms (MOEA) to accelerate convergence speed and to produce a set of high quality solutions. Numerical results obtained from both optimization methods are compared in terms of computational expense and model quality. The benefits of using Hybrid-Game Strategies are clearly demonstrated
Abstract
A number of Game Strategies (GS) have been developed in past decades. They have been used in the fields of economics, engineering, computer science and biology due to their [...]
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Lift maximization with uncertainties for the optimization of high‐lift devices
Z. Tang, J. Périaux, G. Bugeda, E. Oñate

Int. J. Numer. Meth. Fluids (2010). Vol. 64 (2), pp. 119-135

Abstract
In this paper, the aerodynamic shape optimization problems with uncertain operating conditions have been addressed. After a review of robust control theory and the possible approaches to take into account uncertainties, the use of Taguchi robust design methods in order to overcome single point design problems in aerodynamics is proposed. Under the Taguchi concept, a design with uncertainties is converted into an optimization problem with two objectives which are the mean performance and its variance, so that the solutions are as less sensitive to the uncertainty of the input parameters as possible. Furthermore, the modified non‐dominated sorting genetic algorithms are used to capture a set of compromised solutions (Pareto front) between these two objectives. The flow field is analyzed by Navier–Stokes computation using an unstructured mesh. In order to reduce the number of expensive evaluations of the fitness function a response surface modeling is employed to estimate the fitness value using the polynomial approximation model. During the solution of the optimization problem, a semi‐torsional spring analogy is used for the adaption of the computational mesh to all the obtained geometrical configurations. The proposed approach is applied to the robust optimization of the 2D high‐lift devices of a business aircraft by maximizing the mean and minimizing the variance of the lift coefficients with uncertain free‐stream angle of attack at landing flight condition.
Abstract
In this paper, the aerodynamic shape optimization problems with uncertain operating conditions have been addressed. After a review of robust control theory and the possible [...]
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Simulation of flows with violent free surface motion and moving objects using unstructured grids
R. Löhner, C. Yang, E. Oñate

Int. J. Numer. Meth. Fluids (2007). Vol. 53 (8), pp 1315-1338

Abstract
A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and three‐dimensional structures. The present implementation follows the classic VOF implementation for the liquid–gas system, considering only the liquid phase. Extrapolation algorithms are used to obtain velocities and pressure in the gas region near the free surface. The VOF technique is validated against the classic dam‐break problem, as well as series of 2D sloshing experiments and results from SPH calculations. These and a series of other examples demonstrate that the ability of the present approach to simulate violent free surface flows with strong nonlinear behaviour.
Abstract
A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate [...]
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Optimum aerodynamic shape design including mesh adaptivity
G. Bugeda, E. Oñate

Int. J. Numer. Meth. Fluids (1995). Vol. 20 (8-9), pp. 915-934

Abstract
This paper presents a methodology for solving shape optimization problems in the context of fluid flow problems including adaptive remeshing. The method is based on the computation of the sensitivities of the geometrical design parameters, the mesh, the flow variables and the error estimator to project the refinement parameters from one design to the next. This sensitivity analysis is described for the incompressible potential equations and the Euler equations. The efficiency of the proposed method is checked by means of two 2D inverse problems.
Abstract
This paper presents a methodology for solving shape optimization problems in the context of fluid flow problems including adaptive remeshing. The method is based on the computation [...]
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A general procedure for deriving stabilized space–time finite element methods for advective–diffusive problems
E. Oñate, M. Manzán

Int. J. Numer. Meth. Fluids (1999). Vol. 31 (1), pp. 203-221

Abstract
A procedure to derive stabilized space–time finite element methods for advective–diffusive problems is presented. The starting point is the stabilized balance equation for the transient case derived by Oñate [Comput. Methods Appl. Mech. Eng., 151, 233–267 (1998)] using a finite increment calculus approach. A description of the new stabilization method and a procedure for computing the stabilization parameter of the space–time solution is given. The efficiency of the stabilization approach is shown in the solution of some transient advective–diffusive problems, including the non‐linear Burger's equation.
Abstract
A procedure to derive stabilized space–time finite element methods for advective–diffusive problems is presented. The starting point is the stabilized balance [...]
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Optimum aerodynamic shape design for fluid flow problems including mesh adaptivity
G. Bugeda, E. Oñate

Int. J. Numer. Meth. Fluids (1999). Vol. 30 (2), pp. 161-178

Abstract
This paper presents a methodology for solving shape optimization problems in the context of fluid flow problems including adaptive remeshing. The method is based on the computation of the sensitivities of the geometrical design parameters, the mesh, the flow variables and the error estimator to project the refinement parameters from one design to the next. The efficiency of the proposed method is checked out in two 2D optimization problems using a full potential model coupled with a boundary layer model. The first one corresponds to an internal flow problem and the second one corresponds to an external flow problem. The work presented here can be considered as a continuation of previous work (Bugeda and Oñate, Int. J. Numer. Methods Fluids, 20, 915–924 (1995)). In that paper, the sensitivity analysis corresponding to both an incompressible potential flow and a Euler flow were derived together with a strategy for the adaptive remeshing. In the present paper, the sensitivity analysis is derived for a full potential flow coupled with a boundary layer model, and a new error estimator is employed.
Abstract
This paper presents a methodology for solving shape optimization problems in the context of fluid flow problems including adaptive remeshing. The method is based on the computation [...]
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A Phenomenological Model for the Solidification of Eutectic and Hypoeutectic Alloys Including Recalescence and Undercooling
M. Chiumenti, M. Cervera, E. Salsi, A. Zonato

J. of Heat Transfer (2018). (preprint) Vol. 140 (8), pp. 12

Abstract
In this work, a novel phenomenological model is proposed to study the liquid-to-solid phase change of eutectic and hypoeutectic alloy compositions. The objective is to enhance the prediction capabilities of the solidification models based on a-priori definition of the solid fraction as a function of the temperature field. However, the use of models defined at the metallurgical level is avoided to minimize the number of material parameters required. This is of great industrial interest because, on the one hand, the classical models are not able to predict recalescence and undercooling phenomena, and, on the other hand, the complexity as well as the experimental campaign necessary to feed most of the microstructure models available in the literature make their calibration difficult and very dependent on the chemical composition and the treatment of the melt. Contrarily, the proposed model allows for an easy calibration by means of few parameters. These parameters can be easily extracted from the temperature curves recorded at the hot spot of the quick cup test, typically used in the differential thermal analysis (DTA) for the quality control of the melt just before pouring. The accuracy of the numerical results is assessed by matching the temperature curves obtained via DTA of eutectic and hypoeutectic alloys. Moreover, the model is validated in more complex casting experiments where the temperature is measured at different thermocouple locations and the metallurgical features such as grain size and nucleation density are obtained from an exhaustive micrography campaign. The remarkable agreement with the experimental evidence validates the predicting capabilities of the proposed model.
Abstract
In this work, a novel phenomenological model is proposed to study the liquid-to-solid phase change of eutectic and hypoeutectic alloy compositions. The objective is to enhance [...]
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Numerical modelling of microstructure evolution in Friction Stir Welding (FSW)"
N. Dialami, M. Cervera, M. Chiumenti

Metals (2018). (preprint) Vol. 8 (3), pp. 183

Abstract
This work studies the metallurgical and microstructural aspects of Friction Stir Welding (FSW) in terms of grain size and microhardness. The modelling is based on the combination of an apropos kinematic framework for the local simulation of FSW processes and a material particle tracing technique for tracking the material flow during the weld. The resulting grain size and microhardness values are validated with experimental observations from an identical processed sample. A Sheppard-Wright constitutive relation is adopted to describe the mechanical behavior of AZ31 Mg alloy considered in this work. The strain rate and temperature histories obtained from the numerical model are stored on the tracers. The relationship among the grain size, microhardness, strain rate, and temperature is obtained using Zener-Hollomon parameter and Hall-Petch relationship. A linear description relates the logarithm of average grain size to the logarithm of Zener-Hollomon parameter. The relationship between microhardness and average grain size stands away from the linear trend.
Abstract
This work studies the metallurgical and microstructural aspects of Friction Stir Welding (FSW) in terms of grain size and microhardness. The modelling is based on the combination [...]
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Finite element analysis and experimental validation of the thermomechanical behavior in laser solid forming of Ti-6Al-4V
X. Lu, X. Lin, M. Chiumenti, M. Cervera, J. Li, L. Ma, L. Wei, Y. Hu, W. Huang

Additive Manufacturing (2018). (preprint) Vol. 21, pp. 30-40

Abstract
A three-dimensional (3D) thermomechanical coupled model for Laser Solid Forming (LSF) of Ti-6Al-4V alloy has been calibrated through experiments of 40-layers metal deposition using different scanning strategies. The sensitivity analysis of the mechanical parameters shows that the thermal expansion coefficient as well as the elastic limit of Ti-6Al-4V have a great impact on the mechanical behavior. Using the validated model and optimal mechanical parameters, the evolution of thermo-mechanical fields in LSF has been analyzed. It has been found that the stresses and distortions develop in two stages, after the deposition of the first layer and during the cooling phase after the manufacturing of the component. The cooling phase is the responsible of 70% of the residual stresses and 60% of the total distortions. The analyses indicate that by controlling the initial substrate temperature (pre-heating phase) and the final cooling phase it is possible to mitigate both distortion and residual stresses. Hence, the influence of different pre-heating procedures on the mechanical fields has been analyzed. The results show that increasing the pre-heating temperature of the substrate is the most effective way to reduce the distortions and residual stresses in Additive Manufacturing.
Abstract
A three-dimensional (3D) thermomechanical coupled model for Laser Solid Forming (LSF) of Ti-6Al-4V alloy has been calibrated through experiments of 40-layers metal [...]
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Appraisement of planar, bending and twisting cracks in 3D with isotropic and orthotropic damage models
G. Barbat, M. Cervera, M. Chiumenti

International Journal of Fracture (2018). (preprint) Vol. 210 (1-2), pp. 45–79

Abstract
This paper discusses the modeling of cracking in quasi-brittle materials using isotropic and orthotropic damage constitutive laws. A mixed strain/displacement finite element formulation is used, taking advantage of its enhanced precision and its enforced interelemental strain continuity. On the one hand, this formulation avoids the spurious mesh dependency of the computed solution associated to standard elements and does not require the use of tracking techniques. On the other hand, it greatly alleviates the spurious stress locking associated to the use of orthotropic models on standard finite elements. The performance of several isotropic and orthotropic damage constitutive laws is assessed through an extensive comparison with analytical solutions, numerical tests and experimental evidence reported in the literature. The behavior of the different damage models in terms of crack surface, collapse mechanism and force displacement curves is investigated performing 3D analyses in several conditions including Mode I, Mixed Mode and Mode III fracture. When performing the appraisement of planar, bending and twisting cracks, the enhanced accuracy of the mixed formulation allows for a distinct assessment of the several damage models considered. Aspects related to the behavior of damage models, such as the influence of Poisson’s ratio, the shape of the damage surface and the adoption of isotropic and orthotropic models are investigated and noteworthy conclusions are drawn
Abstract
This paper discusses the modeling of cracking in quasi-brittle materials using isotropic and orthotropic damage constitutive laws. A mixed strain/displacement finite element [...]
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A novel positive/negative projection in energy norm for the damage modeling of quasi-brittle solids
J. Wu, M. Cervera

Int. J. Solids and Structures (2018). (preprint) Vol. 139–140, pp. 250–269

Abstract
The asymmetric tensile/compressive material behavior and microcracks closure-reopening (MCR) effects exhibited by quasi-brittle solids are of significant importance to the nonlinear responses of engineering structures under cyclic loading, e.g., earthquake excitations. Based on our previous work (Cervera et al., 1995; Faria et al., 1998; Wu et al., 2006) this work addresses a novel thermodynamically consistent unilateral damage model for concrete. In particular, the positive/negative projection (PNP) of the effective stress tensor and the additive bi-scalar damage constitutive relation are maintained owing to the conceptual simplicity and computational efficiency. It is found that the classical PNP widely adopted in the literature is not optimal for this damage model, since the resulting stiffness is not always of major symmetry. Consequently, a well-defined free energy potential does not exist in general cases and the model cannot be cast into the framework of thermodynamics with internal variables. Furthermore, the damage induced anisotropy cannot be captured, exhibiting excessive lateral deformationsunder uniaxial tension. To overcome the above issues, a novel PNP, variationally interpreted as the closest point projection of the effective stress in energy norm, is proposed with closed-form solution. With the novel PNP, the secant stiffness tensorof the proposed unilateral damage model always possesses major symmetry and exhibits orthotropic behavior under uniaxial tension and mixed tension/compression. The corresponding thermodynamics framework is then given, resulting in an energy release rate based rounded-Rankine type damage criterion appropriate for tensile failure in quasi-brittle solids. Several numerical examples of single-point verifications and benchmark tests are presented. It is demonstrated that the proposed model is capable of characterizing localized failureof concrete under proportional and non-proportional static loading, as well as the MCR effects under seismic cyclic loading.
Abstract
The asymmetric tensile/compressive material behavior and microcracks closure-reopening (MCR) effects exhibited by quasi-brittle solids are of significant [...]
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Cracking of quasi-brittle structures under monotonic and cyclic loadings: A d+/d− damage model with stiffness recovery in shear
M. Cervera, C. Tesei, G. Ventura

Int. J. Solids and Structures (2017). (preprint) Vol. 135, pp. 148–171

Abstract
In the present paper, a new d+/d− damage model apt for quasi-brittle materials is described and its validation is carried out considering unreinforced concrete, reinforced concrete and masonry elements. Two independent scalar damage variables, d+ and d−, in combination with the split of the reversible strain tensor into its positive and negative counterparts, are adopted in order to simulate the pronounced dissimilar response under tension and compression, typical of these materials. An energy-equivalent framework is considered for representing the orthotropy induced in the material by the degradation process, with the consequence that a thermodynamically consistent constitutive operator, positive definite, symmetric and strain-driven, is derived. In addition to the degradation parameters, the permanent strain tensor is also contemplated by the model and a modification of the exponential softening modulus is proposed in order to treat the evolution of the two causes of dissipation, damage and irreversible deformations, in a coupled way. The formulation is integrated with a multidirectional damage procedure, addressed to extend the microcrack closure-reopening (MCR) capabilities of the model to shear cyclic conditions, characterized by orthogonal (or however intersecting) sets of cracks. Maintaining unaltered the dependence of the constitutive law from two scalar indeces, d+ and d−, this approach activates or deactivates a tensile(compressive) damage value on the base of the current maximum (minimum) principal strain direction. In correspondence with damage activation (crack opening) or deactivation (crack closure), a smooth transition is introduced, in order to avoid abrupt changes in stiffness and enhance the numerical performance and robustness of the multidirectional procedure. The adequacy of the proposed constitutive model in reproducing experimental results has been proven for both monotonic and cyclic loading conditions. The two examples of application involving cyclic loads, dominated by shear, constitute a validation of the multidirectional damage approach, showing how the suitable representation of unilateral effects and permanent deformations is essential to model the observed structural response in terms of maximum resistance, evolution of stiffness degradation and dissipation capacity.
Abstract
In the present paper, a new d+/d− damage model apt for quasi-brittle materials is described and its validation is carried out considering unreinforced [...]
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Experimental validation of a FSW model with an enhanced friction model: application to a threaded cylindrical pin tool
N. Dialami, M. Cervera, M. Chiumenti, A. Segatori, W. Osikowicz

Metals (2017). (preprint) Vol. 7 (11), pp. 491

Abstract
This work adopts a fast and accurate two-stage computational strategy for the analysis of FSW (Friction stir welding) processes using threaded cylindrical pin tools. The coupled thermo-mechanical problem is equipped with an enhanced friction model to include the effect of non-uniform pressure distribution under the pin shoulder. The overall numerical strategy is successfully validated by the experimental measurements provided by the industrial partner (Sapa). The verification of the numerical model using the experimental evidence is not only accomplished in terms of temperature evolution but also in terms of torque, longitudinal, transversal and vertical forces.
Abstract
This work adopts a fast and accurate two-stage computational strategy for the analysis of FSW (Friction stir welding) processes using threaded cylindrical pin tools. The coupled [...]
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Enhanced friction model for Friction Stir Welding (FSW) analysis: Simulation and experimental validation
N. Dialami, M. Chiumenti, M. Cervera, A. Segatori, W. Osikowicz

Int. J. Mechanical Sciences (2017). (preprint) Vol. 133, pp. 555-567

Abstract
Friction is one of the main heat generation mechanisms in Friction Stir Welding (FSW). This phenomenon occurs between the pin and the workpiece as the rotating tool moves along the weld line. An accurate friction model is essential for obtaining realistic results in a FSW simulation in particular temperature, forces and torque. In this work, a modified Norton's friction law is developed. The suggested enhanced friction model aims at providing not only the realistic temperature field but also the forces and torque. This model does not exclusively relate the frictional shear stress to the sliding velocity; conversely it takes into account the effect of non-uniform pressure distribution under the shoulder, as this latter has an important role in the process of heat generation. Longitudinal, transversal and vertical forces and torque are numerically calculated. The effect of the enhanced friction model is reflected in these forces. In particular, it leads to a more realistic estimation of the transversal and longitudinal forces in comparison with the results obtained using former models. The friction model is successfully validated by the experimental measurements provided by the industrial partner (Sapa). The experimental analysis is performed for the material characterization, the calibration of the friction model and, more generally, the assessment of the overall numerical strategy proposed for the FSW simulation.
Abstract
Friction is one of the main heat generation mechanisms in Friction Stir Welding (FSW). This phenomenon occurs between the pin and the workpiece as the rotating tool moves [...]
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Numerical modelling and experimental validation in Selective Laser Melting
M. Chiumenti, E. Neiva, E. Salsi, M. Cervera, E. Badia, J. Moya, Z. Chen, C. Lee, C. Davies

Additive Manufacturing (2017). (preprint) Vol. 18, pp. 171-185

Abstract
In this work a finite-element framework for the numerical simulation of the heat transfer analysis of additive manufacturing processes by powder-bed technologies, such as Selective Laser Melting, is presented. These kind of technologies allow for a layer-by-layer metal deposition process to cost-effectively create, directly from a CAD model, complex functional parts such as turbine blades, fuel injectors, heat exchangers, medical implants, among others. The numerical model proposed accounts for different heat dissipation mechanisms through the surrounding environment and is supplemented by a finite-element activation strategy, based on the born-dead elements technique, to follow the growth of the geometry driven by the metal deposition process, in such a way that the same scanning pattern sent to the numerical control system of the AM machine is used. An experimental campaign has been carried out at the Monash Centre for Additive Manufacturing using an EOSINT-M280 machine where it was possible to fabricate different benchmark geometries, as well as to record the temperature measurements at different thermocouple locations. The experiment consisted in the simultaneous printing of two walls with a total deposition volume of 107 cm3 in 992 layers and about 33,500 s build time. A large number of numerical simulations have been carried out to calibrate the thermal FE framework in terms of the thermophysical properties of both solid and powder materials and suitable boundary conditions. Furthermore, the large size of the experiment motivated the investigation of two different model reduction strategies: exclusion of the powder-bed from the computational domain and simplified scanning strategies. All these methods are analysed in terms of accuracy, computational effort and suitable applications
Abstract
In this work a finite-element framework for the numerical simulation of the heat transfer analysis of additive manufacturing processes by powder-bed technologies, [...]
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Finite element modeling of quasi-brittle cracks in 2D and 3D with enhanced strain accuracy
M. Cervera, G. Barbat, M. Chiumenti

Computational Mechanics (2017). (preprint) Vol. 60 (5), pp. 767–796

Abstract
This paper discusses the finite element modeling of cracking in quasi-brittle materials. The problem is addressed via a mixed strain/displacement finite element formulation and an isotropic damage constitutive model. The proposed mixed formulation is fully general and is applied in 2D and 3D. Also, it is independent of the specific finite element discretization considered; it can be equally used with triangles/tetrahedra, quadrilaterals/hexahedra and prisms. The feasibility and accuracy of the method is assessed through extensive comparison with experimental evidence. The correlation with the experimental tests shows the capacity of the mixed formulation to reproduce the experimental crack path and the force–displacement curves with remarkable accuracy. Both 2D and 3D examples produce results consistent with the documented data. Aspects related to the discrete solution, such as convergence regarding mesh resolution and mesh bias, as well as other related to the physical model, like structural size effect and the influence of Poisson’s ratio, are also investigated. The enhanced accuracy of the computed strain field leads to accurate results in terms of crack paths, failure mechanisms and force displacement curves. Spurious mesh dependency suffered by both continuous and discontinuous irreducible formulations is avoided by the mixed FE, without the need of auxiliary tracking techniques or other computational schemes that alter the continuum mechanical problem.
Abstract
This paper discusses the finite element modeling of cracking in quasi-brittle materials. The problem is addressed via a mixed strain/displacement finite element formulation [...]
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Tracking multi-directional intersecting cracks in numerical modelling of masonry shear walls under cyclic loading
S. Salaustros, M. Cervera, L. Pelà

Meccanica (2017). (preprint) Vol. 53 (7), pp. 1757–1776

Abstract
In-plane cyclic loading of masonry walls induces a complex failure pattern composed of multiple diagonal shear cracks, as well as flexural cracks. The realistic modelling of such induced localized cracking necessitates the use of costly direct numerical simulations with detailed information on both the properties and geometry of masonry components. On the contrary, computationally efficient macro-models using standard smeared-crack approaches often result in a poor representation of fracture in the simulated material, not properly localized and biased by the finite element mesh orientation. This work proposes a possible remedy to these drawbacks of macro-models through the use of a crack-tracking algorithm. The macro-modelling approach results in an affordable computational cost, while the tracking algorithm aids the mesh-bias independent and localized representation of cracking. A novel methodology is presented that allows the simulation of intersecting and multi-directional cracks using tracking algorithms. This development extends the use of localized crack approaches using tracking algorithms to a wider field of applications exhibiting multiple, arbitrary and interacting cracking. The paper presents also a novel formulation including into an orthotropic damage model the description of irreversible deformations under shear loading. The proposed approach is calibrated through the comparison with an experimental test on a masonry shear wall against in-plane cyclic loading.
Abstract
In-plane cyclic loading of masonry walls induces a complex failure pattern composed of multiple diagonal shear cracks, as well as flexural cracks. The realistic modelling [...]
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An enhanced finite element macro-model for the realistic simulation of localized cracks in masonry structures: A large-scale application
S. Salaustros, L. Pelà, M. Cervera, P. Roca

International Journal of Architectural Heritage (2017). (preprint) Vol. 12 (3), pp. 432-447

Abstract
Finite element macro-modeling approaches are widely used for the analysis of large-scale masonry structures. Despite their efficiency, they still face two important challenges: the realistic representation of damage and a reasonable independency of the numerical results to the used discretization. In this work, the classical smeared crack approach is enhanced with a crack-tracking algorithm, originating from the analysis of localized cracking in quasi-brittle materials. The proposed algorithm is for the first time applied to a large-scale wall exhibiting multiple shear and flexural cracking. Discussion covers structural aspects, as the response of the structure under different assumptions regarding the floor rigidity, but also numerical issues, commonly overlooked in the simulation of large structures, such the mesh-dependency of the numerical results.
Abstract
Finite element macro-modeling approaches are widely used for the analysis of large-scale masonry structures. Despite their efficiency, they still face two important challenges: [...]
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Strain localization analysis of elastic-damaging frictional-cohesive materials: Analytical results and numerical verification
J. Wu, M. Cervera

Materials (2017). (preprint) Vol. 10 (4), pp. 434

Abstract
Damage-induced strain softening is of vital importance for the modeling of localized failure in frictional-cohesive materials. This paper addresses strain localization of damaging solids and the resulting consistent frictional-cohesive crack models. As a supplement to the framework recently established for stress-based continuum material models in rate form (Wu and Cervera 2015, 2016), several classical strain-based damage models, expressed usually in total and secant format, are considered. Upon strain localization of such damaging solids, Maxwell’s kinematics of a strong (or regularized) discontinuity has to be reproduced by the inelastic damage strains, which are defined by a bounded characteristic tensor and an unbounded scalar related to the damage variable. This kinematic constraint yields a set of nonlinear equations from which the discontinuity orientation and damage-type localized cohesive relations can be derived. It is found that for the “Simó and Ju 1987” isotropic damage model, the localization angles and the resulting cohesive model heavily depend on lateral deformations usually ignored in classical crack models for quasi-brittle solids. To remedy this inconsistency, a modified damage model is proposed. Its strain localization analysis naturally results in a consistent frictional-cohesive crack model of damage type, which can be regularized as a classical smeared crack model. The analytical results are numerically verified by the recently-proposed mixed stabilized finite element method, regarding a singly-perforated plate under uniaxial tension. Remarkably, for all of the damage models discussed in this work, the numerically-obtained localization angles agree almost exactly with the closed-form results. This agreement, on the one hand, consolidates the strain localization analysis based on Maxwell’s kinematics and, on the other hand, illustrates versatility of the mixed stabilized finite element method.
Abstract
Damage-induced strain softening is of vital importance for the modeling of localized failure in frictional-cohesive materials. This paper addresses strain localization of [...]
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3D numerical modelling of twisting cracks under bending and torsion of skew notched beams
L. Benedetti, M. Cervera, M. Chiumenti

Engineering Fracture Mechanics (2017). (preprint) Vol. 176, pp. 235–256

Abstract
The testing of mode III and mixed mode failure is every so often encountered in the dedicated literature of mechanical characterization of brittle and quasi-brittle materials. In this work, the application of the mixed strain displacement ε-u finite element formulation to three examples involving skew notched beams is presented. The use of this FE technology is effective in problems involving localization of strains in softening materials. The objectives of the paper are: (i) to test the mixed formulation in mode III and mixed mode failure and (ii) to present an enhancement in terms of computational time given by the kinematic compatibility between irreducible displacement-based and the mixed strain-displacement elements. Three tests of skew-notched beams are presented: firstly, a three point bending test of a PolyMethyl MethaAcrylate beam; secondly, a torsion test of a plain concrete prismatic beam with square base; finally, a torsion test of a cylindrical beam made of plain concrete as well. To describe the mechanical behavior of the material in the inelastic range, Rankine and Drucker-Prager failure criteria are used in both plasticity and isotropic continuum damage formats. The proposed mixed formulation is capable of yielding results close to the experimental ones in terms of fracture surface, peak load and global loss of carrying capability. In addition, the symmetric secant formulation and the compatibility condition between the standard irreducible method and the strain-displacement one is exploited, resulting in a significant speedup of the computational procedure.
Abstract
The testing of mode III and mixed mode failure is every so often encountered in the dedicated literature of mechanical characterization of brittle and quasi-brittle [...]
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A fast and accurate two-stage strategy to evaluate the effect of the pin tool profile on metal flow, torque and forces during friction stir welding
N. Dialami, M. Cervera, M. Chiumenti, C. Agelet de Saracibar

Int. J. Mechanical Sciences (2017). (preprint) Vol. 122, pp. 215–227

Abstract
Pin geometry is a fundamental consideration in friction stir welding (FSW). It influences the thermal behaviour, material flow and forces during the weld and reflects on the joint quality. This work studies four pin tools with circular, triflute, trivex, and triangular profiles adopting a validated model of FSW process developed by the authors. The effect of the rotating tool geometry on the flow behaviour and process outcomes is analysed. Additionally, longitudinal and transversal forces and torque are numerically calculated and compared for the different pin shapes. The study is carried out for slip and stick limiting friction cases between pin and workpiece. The main novelties of the paper are a “speed-up” two-stage simulation methodology and a piecewise linear version of the constitutive model, both of them conceived for the use in real case industrial applications, where the achievement of accuracy with affordable simulation times is of importance. The Norton-Hoff constitutive model is adopted to characterize the material behaviour during the weld. The piecewise linear version of the model developed by the authors greatly facilitates the convergence of the numerical solution ensuring both computational efficiency and accuracy. A two-stage computational procedure is applied. In the first stage, a forced transient is carried out; in the second one, the magnitudes of interest are computed. The study shows that the proposed modelling approach can be used to predict and interpret the FSW behaviour for a specific pin geometry. Moreover, the reduction of the simulation time using the two-stage strategy can be up to 90%, compared to a standard single stage strategy.
Abstract
Pin geometry is a fundamental consideration in friction stir welding (FSW). It influences the thermal behaviour, material flow and forces during the weld and [...]
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An energy-equivalent d+/d− damage model with enhanced microcrack closure-reopening capabilities for cohesive-frictional materials
M. Cervera, C. Tesei

Materials (2017). (preprint) Vol. 10 (4), pp. 433

Abstract
In this paper, an energy-equivalent orthotropic d+/d− damage model for cohesive-frictional materials is formulated. Two essential mechanical features are addressed, the damage-induced anisotropy and the microcrack closure-reopening (MCR) effects, in order to provide an enhancement of the original d+/d−model proposed by Faria et al. 1998, while keeping its high algorithmic efficiency unaltered. First, in order to ensure the symmetry and positive definiteness of the secant operator, the new formulation is developed in an energy-equivalence framework. This proves thermodynamic consistency and allows one to describe a fundamental feature of the orthotropic damage models, i.e., the reduction of the Poisson’s ratio throughout the damage process. Secondly, a “multidirectional” damage procedure is presented to extend the MCR capabilities of the original model. The fundamental aspects of this approach, devised for generic cyclic conditions, lie in maintaining only two scalar damage variables in the constitutive law, while preserving memory of the degradation directionality. The enhanced unilateral capabilities are explored with reference to the problem of a panel subjected to in-plane cyclic shear, with or without vertical pre-compression; depending on the ratio between shear and pre-compression, an absent, a partial or a complete stiffness recovery is simulated with the new multidirectional procedure.
Abstract
In this paper, an energy-equivalent orthotropic d+/d− damage model for cohesive-frictional materials is formulated. Two essential mechanical features are addressed, [...]
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Finite element modelling of internal and multiple localized cracks
S. Salaustros, L. Pelà, M. Cervera, P. Roca

Computational Mechanics (2017). (preprint) Vol. 59 (2), pp. 299–316

Abstract
Tracking algorithms constitute an efficient numerical technique for modelling fracture in quasi-brittle materials. They succeed in representing localized cracks in the numerical model without mesh-induced directional bias. Currently available tracking algorithms have an important limitation: cracking originates either from the boundary of the discretized domain or from predefined “crack-root” elements and then propagates along one orientation. This paper aims to circumvent this drawback by proposing a novel tracking algorithm that can simulate cracking starting at any point of the mesh and propagating along one or two orientations. This enhancement allows the simulation of structural case-studies experiencing multiple cracking. The proposed approach is validated through the simulation of a benchmark example and an experimentally tested structural frame under in-plane loading. Mesh-bias independency of the numerical solution, computational cost and predicted collapse mechanisms with and without the tracking algorithm are discussed.
Abstract
Tracking algorithms constitute an efficient numerical technique for modelling fracture in quasi-brittle materials. They succeed in representing localized cracks in the numerical [...]
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Numerical simulation and experimental calibration of Additive Manufacturing by blown powder technology. Part I: thermal analysis
M. Chiumenti, X. Lin, M. Cervera, W. Lei, Y. Zheng, W. Huang

Rapid Prototyping Journal (2017). (preprint) Vol. 23 (2), pp. 448-463

Abstract
In this work the numerical simulation of Additive Manufacturing (AM) processes is addressed. The numerical results are compared with the experimental campaign carried out at SKLSP laboratories, where a Laser Solid Forming (LSF) machine, also referred to as Laser Engineered Net Shaping (LENS), is used to fabricate metal parts directly from CAD models. Ti-6Al-4V metal powder is injected into the molten pool created by a focused, high-energy laser beam and a layer of added material is sinterized according to the laser scanning pattern speciÖed by the user. The objectives of this paper are twofold: Örstly, this work is intended to calibrate the software for the numerical simulation of the AM process, to achieve high accuracy. Secondly, the sensitivity of the numerical model to the process parameters and modelling data is analysed. The numerical model adopts an apropos FE activation technology, which reproduces the same scanning pattern set for the numerical control system of the AM machine. This consists of a complex sequence of polylines, used to deÖne the contour of the component, and hatches patterns to Öll the inner section. The full sequence is given through the Common Layer Interface (CLI) format, a standard format for di§erent manufacturing processes such as Rapid Prototyping (RP), Shape Metal Deposition (SMD) or machining processes, among others. The result is a layer-by-layer metal deposition which can be used to build-up complex structures for components such as turbine blades, aircraft sti§eners, cooling systems, or medical implants, among others.
Abstract
In this work the numerical simulation of Additive Manufacturing (AM) processes is addressed. The numerical results are compared with the experimental campaign carried out [...]
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Local–global strategy for the prediction of residual stresses in FSW processes
N. Dialami, M. Cervera, M. Chiumenti, C. Agelet de Saracibar

International Journal of Advanced Manufacturing Technology (2017). (preprint) Vol. 88 (9), pp. 3099–3111

Abstract
This work describes the local–global strategy proposed for the computation of residual stresses in friction stir welding (FSW) processes. A coupling strategy between the analysis of the process zone nearby the pin tool (local level analysis) and the simulation carried out for the entire structure to be welded (global level analysis) is implemented to accurately predict the temperature histories and, thereby, the residual stresses in FSW. As a first step, the local problem solves the material stirring as well as the heat generation induced by the pin and shoulder rotation at the heat affected zone. The Arbitrary Lagrangian Eulerian (ALE) formulation is adopted to deal with the rotation of complex pin shapes. A thermo-rigid-viscoplastic constitutive law is employed to characterize the viscous flow of the material, driven by the high-strain rates induced by the FSW process. A mixed temperature–velocity–pressure finite element technology is used to deal with the isochoric nature of the strains. The output of this local analysis is the heat generated either by plastic dissipation or by friction, and it is used as the power input for the welding analysis at structural (global) level. The global problem is tackled within the Lagrangian framework together with a thermo-elasto-viscoplastic constitutive model. In addition, in this case, the mixed temperature–displacement–pressure format is introduced to deal with the deviatoric nature of the plastic strains. The outcomes of this analysis are the distortions and the residual stresses after welding. The material used in this work is stainless steel 304 L; however, the methodology presented is applicable to a wide range of materials. The proposed numerical strategy is validated by the experimental evidence.
Abstract
This work describes the local–global strategy proposed for the computation of residual stresses in friction stir welding (FSW) processes. A coupling strategy between [...]
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Numerical modeling of the electron beam welding and its experimental validation
M. Chiumenti, M. Cervera, N. Dialami, B. Wu, L. Jinwei, C. Agelet de Saracibar

Finite Elements in Analysis and Design (2016). (preprint) Vol. 121, pp. 118–133

Abstract
Electron Beam Welding (EBW) is a highly efficient and precise welding method increasingly used within the manufacturing chain and of growing importance in different industrial environments such as the aeronautical and aerospace sectors. This is because, compared to other welding processes, EBW induces lower distortions and residual stresses due to the lower and more focused heat input along the welding line. This work describes the formulation adopted for the numerical simulation of the EBW process as well as the experimental work carried out to calibrate and validate it. The numerical simulation of EBW involves the interaction of thermal, mechanical and metallurgical phenomena. For this reason, in this work the numerical framework couples the heat transfer process to the stress analysis to maximize accuracy. An in-house multi-physics FE software is used to deal with the numerical simulation. The definition of an ad hoc moving heat source is proposed to simulate the EB power surface distribution and the corresponding absorption within the work-piece thickness. Both heat conduction and heat radiation models are considered to dissipate the heat through the boundaries of the component. The material behavior is characterized by an apropos thermo-elasto-viscoplastic constitutive model. Titanium-alloy Ti6A14V is the target material of this work. From the experimental side, the EB welding machine, the vacuum chamber characteristics and the corresponding operative setting are detailed. Finally, the available facilities to record the temperature evolution at different thermo-couple locations as well as to measure both distortions and residual stresses are described. Numerical results are compared with the experimental evidence.
Abstract
Electron Beam Welding (EBW) is a highly efficient and precise welding method increasingly used within the manufacturing chain and of growing importance in different industrial [...]
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Continuum FE models for the analysis of a representative bay in Mallorca Cathedral
P. Roca, M. Cervera, L. Pelà

Engineering Structures (2013). (preprint) Vol. 46, pp. 653-670

Abstract
From the theoretical point of view, systems composed by masonry arches or vaults would require, during construction, the simultaneous activation of all structural elements in order to reach the optimum balance of thrusts. This is not obviously the case of complex ancient masonry constructions, whose long and gradual building process may have contributed to their deformed condition and even to damage.In this paper, the possible influence of the construction process as well as that of later long-term deformation on the final condition of the building is investigated in the case of a complex and large historical structure, namely Mallorca Cathedral. A FE code has been specifically developed for the present study. The code is able to account for construction processes through sequential-evolutionary analyses, with the description of masonry mechanical damage and long-term deformation. The representative bay of the cathedral is analyzed taking into account different construction phases, as emerged from historical research. The response of such substructure to transverse earthquake equivalent forces is then investigated. In this case, the damage model is improved with a local crack-tracking algorithm. This numerical strategy models the tensile damage as distinct cracks, leading to a better prediction of realistic collapsing mechanisms.
Abstract
From the theoretical point of view, systems composed by masonry arches or vaults would require, during construction, the simultaneous activation of all structural elements [...]
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Structural Analysis of Masonry Historical Constructions. Classical and Advanced Approaches
P. Roca, M. Cervera, G. Gariup, L. Pelà

Archives of Comp. Meths. Engng. (2010). 17 (3), pp. 299-325

Abstract
A review of methods applicable to the study of masonry historical construction, encompassing both classical and advanced ones, is presented. Firstly, the paper offers a discussion on the main challenges posed by historical structures and the desirable conditions that approaches oriented to the modeling and analysis of this type of structures should accomplish. Secondly, the main available methods which are actually used for study masonry historical structures are referred to and discussed. The main available strategies, including limit analysis, simplified methods, FEM macro- or micro-modeling and discrete element methods (DEM) are considered with regard to their realism, computer efficiency, data availability and real applicability to large structures. A set of final considerations are offered on the real possibility of carrying out realistic analysis of complex historic masonry structures. In spite of the modern developments, the study of historical buildings is still facing significant difficulties linked to computational effort, possibility of input data acquisition and limited realism of methods.
Abstract
A review of methods applicable to the study of masonry historical construction, encompassing both classical and advanced ones, is presented. Firstly, the paper offers a discussion [...]
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Explicit mixed strain-displacement finite elements for compressible and quasi-incompressible elasticity and plasticity
M. Cervera, N. Lafontaine, R. Rossi, M. Chiumenti

Computational Mechanics (2016). (Preprint) Vol. 58 (3), pp. 511–532

Abstract
This paper presents an explicit mixed finite element formulation to address compressible and quasi-incompressible problems in elasticity and plasticity. This implies that the numerical solution only involves diagonal systems of equations. The formulation uses independent and equal interpolation of displacements and strains, stabilized by variational subscales. A displacement sub-scale is introduced in order to stabilize the mean-stress field. Compared to the standard irreducible formulation, the proposed mixed formulation yields improved strain and stress fields. The paper investigates the effect of this enhancement on the accuracy in problems involving strain softening and localization leading to failure, using low order finite elements with linear continuous strain and displacement fields (P1P1 triangles in 2D and tetrahedra in 3D) in conjunction with associative frictional Mohr–Coulomb and Drucker–Prager plastic models. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to analytical solutions for plane stress and plane strain situations. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.
Abstract
This paper presents an explicit mixed finite element formulation to address compressible and quasi-incompressible problems in elasticity and plasticity. This implies that [...]
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High-fidelity prediction of crack formation in 2D and 3D pullout tests
L. Benedetti, M. Cervera, M. Chiumenti

Computers and Structures (2016). (preprint) Vol. 172, pp. 93–109

Abstract
This paper presents the 2D and 3D numerical analysis of pullout tests on steel anchorages in concrete blocks using standard and mixed finite elements. A novel (stabilized) mixed formulation in the variables of total strain ε and displacements u is introduced to overcome the intrinsic deficiencies of the standard displacement-based one in the context of localization of strains, such as mesh dependency. The quasi-brittle behavior of concrete is described through an elastoplastic constitutive law with a local Rankine yielding criterion. The proposed formulation is shown to be a reliable and accurate tool, sensitive to the physical parameters of the pullout tests, but objective with respect to the adopted FE mesh. Furthermore, the mixed ε/u finite element is able to capture the correct failure mechanism with relatively coarse discretizations. At the same time, the spurious behavior of the standard formulation is not alleviated by mesh-refinement.
Abstract
This paper presents the 2D and 3D numerical analysis of pullout tests on steel anchorages in concrete blocks using standard and mixed finite elements. A novel (stabilized) [...]
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Analysis of the effect of provisional ties in the construction and current deformation of Mallorca cathedral
L. Pelà, J. Bourgeois, P. Roca, M. Cervera, M. Chiumenti

International Journal of Architectural Heritage (2016). (preprint) Vol. 10 (4), pp. 418–437

Abstract
This article presents the analysis of the structure of Mallorca Cathedral taking into account the influence on the structural behavior of auxiliary iron ties used during the construction process. Recent studies (Roca et al. 2012, 2013) presented some hypotheses about the construction process of the cathedral. This article complements the previous results by considering the use of auxiliary ties as temporary stabilizing device during the construction. Evidence of the use of ties during the construction has been recognized after a comprehensive survey. The study of the role of such ties and the effect of their later removal are studied by a FE analysis carried out on a representative bay of the structure. The study includes a time-dependent FE analysis after the removal of the ties to assess the long-term structural behavior. The results of the numerical analysis are compared with the deformation trends identified by means of a recent monitoring campaign.
Abstract
This article presents the analysis of the structure of Mallorca Cathedral taking into account the influence on the structural behavior of auxiliary iron ties used during the [...]
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A thermodynamically consistent plastic-damage framework for localized failure in quasi-brittle solids: Material model and strain localization analysis
J. Wu, M. Cervera

Int. J. Solids and Structures (2016). (preprint) Vol. 88–89, pp. 227–247

Abstract
Aiming for the modeling of localized failure in quasi-brittle solids, this paper addresses a thermodynamically consistent plastic-damage framework and the corresponding strain localization analysis. A unified elastoplastic damage model is first presented based on two alternative kinematic decompositions assuming infinitesimal deformations, with the evolution laws of involved internal variables characterized by a dissipative flow tensor. For the strong (or regularized) discontinuity to form in such inelastic quasi-brittle solids and to evolve eventually into a fully softened one, a novel strain localization analysis is then suggested. A kinematic constraint more demanding than the classical discontinuous bifurcation condition is derived by accounting for the traction continuity and the loading/unloading states consistent with the kinematics of a strong (or regularized) discontinuity. More specifically, the strain jumps characterized by Maxwell’s kinematic condition have to be completely inelastic (energy dissipative). Reproduction of this kinematics implies vanishing of the aforesaid dissipative flow tensorial components in the directions orthogonal to the discontinuity orientation. This property allows naturally developing a localized plastic-damage model for the discontinuity (band), with its orientation and the traction-based failure criterion consistently determined a posteriori from the given stress-based counterpart. The general results are then particularized to the 2D conditions of plane stress and plane strain. It is found that in the case of plane stress, strain localization into a strong (or regularized) discontinuity can occur at the onset of strain softening. Contrariwise, owing to an extra kinematic constraint, in the condition of plane strain some continuous inelastic deformations and substantial re-orientation of principal strain directions in general have to take place in the softening regime prior to strain localization. The classical Rankine, Mohr–Coulomb, von Mises (J2) and Drucker–Prager criteria are analyzed as illustrative examples. In particular, both the closed-form solutions for the discontinuity angles validated by numerical simulations and the corresponding traction-based failure criteria are obtained.
Abstract
Aiming for the modeling of localized failure in quasi-brittle solids, this paper addresses a thermodynamically consistent plastic-damage framework and the corresponding strain [...]
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Challenges in thermo-mechanical analysis of Friction Stir Welding processes
N. Dialami, M. Chiumenti, M. Cervera, C. Agelet de Saracibar

Archives of Comp. Meths. Engng. (2017). (preprint) Vol. 24 (1), pp. 198-225

Abstract
This paper deals with the numerical simulation of friction stir welding (FSW) processes. FSW techniques are used in many industrial applications and particularly in the aeronautic and aerospace industries, where the quality of the joining is of essential importance. The analysis is focused either at global level, considering the full component to be jointed, or locally, studying more in detail the heat affected zone (HAZ). The analysis at global (structural component) level is performed defining the problem in the Lagrangian setting while, at local level, an apropos kinematic framework which makes use of an efficient combination of Lagrangian (pin), Eulerian (metal sheet) and ALE (stirring zone) descriptions for the different computational sub-domains is introduced for the numerical modeling. As a result, the analysis can deal with complex (non-cylindrical) pin-shapes and the extremely large deformation of the material at the HAZ without requiring any remeshing or remapping tools. A fully coupled thermo-mechanical framework is proposed for the computational modeling of the FSW processes proposed both at local and global level. A staggered algorithm based on an isothermal fractional step method is introduced. To account for the isochoric behavior of the material when the temperature range is close to the melting point or due to the predominant deviatoric deformations induced by the visco-plastic response, a mixed finite element technology is introduced. The Variational Multi Scale method is used to circumvent the LBB stability condition allowing the use of linear/linear P1/P1 interpolations for displacement (or velocity, ALE/Eulerian formulation) and pressure fields, respectively. The same stabilization strategy is adopted to tackle the instabilities of the temperature field, inherent characteristic of convective dominated problems (thermal analysis in ALE/Eulerian kinematic framework). At global level, the material behavior is characterized by a thermo–elasto–viscoplastic constitutive model. The analysis at local level is characterized by a rigid thermo–visco-plastic constitutive model. Different thermally coupled (non-Newtonian) fluid-like models as Norton–Hoff, Carreau or Sheppard–Wright, among others are tested. To better understand the material flow pattern in the stirring zone, a (Lagrangian based) particle tracing is carried out while post-processing FSW results. A coupling strategy between the analysis of the process zone nearby the pin-tool (local level analysis) and the simulation carried out for the entire structure to be welded (global level analysis) is implemented to accurately predict the temperature histories and, thereby, the residual stresses in FSW.
Abstract
This paper deals with the numerical simulation of friction stir welding (FSW) processes. FSW techniques are used in many industrial applications and particularly in the aeronautic [...]
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Modelling of Bingham and Herschel–Bulkley flows with mixed P1/P1 finite elements stabilized with orthogonal subgrid scale
E. Moreno, A. Larese, M. Cervera

Journal of Non-Newtonian Fluid Mechanics (2016). (preprint) Vol. 228, pp. 1-16

Abstract
This paper presents the application of a stabilized mixed pressure/velocity finite element formulation to the solution of viscoplastic non-Newtonian flows. Both Bingham and Herschel–Bulkley models are considered. The detail of the discretization procedure is presented and the Orthogonal Subgrid Scale (OSS) stabilization technique is introduced to allow for the use of equal order interpolations in a consistent way. The matrix form of the problem is given. A series of examples is presented to assess the accuracy of the method by comparison with the results obtained by other authors. The extrusion in a Bingham fluid and the movement of a moving and rotating cylinder are analyzed in detail. The evolution of the streamlines, the yielded and unyielded regions, the drag and lift forces are presented. These benchmark examples show the capacity of the mixed OSS formulation to reproduce the behavior of a Bingham and Herschel–Bulkley flows with the required accuracy.
Abstract
This paper presents the application of a stabilized mixed pressure/velocity finite element formulation to the solution of viscoplastic non-Newtonian flows. Both Bingham and [...]
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3D numerical models of FSW processes with non-cylindrical pin
P. Bussetta, N. Dialami, M. Chiumenti, C. Agelet de Saracibar, M. Cervera, J. Ponthot

Advances in Materials and Processing Technologies (2016). (preprint) Vol. 1 (3-4), pp. 275-287

Abstract
Friction stir welding (FSW) process is a relatively recent welding process (patented in 1991). FSW is a solid-state joining process during which materials to be joined are not melted. During the FSW process, the behaviour of the material is at the interface between solid mechanics and fluid mechanics. In this paper, a 3D numerical model of the FSW process with a non-cylindrical tool based on a solid formulation is compared to another one based on a fluid formulation. Both models use advanced numerical techniques such as the arbitrary Lagrangian–Eulerian formulation, remeshing or the orthogonal sub-grid scale method. It is shown that these two formulations essentially deliver the same results.
Abstract
Friction stir welding (FSW) process is a relatively recent welding process (patented in 1991). FSW is a solid-state joining process during which materials to be joined are [...]
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A crack-tracking technique for localized cohesive-frictional damage
S. Saloustros, L. Pelà, M. Cervera

Engineering Fracture Mechanics (2015). (preprint) Vol. 150, pp. 96-114

Abstract
This paper extends the use of crack-tracking techniques within the smeared crack approach for the numerical simulation of cohesive–frictional damage on quasi-brittle materials. The mechanical behaviour is described by an isotropic damage model with a Mohr–Coulomb failure surface. The correct crack propagation among the two alternative fracture planes proposed by the Mohr–Coulomb theory is selected with the use of an energy criterion based on the total elastic strain energy. The simulation of three benchmark problems of mixed-mode fracture in concrete demonstrates that the proposed methodology can reproduce the material’s frictional characteristics, showing robustness, as well as mesh-size and mesh-bias independence.
Abstract
This paper extends the use of crack-tracking techniques within the smeared crack approach for the numerical simulation of cohesive–frictional damage on quasi-brittle [...]
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3D numerical models of FSW processes with non-cylindrical pin
P. Bussetta, N. Dialami, M. Chiumenti, C. Agelet de Saracibar, M. Cervera, R. Boman, J. Ponthot

Advanced Modeling and Simulation in Engineering Sciences (2015). (preprint) Vol. 2 (27), pp. 1-19

Abstract
Friction stir welding process is a relatively recent welding process (patented in 1991). FSW is a solid-state joining process during which materials to be joined are not melted. During the FSW process, the behaviour of the material is at the interface between solid mechanics and fluid mechanics. In this paper, a 3D numerical model of the FSW process with a non-cylindrical tool based on a solid formulation is compared to another one based on a fluid formulation. Both models use advanced numerical techniques such as the Arbitrary Lagrangian Eulerian formulation, remeshing or the Orthogonal Sub-Grid Scale method. It is shown that these two formulations essentially deliver the same results.
Abstract
Friction stir welding process is a relatively recent welding process (patented in 1991). FSW is a solid-state joining process during which materials to be joined are not melted. [...]
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On the equivalence between traction- and stress-based approaches for the modeling of localized failure in solids
J. Wu, M. Cervera

Journal of the Mechanics and Physics of Solids (2015). (preprint) Vol. 82, pp. 137-163

Abstract
This work investigates systematically traction- and stress-based approaches for the modeling of strong and regularized discontinuities induced by localized failure in solids. Two complementary methodologies, i.e., discontinuities localized in an elastic solid and strain localization of an inelastic softening solid, are addressed. In the former it is assumed a priori that the discontinuity forms with a continuous stress field and along the known orientation. A traction-based failure criterion is introduced to characterize the discontinuity and the orientation is determined from Mohr's maximization postulate. If the displacement jumps are retained as independent variables, the strong/regularized discontinuity approaches follow, requiring constitutive models for both the bulk and discontinuity. Elimination of the displacement jumps at the material point level results in the embedded/smeared discontinuity approaches in which an overall inelastic constitutive model fulfilling the static constraint suffices. The second methodology is then adopted to check whether the assumed strain localization can occur and identify its consequences on the resulting approaches. The kinematic constraint guaranteeing stress boundedness and continuity upon strain localization is established for general inelastic softening solids. Application to a unified stress-based elastoplastic damage model naturally yields all the ingredients of a localized model for the discontinuity (band), justifying the first methodology. Two dual but not necessarily equivalent approaches, i.e., the traction-based elastoplastic damage model and the stress-based projected discontinuity model, are identified. The former is equivalent to the embedded and smeared discontinuity approaches, whereas in the later the discontinuity orientation and associated failure criterion are determined consistently from the kinematic constraint rather than given a priori. The bi-directional connections and equivalence conditions between the traction- and stress-based approaches are classified. Closed-form results under plane stress condition are also given. A generic failure criterion of either elliptic, parabolic or hyperbolic type is analyzed in a unified manner, with the classical von Mises (J2), Drucker–Prager, Mohr–Coulomb and many other frequently employed criteria recovered as its particular cases.
Abstract
This work investigates systematically traction- and stress-based approaches for the modeling of strong and regularized discontinuities induced by localized failure in [...]
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On the conformity of strong, regularized, embedded and smeared discontinuity approaches for the modeling of localized failure in solids
M. Cervera, J. Wu

Int. J. Solids and Structures (2015). (preprint) Vol. 71 (1), pp. 19-38

Abstract
Once strain localization occurs in softening solids, inelastic loading behavior is restricted within a narrow band while the bulk unloads elastically. Accordingly, localized failure in solids can be approached by embedding or smearing a traction-based inelastic discontinuity (band) within an (equivalent) elastic matrix along a specific orientation. In this context, the conformity of the strong/regularized and embedded/smeared discontinuity approaches are investigated, regarding the strategies dealing with the kinematics and statics. On one hand, the traction continuity condition imposed in weak form results in the strong and regularized discontinuity approaches, with respect to the approximation of displacement and strain discontinuities. In addition to the elastic bulk, consistent plastic-damage cohesive models for the discontinuities are established. The conformity between the strong discontinuity approach and its regularized counterpart is shown through the fracture energy analysis. On the other hand, the traction continuity condition can also be enforced point-wisely in strong form so that the standard principle of virtual work applies. In this case, the static constraint resulting from traction continuity can be used to eliminate the kinematic variable associated with the discontinuity (band) at the material level. This strategy leads to embedded and smeared discontinuity models for the overall weakened solid which can also be cast into the elastoplastic degradation framework with a different kinematic decomposition. Being equivalent to the kinematic constraint guaranteeing stress continuity upon strain localization, Mohr’s maximization postulate is adopted for the determination of the discontinuity orientation. Closed-form results are presented in plane stress conditions, with the classical Rankine, Mohr–Coulomb, von Mises and Drucker–Prager criteria as illustrative examples. The orientation of the discontinuity (band) and the stress-based failure criteria consistent with the given traction-based counterparts are derived. Finally, a generic failure criterion of either elliptic, parabolic or hyperbolic type, appropriate for the modeling of mixed-mode failure, is analyzed in a unified manner. Furthermore, a novel method is proposed to calibrate the involved mesoscopic parameters from available macroscopic test data, which is then validated against Willam’s numerical test.
Abstract
Once strain localization occurs in softening solids, inelastic loading behavior is restricted within a narrow band while the bulk unloads elastically. Accordingly, localized [...]
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Material flow visualization in Friction Stir Welding via particle tracing
N. Dialami, M. Chiumenti, M. Cervera, C. Agelet de Saracibar, J. Ponthot

Int. J. of Material Forming (2015). (preprint) Vol. 8 (2), pp. 167-181

Abstract
This work deals with the modeling of the material flow in Friction Stir Welding (FSW) processes using particle tracing method. For the computation of particle trajectories, three accurate and computationally efficient integration methods are implemented within a FE model for FSW process: the Backward Euler with Sub-stepping (BES), the 4-th order Runge–Kutta (RK4) and the Back and Forth Error Compensation and Correction (BFECC) methods. Firstly, their performance is compared by solving the Zalesak’s disk benchmark. Later, the developed methodology is applied to some FSW problems providing a quantitative 2D and 3D view of the material transport in the process area. The material flow pattern is compared to the experimental evidence.
Abstract
This work deals with the modeling of the material flow in Friction Stir Welding (FSW) processes using particle tracing method. For the computation of particle trajectories, [...]
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Explicit mixed strain-displacement finite element for dynamic geometrically non-linear solid mechanics
N. Lafontaine, R. Rossi, M. Cervera, M. Chiumenti

Computational Mechanics (2015). (preprint) Vol. 55 (3), pp. 543-559

Abstract
Low-order finite elements face inherent limitations related to their poor convergence properties. Such difficulties typically manifest as mesh-dependent or excessively stiff behaviour when dealing with complex problems. A recent proposal to address such limitations is the adoption of mixed displacement-strain technologies which were shown to satisfactorily address both problems. Unfortunately, although appealing, the use of such element technology puts a large burden on the linear algebra, as the solution of larger linear systems is needed. In this paper, the use of an explicit time integration scheme for the solution of the mixed strain-displacement problem is explored as an alternative. An algorithm is devised to allow the effective time integration of the mixed problem. The developed method retains second order accuracy in time and is competitive in terms of computational cost with the standard irreducible formulation.
Abstract
Low-order finite elements face inherent limitations related to their poor convergence properties. Such difficulties typically manifest as mesh-dependent or excessively stiff [...]
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Stress-accurate Mixed FEM for soil failure under shallow foundations involving strain localization in plasticity
L. Benedetti, M. Cervera, M. Chiumenti

Computers and geotechnics (2015). (preprint) Vol. 64, pp. 32-47

Abstract
The development of slip lines, due to strain localization, is a common cause for failure of soil in many circumstances investigated in geotechnical engineering. Through the use of numerical methods – like finite elements – many practitioners are able to take into account complex geometrical and physical conditions in their analyses. However, when dealing with shear bands, standard finite elements display lack of precision, mesh dependency and locking. This paper introduces a (stabilized) mixed finite element formulation with continuous linear strain and displacement interpolations. Von Mises and Drucker–Prager local plasticity models with strain softening are considered as constitutive law. This innovative formulation succeeds in overcoming the limitations of the standard formulation and provides accurate results within the vicinity of the shear bands, specifically without suffering from mesh dependency. Finally, 2D and 3D numerical examples demonstrate the accuracy and robustness in the computation of localization bands, without the introduction of additional tracking techniques as usually required by other methods.
Abstract
The development of slip lines, due to strain localization, is a common cause for failure of soil in many circumstances investigated in geotechnical engineering. Through the [...]
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A localized mapped damage model for orthotropic materials
L. Pelà, M. Cervera, S. Oller, M. Chiumenti

Engineering Fracture Mechanics (2014). (preprint) Vol. 124-125, pp. 196-216

Abstract
This paper presents an implicit orthotropic model based on the Continuum Damage Mechanics isotropic models. A mapping relationship is established between the behaviour of the anisotropic material and that of an isotropic one. The proposed model is used to simulate the failure loci of common orthotropic materials, such as masonry, fibre-reinforced composites and wood. The damage model is combined with a crack-tracking technique to reproduce the propagation of localized cracks in the discrete FE problem. The proposed numerical model is used to simulate the mixed mode fracture in masonry members with different orientations of the brick layers.
Abstract
This paper presents an implicit orthotropic model based on the Continuum Damage Mechanics isotropic models. A mapping relationship is established between the behaviour of [...]
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Computational Modeling and Sub-Grid Scale Stabilization of Incompressibility and Convection in the Numerical Simulation of Friction Stir Welding Processes
C. Agelet de Saracibar, M. Chiumenti, M. Cervera, N. Dialami, A. Seret

Archives of Comp. Meths. Engng. (2014). (preprint) Vol. 21 (1), pp. 3-37

Abstract
This paper deals with the computational modeling and sub-grid scale stabilization of incompressibility and convection in the numerical simulation of the material flow around the probe tool in a friction stir welding (FSW) process. Within the paradigmatic framework of the multiscale stabilization methods, suitable pressure and convective derivative of the temperature sub-grid scale stabilized coupled thermomechanical formulations have been developed using an Eulerian description. Norton-Hoff and Sheppard-Wright thermo-rigid-viscoplastic constitutive material models have been considered. Constitutive equations for the sub-grid scale models have been proposed and an approximation of the sub-grid scale variables has been given. In particular, algebraic sub-grid scale (ASGS) and orthogonal sub-grid scale (OSGS) methods for mixed velocity, pressure and temperature P1/P1/P1 linear elements have been considered. Furthermore, it has been shown that well known classical stabilized formulations, such as the Galerkin least-squares (GLS) for incompressible (or quasi-incompressible) problems or the Streamline Upwind/Petrov-Galerkin (SUPG) method for convection dominant problems, can be recovered as particular cases of the multiscale stabilization framework considered. Using a product formula algorithm for the solution of the coupled thermomechanical problem, the resulting algebraic system of equations has been solved using a staggered procedure in which a mechanical problem, defined by the linear momentum balance equation, under quasi-static conditions, and the incompressibility equation, is solved first at constant temperature. Then a thermal problem, defined by the energy balance equation, is solved keeping constant the mechanical variables, i.e. velocity and pressure. The computational model has been implemented in an enhanced version of the finite element software COMET, developed by the authors at the International Center for Numerical Methods in Engineering (CIMNE). Two numerical examples have been considered. The first one deals with the numerical simulation of a coupled thermomechanical flow in a 2D rectangular domain. Steady-state and transient conditions have been considered. The goal of this numerical example has been the comparison between different sub-grid scale stabilization methods for the velocity and temperature equations. In particular, using a GLS stabilization method for the pressure equation, a comparison between SUPG and OSGS convective stabilization methods has been performed. Additionally, using a SUPG stabilization method for the temperature equation, a comparison between GLS and OSGS pressure stabilization methods has been done. The second example deals with the 3D numerical simulation of a representative FSW process. Numerical results obtained have been compared with experimental results available in the literature. A good agreement on the temperature distribution has been obtained and predicted peak temperatures compare well, both in value and position, with the experimental results available.
Abstract
This paper deals with the computational modeling and sub-grid scale stabilization of incompressibility and convection in the numerical simulation of the material flow around [...]
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Comparison of a Fluid and a Solid Approach for the Numerical Simulation of Friction Stir Welding with a Non‐Cylindrical Pin
P. Bussetta, N. Dialami, R. Boman, M. Chiumenti, C. Agelet de Saracibar, M. Cervera, J. Ponthot

Steel Research International (2014). (preprint) Vol. 85 (6), pp. 968-979

Abstract
Friction stir welding (FSW) process is a solid‐state joining process during which materials to be joined are not melted. As a consequence, the heat‐affected zone is smaller and the quality of the weld is better with respect to more classical welding processes. Because of extremely high strains in the neighborhood of the tool, classical numerical simulation techniques have to be extended in order to track the correct material deformations. The Arbitrary Lagrangian–Eulerian (ALE) formulation is used to preserve a good mesh quality throughout the computation. With this formulation, the mesh displacement is independent from the material displacement. Moreover, some advanced numerical techniques such as remeshing or a special computation of transition interface is needed to take into account non‐cylindrical tools. During the FSW process, the behavior of the material in the neighborhood of the tool is at the interface between solid mechanics and fluid mechanics. Consequently, a numerical model of the FSW process based on a solid formulation is compared to another one based on a fluid formulation. It is shown that these two formulations essentially deliver the same results in terms of pressures and temperatures.
Abstract
Friction stir welding (FSW) process is a solid‐state joining process during which materials to be joined are not melted. As a consequence, the heat‐affected zone is smaller [...]
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An apropos kinematic framework for the numerical modelling of Friction Stir Welding
N. Dialami, M. Chiumenti, M. Cervera, C. Agelet de Saracibar

Computers and Structures (2013). (prepint) Vol. 117, pp. 48-57.

Abstract
This paper describes features of a fully coupled thermo-mechanical model for Friction Stir Welding (FSW) simulation. An apropos kinematic setting for different zones of the computational domain is introduced and an efficient coupling strategy is proposed. Heat generation via viscous dissipation as well as frictional heating is considered. The results of the simulation using the proposed model are compared with the experimental evidence. The effect of slip and stick condition on non-circular pin shapes is analyzed. Simulation of material stirring is also carried out via particle tracing, providing insight of the material flow pattern in the vicinity of the pin.
Abstract
This paper describes features of a fully coupled thermo-mechanical model for Friction Stir Welding (FSW) simulation. An apropos kinematic setting for different zones of the [...]
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An orthotropic damage model for the analysis of masonry structures
L. Pelà, M. Cervera, P. Roca

Construction and Building Materials (2013). (preprint) Vol. 41, pp. 957-967.

Abstract
This paper presents a numerical model for nonlinear analysis of masonry structural elements based on Continuum Damage Mechanics. The material is described at the macro-level, i.e. it is modeled as a homogeneous orthotropic continuum. The orthotropic behavior is simulated by means of an original methodology, resulting from the concept of mapped tensors from the anisotropic field to an auxiliary workspace. The application of this idea to strain-based Continuum Damage Models is innovative and leads to several computational benefits. The suitability of the model for representing the behavior of different types of brickwork masonry is shown via the simulation of experimental tests.
Abstract
This paper presents a numerical model for nonlinear analysis of masonry structural elements based on Continuum Damage Mechanics. The material is described at the macro-level, [...]
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Viscoelasticity and damage model for creep behaviour of historical masonry structures
P. Roca, M. Cervera, L. Pelà, R. Clemente, M. Chiumenti

The Open Civil Engineering Journal (2012). Vol. 6 (Suppl. 1-M7), pp. 188-199.

Abstract
This paper presents a continuum model for the simulation of the viscous effects and the long-term damage accumulation in masonry structures. The rheological model is based on a generalized Maxwell chain representation with a constitutive law utilizing a limited number of internal variables. Thanks to its computational efficiency, this approach is suitable for the analysis of large and complex structures. In the paper, the viscous and damage models are presented and their coupling is discussed. The FE simulation of the construction process of the representative bay of Mallorca Cathedral is presented, together with the analysis of the long-term effects. The parameters of the model are tentatively calibrated on the basis of the time-dependent viscous deformations detected during the cathedral monitoring.
Abstract
This paper presents a continuum model for the simulation of the viscous effects and the long-term damage accumulation in masonry structures. The rheological model is based [...]
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A crack-tracking technique for localized damage in quasi-brittle materials
M. Cervera, L. Pelà, R. Clemente, P. Roca

Engineering Fracture Mechanics (2010). Vol. 77 (13), pp. 2431-2450.

Abstract
This work presents a procedure to simulate the growth and propagation of localized tensile cracks on quasi-brittle materials. The so-called smeared damage approach, which consists in standard finite elements and local nonlinear constitutive laws, is recovered and improved in order to represent crack localization and avoid spurious mesh-bias dependence in the discrete problem. This is achieved by means of the implementation of a local crack-tracking algorithm which can reproduce individual (discrete) cracks and ensure objectivity of the finite element problem solution. The performance of the localized damage model is stressed by means of the analyses of structural case-studies. Compared to the Smeared Crack Approach in its original form, the presented procedure shows clearly a better capacity to predict realistic collapse mechanisms. The proposed tracking technique is relatively inexpensive.
Abstract
This work presents a procedure to simulate the growth and propagation of localized tensile cracks on quasi-brittle materials. The so-called smeared damage approach, which [...]
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Size effect and localization in J2 plasticity
M. Cervera, M. Chiumenti

Int. J. Solids and Structures (2009). Vol. 46 (17), pp. 3301-3312.

Abstract
This paper studies the phenomenon of structural size effect and strain localization in J2 plasticity. Size effect is here understood as the change in the response of a given structure when the spatial dimensions are scaled up or down while the geometry and other relevant properties of the structure are preserved. The work exploits the advantages of the mixed displacement–pressure formulation in incompressible or quasi-incompressible situations. Elasto-J2-plastic constitutive behaviour with regularized softening is considered. Stability issues are discussed to ensure existence and uniqueness of the solution of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is able to solve a wide range of structural scales, including real life engineering applications. The results obtained do not suffer from spurious mesh dependence. Furthermore, the formulation includes the classical theories of perfect plasticity and linear fracture mechanics as limit cases.
Abstract
This paper studies the phenomenon of structural size effect and strain localization in J2 plasticity. Size effect is here understood as the change in the response of a given [...]
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On the Numerical modeling of the thermomechanical contact for metal casting analysis
M. Chiumenti, C. Agelet de Saracibar, M. Cervera

J. Heat Transfer (2008). Vol. 130 (6), 10 pp.

Abstract
The paper shows the intrinsic difficulties found in the numerical simulation of industrial casting processes using finite element (FE) analysis. Up until now, uncoupled pure thermal simulations have been mostly considered to model solidification and cooling phenomena. However, a fully coupled thermomechanical analysis provides a more complete insight of the casting process and the final outcome regarding the quality of the part. In this type of analysis, the thermomechanical model used plays a role of paramount importance, as the problem is coupled both ways through contact between part and mould. The paper presents the full statement of the problem regarding contact, and it considers the difficulties associated with FE mesh generation and time integration strategy. It also reviews soft and hard algorithms for mechanical contact presenting some new alternatives. Evaluation of coefficients used for thermal contact is also discussed, and a new proposal is presented. Finally, some numerical applications are presented to assess the performance of the proposed strategies both in benchmark and industrial problems.
Abstract
The paper shows the intrinsic difficulties found in the numerical simulation of industrial casting processes using finite element (FE) analysis. Up until now, uncoupled pure [...]
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Current Developments on the Coupled Thermomechanical Computational Modeling of Metal Casting Processes
C. Agelet de Saracibar, M. Chiumenti, M. Cervera

Computer Methods in Material Science (2006). Vol. 6 (1-2), pp. 15-25

Abstract
In this paper, current developments on the coupled thermomechanical computational simulation of metal casting processes are presented A thermodynamically consistent constitutive material model is derived from a thermoviscoplastic free energy function. A continuous transition between the initial fluid-like and the final solid-like is modeled by considering a J2 thermoviscoplastic model. Thus, an thermoelastoviscoplastic model, suitable for the solid-like phase, degenerates into a pure thermoviscous model, suitable for the liquid-like phase, according to the evolution of the solid fraction function. A thermomechanical contact model, taking into account the insulated effects of the air-gap due to thermal shrinkage of the part during solidification and cooling, is introduced. A fractional step method, arising from an operator split of the governing differential equations, is considered to solve the coupled problem using a staggered scheme. Within a finite element setting, using low-order interpolation elements, a multiscale stabilization technique is introduced as a convenient framework to overcome the Babuska-Brezzi condition and avoid volumetric locking and pressure instabilities arising in incompressible or quasi-incompressible problems. Computational simulation of industrial castings show the good performance of the model.
Abstract
In this paper, current developments on the coupled thermomechanical computational simulation of metal casting processes are presented A thermodynamically consistent constitutive [...]
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Smeared crack approach: back to the original track
M. Cervera, M. Chiumenti

Int. J. Numer. Anal. Meth. Geomech. (2006). Vol. 30 (12), pp. 1173-1199.

Abstract
This paper briefly reviews the formulations used over the last 40 years for the solution of problems involving tensile cracking, with both the discrete and the smeared crack approaches. The paper focuses on the smeared approach, identifying as its main drawbacks the observed mesh‐size and mesh‐bias spurious dependence when the method is applied ‘straightly’. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and the strong discontinuity (discrete cracks) approaches are analysed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure stability of the solution, attaining the necessary convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious mesh‐size or mesh‐bias dependence, comparing very favourably with those obtained with other fracture and continuum mechanics approaches.
Abstract
This paper briefly reviews the formulations used over the last 40 years for the solution of problems involving tensile cracking, with both the discrete and the smeared crack [...]
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Modeling material failure in concrete structures under cyclic actions
R. Faria, M. Cervera, J. Oliver

Journal of Structural Engineering (2004). 130 (12), pp. 1997-2005.

Abstract
A constitutive model devised for the analysis of concrete structures, and suitable for generic two- or three-dimensional applications, is presented and validated. For plain concrete a tension-compression distinguishing stress split is performed, and two scalar damage variables account for the degradation induced by the tensile and compressive stress components. As outcomes the model reproduces the stiffness recovery upon load reversal, and it captures the strength enhancement under multiaxial compression. Besides, the simple formulation as well as the extremely reduced number of parameters involved in the concrete model makes it quite suitable for the analysis of real structures, and constitutes a useful design tool. As regards to the nonlinear performance of the steel reinforcement, the explicit Giuffrè–Menegotto–Pinto model is adopted. Efficiency of the global model is illustrated via two seismic applications: one concerning an arch dam, and the other a six-floor reinforced concrete wall. The latter application is presented for validation purposes.
Abstract
A constitutive model devised for the analysis of concrete structures, and suitable for generic two- or three-dimensional applications, is presented and validated. For plain [...]
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A stabilized formulation for incompressible plasticity using linear triangles and tetrahedra
M. Chiumenti, Q. Valverde, C. Agelet de Saracibar, M. Cervera

International Journal of Plasticity (2004). 20 (8-9), pp. 1487-1504

Abstract
In this paper, a stabilized finite element method to deal with incompressibility in solid mechanics is presented. Both elastic and J2-plastic constitutive behavior have been considered. A mixed formulation involving pressure and displacement fields is used and a continuous linear interpolation is considered for both fields. To circumvent the Babuška–Brezzi condition a stabilization technique based on the orthogonal sub-scale method is introduced. The main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements, which are easy to generate for real industrial applications. Results are compared with standard Galerkin and Q1P0 mixed formulations in either elastic or elasto-plastic incompressible problems.
Abstract
In this paper, a stabilized finite element method to deal with incompressibility in solid mechanics is presented. Both elastic and J2-plastic constitutive behavior have been [...]
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Softening, localization and stabilization: capture of discontinuous solutions in J2 plasticity
M. Cervera, M. Chiumenti, C. Agelet de Saracibar

Int. J. Numer. Anal. Meth. Geomech. (2004). 28 (5), pp. 373-393.

Abstract
This paper exploits the concept of stabilization techniques to improve the behaviour of mixed linear/linear simplicial elements (triangles and tetrahedra) in incompressible or nearly incompressible situations. Elasto‐J2‐plastic constitutive behaviour has been considered with linear and exponential softening. Two different stabilization methods are used to attain global stability of the corresponding discrete finite element formulation. Implementation and computational aspects are also discussed, showing that a robust application of the proposed formulation is feasible. Numerical examples show that the formulation derived is free of volumetric locking and spurious oscillations of the pressure. The results obtained do not suffer from spurious mesh‐size or mesh‐bias dependence, comparing very favourably with those obtained with the standard, non‐stabilized, approaches.
Abstract
This paper exploits the concept of stabilization techniques to improve the behaviour of mixed linear/linear simplicial elements (triangles and tetrahedra) in incompressible [...]
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Numerical modelling of concrete curing, regarding hydration and temperature phenomena
M. Cervera, R. Faria, T. Prato, J. Oliver

Computers and Structures (2002). Vol. 80 (18–19), pp. 1511-1521

Abstract
A numerical model that accounts for the hydration and aging phenomena during the early ages of concrete curing is presented in a format suitable for a finite element implementation. Assuming the percolation of water through the hydrates already formed as the dominant mechanism of cement hydration, the model adopts an internal variable called hydration degree, whose evolution law is easily calibrated and allows an accurate prediction of the hydration heat production. Compressive strength evolution is related to the aging degree, a concept that accounts for the influences of the hydration and curing temperature on the final mechanical properties of concrete. The model capabilities are illustrated by means of a wide set of experimental tests involving ordinary and high performance concretes, and through the simulation of the concrete curing on a viaduct deck of the Öresund Link.
Abstract
A numerical model that accounts for the hydration and aging phenomena during the early ages of concrete curing is presented in a format suitable for a finite element implementation. [...]
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On the constitutive modeling of coupled thermomechanical phase-change problems
C. Agelet de Saracibar, M. Cervera, M. Chiumenti

International Journal of Plasticity (2001). 17 (12), pp. 1565-1622.

Abstract
This paper deals with a thermodynamically consistent numerical formulation for coupled thermoplastic problems including phase-change phenomena and frictional contact. The final goal is to get an accurate, efficient and robust numerical model, able for the numerical simulation of industrial solidification processes. Some of the current issues addressed in the paper are the following. A fractional step method arising from an operator split of the governing differential equations has been used to solve the nonlinear coupled system of equations, leading to a staggered product formula solution algorithm. Nonlinear stability issues are discussed and isentropic and isothermal operator splits are formulated. Within the isentropic split, a strong operator split design constraint is introduced, by requiring that the elastic and plastic entropy, as well as the phase-change induced elastic entropy due to the latent heat, remain fixed in the mechanical problem. The formulation of the model has been consistently derived within a thermodynamic framework. All the material properties have been considered to be temperature dependent. The constitutive behavior has been defined by a thermoviscous/elastoplastic free energy function, including a thermal multiphase change contribution. Plastic response has been modeled by a J2 temperature dependent model, including plastic hardening and thermal softening. The constitutive model proposed accounts for a continuous transition between the initial liquid state, the intermediate mushy state and the final solid state taking place in a solidification process. In particular, a pure viscous deviatoric model has been used at the initial fluid-like state. A thermomecanical contact model, including a frictional hardening and temperature dependent coupled potential, is derived within a fully consistent thermodinamical theory. The numerical model has been implemented into the computational finite element code COMET developed by the authors. Numerical simulations of solidification processes show the good performance of the computational model developed.
Abstract
This paper deals with a thermodynamically consistent numerical formulation for coupled thermoplastic problems including phase-change phenomena and frictional contact. The [...]
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Simulation of Construction of RCC Dams. II: Stress and Damage
M. Cervera, T. Prato, J. Oliver

Journal of Structural Engineering (2000). 126 (9), pp. 1062-1068

Abstract
The increasing number of roller compacted concrete (RCC) dams being built around the world demands accurate methodologies for the realistic short- and long-term evaluations of the risk of thermally induced cracking in these constructions. In this work a numerical procedure for the simulation of the construction process of RCC dams is presented. It takes into account the more relevant features of the behavior of concrete at early ages, such as hydration, aging, creep, and damage. A 2D model of the Urugua-;aaı RCC Dam, built in Argentina, is used to perform the corresponding analyses. In this second part of the paper, the mechanical aspects of the simulation are presented; long-term effects are included by incorporating a creep model that naturally accounts for the aging effects, and the risk of tensile damage is also considered. The methodology determines the stress field inside the dam at any time during the construction and in the following years. Results for the reference case assess the suitability of the adopted design. This is compared to alternative studies considering different construction schedules to conclude that for these cases changes should be introduced in the dam design.
Abstract
The increasing number of roller compacted concrete (RCC) dams being built around the world demands accurate methodologies for the realistic short- and long-term evaluations [...]
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Simulation of Construction of RCC Dams. I: Temperature and Aging
M. Cervera, J. Oliver, T. Prato

Journal of Structural Engineering (2000). 126 (9), pp. 1053-1060

Abstract
The increasing number of roller compacted concrete (RCC) dams being built around the world demands accurate methodologies for the realistic short- and long-term evaluations of the risk of thermally induced cracking in these constructions. In this work a numerical procedure for the simulation of the construction process of RCC dams is presented. It takes into account the more relevant features of the behavior of concrete at early ages, such as hydration, aging, creep, and damage. A 2D model of the Urugua-í RCC Dam, built in Argentina, is used to perform the corresponding analyses. In this first part only the thermochemical aspects of the simulation of the construction process are presented. The temperature distribution and evolution inside the dam are obtained before and after the completion of the dam. The evolution of the compressive and tensile strengths and elastic moduli and their final distribution inside the dam can also be predicted. Results from 2D and simplified vertical 1D models are compared to assess the validity of the latter, and several parametric studies are carried out. The simulation and discussion of the mechanical aspects of the construction process are relegated to a companion paper that follows.
Abstract
The increasing number of roller compacted concrete (RCC) dams being built around the world demands accurate methodologies for the realistic short- and long-term evaluations [...]
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Thermo-Chemo-Mechanical Model for Concrete. II: Damage and Creep
M. Cervera, J. Oliver, T. Prato

Journal of Engineering Mechanics (1999). Vol. 125 (9), pp. 1028-1038

Abstract
In this work a coupled thermo-chemo-mechanical model for the behavior of concrete at early ages is proposed. This paper presents the formulation and assessment of the mechanical aspects of the model. Short- and long-term mechanical behaviors are modeled via a viscoelastic damage model that accounts for the aging effects. The short-term model is based on the framework of the continuum damage mechanics theory. A novel normalized format of the damage model is proposed, so that the phenomenon of aging is accounted for in a natural fashion. Long-term effects are included by incorporating a creep model inspired in the microprestress-solidification theory.
Abstract
In this work a coupled thermo-chemo-mechanical model for the behavior of concrete at early ages is proposed. This paper presents the formulation and assessment of the mechanical [...]
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Thermo-chemo-mechanical model for concrete. I: Hydration and aging
M. Cervera, T. Prato, J. Oliver

Journal of Engineering Mechanics (1999). Vol. 125 (9), pp. 1018-1027

Abstract
In this work a coupled thermo-chemo-mechanical model for the behavior of concrete at early ages is proposed. The model allows simulation of the observed phenomena of hydration, aging, damage, and creep. It is formulated within an appropriate thermodynamic framework, from which the state equations are derived. In this first part, the formulation and assessment of the thermochemical aspects of the model are presented. It is based on the reactive porous media theory, and it can accurately predict the evolution in time of the hydration degree and the hydration heat production. The evolution of the compressive and tensile strengths and elastic moduli is related to the aging degree, a concept introduced to account for the effect of the curing temperature in the evolution of the mechanical properties. The short- and long-term mechanical behavior is modeled by means of a viscoelastic damage model that accounts for the aging effects. The formulation and assessment of the mechanical part of the model are relegated to a companion paper.
Abstract
In this work a coupled thermo-chemo-mechanical model for the behavior of concrete at early ages is proposed. The model allows simulation of the observed phenomena of hydration, [...]
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Strong discontinuities and continuum plasticity models: the strong discontinuity approach
M. Cervera, O. Manzoli, J. Oliver

International Journal of Plasticity (1999). Vol. 15 (3), pp. 319-351

Abstract
The paper presents the Strong Discontinuity Approach for the analysis and simulation of strong discontinuities in solids using continuum plasticity models. Kinematics of weak and strong discontinuities are discussed, and a regularized kinematic state of discontinuity is proposed as a mean to model the formation of a strong discontinuity as the collapsed state of a weak discontinuity (with a characteristic bandwidth) induced by a bifurcation of the stress–strain field, which propagates in the solid domain. The analysis of the conditions to induce the bifurcation provides a critical value for the bandwidth at the onset of the weak discontinuity and the direction of propagation. Then a variable bandwidth model is proposed to characterize the transition between the weak and strong discontinuity regimes. Several aspects related to the continuum and, their associated, discrete constitutive equations, the expended power in the formation of the discontinuity and relevant computational details related to the finite element simulations are also discussed. Finally, some representative numerical simulations are shown to illustrate the proposed approach.
Abstract
The paper presents the Strong Discontinuity Approach for the analysis and simulation of strong discontinuities in solids using continuum plasticity models. Kinematics [...]
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On the formulation of coupled thermoplastic problems with phase-change
C. Agelet de Saracibar, M. Cervera, M. Chiumenti

International Journal of Plasticity (1999). Vol. 15 (1), pp. 1-34

Abstract
This paper deals with a numerical formulation for coupled thermoplastic problems including phase-change phenomena. The final goal is to get an accurate, efficient and robust numerical model, allowing the numerical simulation of solidification processes in the metal casting industry. Some of the current issues addressed in the paper are the following. A fractional step method arising from an operator split of the governing differential equations has been used to solve the nonlinear coupled system of equations, leading to a staggered product formula solution algorithm. Nonlinear stability issues are discussed and isentropic and isothermal operator splits are formulated. Within the isentropic split, a strong operator split design constraint is introduced, by requiring that the elastic and plastic entropy, as well as the phase-change induced elastic entropy due to the latent heat, remain fixed in the mechanical problem. The formulation of the model has been consistently derived within a thermodynamic framework. The constitutive behavior has been defined by a thermoelastoplastic free energy function, including a thermal multiphase change contribution. Plastic response has been modeled by a J2 temperature dependent model, including plastic hardening and thermal softening. A brief summary of the thermomechanical frictional contact model is included. The numerical model has been implemented into the computational Finite Element code COMET developed by the authors. A numerical assessment of the isentropic and isothermal operator splits, regarding the nonlinear stability behavior, has been performed for weakly and strongly coupled thermomechanical problems. Numerical simulations of solidification processes show the performance of the computational model developed.
Abstract
This paper deals with a numerical formulation for coupled thermoplastic problems including phase-change phenomena. The final goal is to get an accurate, efficient and robust [...]
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Numerical prediction of temperature and density distributions in selective laser sintering processes
G. Bugeda, M. Cervera, G. Lombera

Rapid Prototyping Journal (1999). Vol. 5 (1), pp. 21-26

Abstract
A finite element model has been developed for the 3D simulation of the sintering of a single track during a selective laser sintering process (SLS). The model takes into account both the thermal and the sintering phenomena involved in the process. Owing to the continuous movement of the laser beam the model takes also into account the transient nature of the problem. This is transformed into a pseudo‐static one through a transformation of the coordinates system of the equations. Nevertheless, this transformation introduces a convective term into the heat equations that produces instabilities in the solution. These instabilities have been solved by using a stream upwind Petrov Galerkin (SUPG) strategy together with a shock capturing scheme. Finally, a fixed point strategy is used for the solution of the analysis. The model has been tested through the solution of some examples.
Abstract
A finite element model has been developed for the 3D simulation of the sintering of a single track during a selective laser sintering process (SLS). The model takes into account [...]
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A strain-based plastic viscous-damage model for massive concrete structures
R. Faria, M. Cervera, J. Oliver

Int. J. Solids and Structures (1998). Vol. 35 (14), pp. 1533-1558

Abstract
Within the framework of continuum damage mechanics, a new constitutive damage model for massive concrete is presented, mainly intended for the seismic analysis of gravity and arch dams. Consistent with thermodynamic requirements, a straindriven formalism is adopted, improving the algorithmic efficiency as much as required for the analysis of large scale problems to become feasible. Two scalar damage variables are introduced as internal variables, as well as a plastic-strain tensor. An extension to account for the concrete strain-rate dependency, suitable for seismic analysis, is presented at the end. The efficiency of numerical predictions from the constitutive model is illustrated through numerical applications and algorithmic implementation is also detailed.
Abstract
Within the framework of continuum damage mechanics, a new constitutive damage model for massive concrete is presented, mainly intended for the seismic analysis of gravity [...]
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A rate-dependent isotropic damage model for the seismic analysis of concrete dams
M. Cervera, O. Manzoli, J. Oliver

Engineering Computations (1996). Vol. 25 (9), pp. 987-1010.

Abstract
In this paper a rate‐dependent isotropic damage model developed for the numerical analysis of concrete dams subjected to seismic excitation is presented. The model is shown to incorporate two features essential for seismic analysis: stiffness degradation and stiffness recovery upon load reversals and strain‐rate sensitivity. The issue of mesh objectivity is addressed using the concept of the ‘characteristic length’ of the fracture zone, to show that both the softening modulus and the fluidity parameter must depend on it to provide consistent results as the computational mesh is refined. Some aspects of the numerical implementation of the model are also treated, to show that the model can be easily incorporated in any standard non‐linear finite element code. The application of the proposed model to the seismic analysis of a large gravity concrete dam shows that the structural response may vary significantly in terms of the development of damage. The inclusion of rate sensitivity is able to reproduce the experimental observation that the tensile peak strength of concrete can be increased up to 50 percent for the range of strain rates that appear in a structural safety analysis of a dam subjected to severe seismic actions.
Abstract
In this paper a rate‐dependent isotropic damage model developed for the numerical analysis of concrete dams subjected to seismic excitation is presented. The model is shown [...]
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On the computational efficiency and implementation of block-iterative algorithms for nonlinear coupled Problems
M. Cervera, R. Codina, M. Galindo

Engineering Computations (1996). Vol. 13 (6), pp. 4-30

Abstract
Outlines a general methodology for the solution of the system of algebraic equations arising from the discretization of the field equations governing coupled problems. Considers that this discrete problem is obtained from the finite element discretization in space and the finite difference discretization in time. Aims to preserve software modularity, to be able to use existing single field codes to solve more complex problems, and to exploit computer resources optimally, emulating parallel processing. To this end, deals with two well-known coupled problems of computational mechanics – the fluid-structure interaction problem and thermally-driven flows of incompressible fluids. Demonstrates the possibility of coupling the block-iterative loop with the nonlinearity of the problems through numerical experiments which suggest that even a mild nonlinearity drives the convergence rate of the complete iterative scheme, at least for the two problems considered here. Discusses the implementation of this alternative to the direct coupled solution, stating advantages and disadvantages. Explains also the need for online synchronized communication between the different codes used as is the description of the master code which will control the overall algorithm.
Abstract
Outlines a general methodology for the solution of the system of algebraic equations arising from the discretization of the field equations governing coupled problems. Considers [...]
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Seismic evaluation of concrete dams via continuum damage models
M. Cervera, R. Faria, J. Oliver

Earthquake Engineering Structural Dynamics (1995). Vol. 24 (9), pp. 1125-1245

Abstract
In this paper a general methodology for the analysis of large concrete dams subjected to seismic excitation is outlined. It is valid both for gravity dams (2D representation) and arch dams (3D representation). The method allows for non‐linear material behaviour of the dam, ‘transparent fictitious boundaries’ for dealing properly with in‐coming and out‐going seismic waves, and an efficient procedure to deal with dam‐soil‐fluid interaction. The mechanical behaviour of concrete is modelled using an isotropic damage model which allows for tension and compression damage, and exhibits stiffness recovery upon load reversals. Emphasis is placed in the treatment of fluid‐structure interaction, regarding both formulation and efficiency aspects. A gravity dam and an arch dam are analysed subjected to artificially generated earthquakes of different intensities, and the results are used to study the degree of (un)safety of the dams.
Abstract
In this paper a general methodology for the analysis of large concrete dams subjected to seismic excitation is outlined. It is valid both for gravity dams (2D representation) [...]
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Numerical Analysis of Dams with Extensive Cracking due to Concrete Hydration: Simulation of a Real Case
M. Cervera, M. Galindo, J. Oliver

Dam Engng. (1992). Vol. 3 (1), pp. 1-22.

Abstract
The paper presents the computational model developed to study an existing large gravity dam suffering from observed "pathological behavior" resulting concrete hydration. The combined effect of water intrusion and chemical and numerical studies. The present study was undertaken to simulate numerically the observed phenomenon and to predict future developments. Concrete is modelled using an isotropic continuum damage model including visco-elastic effects. The triggering of the volumetric expansion resulting from water intrusion is linked to the onset of damage at each a point, assuming that water enters dam mostly through the damaged areas. Transversal construction joints are modelled using smeared joints. Temperature and porewater pressure effects are included using assumed distributions based on available field data. Results are presented which match reasonably well with the available filed measurements.
Abstract
The paper presents the computational model developed to study an existing large gravity dam suffering from observed "pathological behavior" resulting concrete hydration. [...]
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Preconditioned conjugate gradient method for the non‐linear finite element analysis with particular reference to 3D reinforced concrete structures
M. Cervera, Y. Liu, E. Hinton

Engineering Computations (1986). Vol. 3 (3), pp.235-242

Abstract
A hierarchically preconditioned conjugate gradient (PCG) method for finite element analysis is presented. Its use is demonstrated for the difficult problem of the non‐linear analysis of 3D reinforced concrete structures. Examples highlight the dramatic savings in computer storage and more modest savings in solution times obtained using PCG especially for large problems.
Abstract
A hierarchically preconditioned conjugate gradient (PCG) method for finite element analysis is presented. Its use is demonstrated for the difficult problem of the non‐linear [...]
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Nonlinear analysis of reinforced concrete plate and shell structures using 20-noded isoparametric brick elements
M. Cervera, E. Hinton, O. Hassan

Computers and Structures (1987). Vol. 25 (6), pp. 845-869

Abstract
This paper describes an efficient and accurate, 3-D finite element model which may be adopted in the nonlinear analysis of reinforced concerete plate and shell structures. Benchmark tests are undertaken to check the computational model.
Abstract
This paper describes an efficient and accurate, 3-D finite element model which may be adopted in the nonlinear analysis of reinforced concerete plate and shell structures. [...]
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Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity
M. Cervera, M. Chiumenti, L. Benedetti, R. Codina

Comput. Methods Appl. Mech. Engrg., (2015). (preprint) Vol. 285, pp. 752-775

Abstract
This paper presents the application of a stabilized mixed strain/displacement finite element formulation for the solution of nonlinear solid mechanics problems involving compressible and incompressible plasticity. The variational multiscale stabilization introduced allows the use of equal order interpolations in a consistent way. Such formulation presents two advantages when compared to the standard, displacement based, irreducible formulation: (a) it provides enhanced rate of convergence for the strain (and stress) field and (b) it is able to deal with incompressible situations. The first advantage also applies to the comparison with the mixed pressure/displacement formulation. The paper investigates the effect of the improved strain and stress fields in problems involving strain softening and localization leading to failure, using low order finite elements with continuous strain and displacement fields (P1P1 triangles or tetrahedra and Q1Q1quadrilaterals, hexahedra, and triangular prisms) in conjunction with an associative frictional Drucker–Prager plastic model. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to a previously proposed pressure/displacement formulation. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.
Abstract
This paper presents the application of a stabilized mixed strain/displacement finite element formulation for the solution of nonlinear solid mechanics problems involving compressible [...]
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A mixed three-field FE formulation for stress accurate analysis including the incompressible limit
M. Chiumenti, M. Cervera, R. Codina

Comput. Methods Appl. Mech. Engrg., (2015). (preprint) Vol. 238, pp. 1095-1116

Abstract
In previous works, the authors have presented the stabilized mixed displacement/pressure formulation to deal with the incompressibility constraint. More recently, the authors have derived stable mixed stress/displacement formulations using linear/linear interpolations to enhance stress accuracy in both linear and non-linear problems. In both cases, the Variational Multi Scale (VMS) stabilization technique and, in particular, the Orthogonal Subgrid Scale (OSS) method allows the use of linear/linear interpolations for triangular and tetrahedral elements bypassing the strictness of the inf–sup condition on the choice of the interpolation spaces. These stabilization procedures lead to discrete problems which are fully stable, free of volumetric locking or stress oscillations. This work exploits the concept of mixed finite element methods to formulate stable displacement/stress/pressure finite elements aimed for the solution of nonlinear problems for both solid and fluid finite element (FE) analyses. The final goal is to design a finite element technology able to tackle simultaneously problems which may involve isochoric behavior (preserve the original volume) of the strain field together with high degree of accuracy of the stress field. These two features are crucial in nonlinear solid and fluid mechanics, as used in most numerical simulations of industrial manufacturing processes. Numerical benchmarks show that the results obtained compare very favorably with those obtained with the corresponding mixed displacement/pressure formulation.
Abstract
In previous works, the authors have presented the stabilized mixed displacement/pressure formulation to deal with the incompressibility constraint. More recently, [...]
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Numerical modeling of friction stir welding processes
M. Chiumenti, M. Cervera, C. Agelet de Saracibar, N. Dialami

Comput. Methods Appl. Mech. Engrg., (2013). (preprint) Vol. 254, pp. 353-369

Abstract
This work describes the formulation adopted for the numerical simulation of the friction stir welding (FSW) process. FSW is a solid-state joining process (the metal is not melted during the process) devised for applications where the original metallurgical characteristics must be retained. This process is primarily used on aluminum alloys, and most often on large pieces which cannot be easily heat treated to recover temper characteristics. Heat is either induced by the friction between the tool shoulder and the work pieces or generated by the mechanical mixing (stirring and forging) process without reaching the melting point (solid-state process). To simulate this kind of welding process, a fully coupled thermo-mechanical solution is adopted. A sliding mesh, rotating together with the pin (ALE formulation), is used to avoid the extremely large distortions of the mesh around the tool in the so called stirring zone while the rest of the mesh of the sheet is fixed (Eulerian formulation). The orthogonal subgrid scale (OSS) technique is used to stabilize the mixed velocity–pressure formulation adopted to solve the Stokes problem. This stabilized formulation can deal with the incompressible behavior of the material allowing for equal linear interpolation for both the velocity and the pressure fields. The material behavior is characterized either by Norton–Hoff or Sheppard–Wright rigid thermo-visco-plastic constitutive models. Both the frictional heating due to the contact interaction between the surface of the tool and the sheet, and the heat induced by the visco-plastic dissipation of the stirring material have been taken into account. Heat convection and heat radiation models are used to dissipate the heat through the boundaries. Both the streamline-upwind/Petrov–Galerkin (SUPG) formulation and the OSS stabilization technique have been implemented to stabilize the convective term in the balance of energy equation. The numerical simulations presented are intended to show the accuracy of the proposed methodology and its capability to study real FSW processes where a non-circular pin is often used.
Abstract
This work describes the formulation adopted for the numerical simulation of the friction stir welding (FSW) process. FSW is a solid-state joining process (the metal is not [...]
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Benchmarking on bifurcation and localization in J2 plasticity for plane stress and plane strain conditions
M. Cervera, M. Chiumenti, D. Di Capua

Comput. Methods Appl. Mech. Engrg., (2012). Vol. 241-244, pp. 206-224

Abstract
This paper studies the phenomenon of strain bifurcation and localization in J2plasticity under plane stress and plane strain conditions. Necessary conditions for the outcome of bifurcation, localization, stress boundedness and decohesion are analytically established. It is shown that the explicit consideration of these conditions allows for the determination of localization angles in certain situations of interest that can be used to conduct benchmark tests on finite element formulations. The relative merits of irreducible, (stabilized) mixed and (displacement and/or strain) enhanced formulations are discussed. Numerical examples show that the mixed displacement/pressure formulation is to be preferred to the standard irreducible schemes in order to predict correct failure mechanisms with localized patterns of plastic deformation. Mixed elements are shown to be practically free from mesh directional bias dependence.
Abstract
This paper studies the phenomenon of strain bifurcation and localization in J2plasticity under plane stress and plane strain conditions. Necessary conditions for the outcome [...]
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Continuum damage model for orthotropic materials: Application to masonry
L. Pelà, M. Cervera, P. Roca

Comput. Methods Appl. Mech. Engrg., (2011). Vol. 200 (9-12), pp. 917-930

Abstract
This paper contributes to the formulation of continuum damage models for orthotropic materials under plane stress conditions. Two stress transformation tensors, related to tensile and compressive stress states, respectively, are used to establish a one-to-one mapping relationship between the orthotropic behaviour and an auxiliary model. This allows the consideration of two individual damage criteria, according to different failure mechanisms, i.e. cracking and crushing. The constitutive model adopted in the mapped space makes use of two scalar variables which monitor the local damage under tension and compression, respectively. The model affords the simulation of orthotropic induced damage, while also accounting for unilateral effects, thanks to a stress tensor split into tensile and compressive contributions. The fundamentals of the method are presented together with the procedure utilized to adjust the model in order to study the mechanical behaviour of masonry material. The validation of the model is carried out by means of comparisons with experimental results on different types of orthotropic masonry at the material level.
Abstract
This paper contributes to the formulation of continuum damage models for orthotropic materials under plane stress conditions. Two stress transformation tensors, related to [...]
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Mixed stabilized finite element methods in nonlinear solid mechanics: Part II: Strain localization
M. Cervera, M. Chiumenti, R. Codina

Comput. Methods Appl. Mech. Engrg., (2010). Vol. 199 (37-40), pp. 2571-2589

Abstract
This paper deals with the question of strain localization associated with materials which exhibit softening due to tensile straining. A standard local isotropic Rankine damage model with strain-softening is used as exemplary constitutive model. Both the irreducible and mixed forms of the problem are examined and stability and solvability conditions are discussed. Lack of uniqueness and convergence difficulties related to the strong material nonlinearities involved are also treated. From this analysis, the issue of local discretization error in the pre-localization regime is deemed as the main difficulty to be overcome in the discrete problem. Focus is placed on low order finite elements with continuous strain and displacement fields (triangular P1P1 and quadrilateral Q1Q1), although the presented approach is very general. Numerical examples show that the resulting procedure is remarkably robust: it does not require the use of auxiliary tracking techniques and the results obtained do not suffer from spurious mesh-bias dependence.
Abstract
This paper deals with the question of strain localization associated with materials which exhibit softening due to tensile straining. A standard local isotropic Rankine damage [...]
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Mixed stabilized finite element methods in nonlinear solid mechanics: Part I: Formulation
M. Cervera, M. Chiumenti, R. Codina

Comput. Methods Appl. Mech. Engrg., (2010). Vol. 199 (37-40), pp. 2559-2570

Abstract
This paper exploits the concept of stabilized finite element methods to formulate stable mixed stress/displacement and strain/displacement finite elements for the solution of nonlinear solid mechanics problems. The different assumptions and approximations used to derive the methods are exposed. The proposed procedure is very general, applicable to 2D and 3D problems. Implementation and computational aspects are also discussed, showing that a robust application of the proposed formulation is feasible. Numerical examples show that the results obtained compare favorably with those obtained with the corresponding irreducible formulation.
Abstract
This paper exploits the concept of stabilized finite element methods to formulate stable mixed stress/displacement and strain/displacement finite elements for the solution [...]
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Finite element modeling of multi-pass welding and shaped metal deposition processes
M. Chiumenti, M. Cervera, A. Salmi, C. Agelet de Saracibar, N. Dialami, K. Matsui

Comput. Methods Appl. Mech. Engrg., (2010). Vol. 199 (37-40), pp. 2343-2359

Abstract
This paper describes the formulation adopted for the numerical simulation of the shaped metal deposition process (SMD) and the experimental work carried out at ITP Industry to calibrate and validate the proposed model. The SMD process is a novel manufacturing technology, similar to the multi-pass welding used for building features such as lugs and flanges on fabricated components (see Fig. 1a and b). A fully coupled thermo-mechanical solution is adopted including phase-change phenomena defined in terms of both latent heat release and shrinkage effects. Temperature evolution as well as residual stresses and distortions, due to the successive welding layers deposited, are accurately simulated coupling the heat transfer and the mechanical analysis. The material behavior is characterized by a thermo-elasto-viscoplastic constitutive model coupled with a metallurgical model. Nickel super-alloy 718 is the target material of this work. Both heat convection and heat radiation models are introduced to dissipate heat through the boundaries of the component. An in-house coupled FE software is used to deal with the numerical simulation and an ad-hoc activation methodology is formulated to simulate the deposition of the different layers of filler material. Difficulties and simplifying hypotheses are discussed. Thermo-mechanical results are presented in terms of both temperature evolution and distortions, and compared with the experimental data obtained at the SMD laboratory of ITP.
Abstract
This paper describes the formulation adopted for the numerical simulation of the shaped metal deposition process (SMD) and the experimental work carried out at ITP Industry [...]
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An orthotropic mesh corrected crack model
M. Cervera

Comput. Methods Appl. Mech. Engrg., (2008). Vol. 197 (17-18), 1603-1619

Abstract
This paper recovers the original spirit of the continuous crack approaches, where displacements jumps across the crack are smeared over the affected elements and the behaviour is established through a softening stress–(total) strain law, using standard finite element displacement interpolations and orthotropic localconstitutive models. The paper focuses on the problem of shear locking observed in the discrete problem when orthotropic models are used. The solution for this drawback is found in the form of a mesh corrected crack model where the structure of the inelastic strain tensor is linked to the geometry of the cracked element. The discrete model is formulated as a non-symmetric orthotropic local damage constitutive model, in which the softening modulus is regularized according to the material fracture energy and the element size. The resulting formulation is easily implemented in standard non-linear FE codes and suitable for engineering applications. Numerical examples show that the results obtained using this crack model do not suffer from dependence on the mesh directional alignment, comparing very favourably with those obtained using related standard isotropic or orthotropic damage models.
Abstract
This paper recovers the original spirit of the continuous crack approaches, where displacements jumps across the crack are smeared over the affected elements and the behaviour [...]
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Mesh objective tensile cracking via a local continuum damage model and a crack tracking technique
M. Cervera, M. Chiumenti

Comput. Methods Appl. Mech. Engrg., (2006). Vol. 196 (1-3), pp. 304-320

Abstract
This paper describes a procedure for the solution of problems involving tensile cracking using the so-called smeared crack approach, that is, standard finite elements with continuous displacement fields and a standard local constitutive model with strain-softening. An isotropic Rankine damage model is considered. The softening modulus is adjusted according to the material fracture energy and the element size. The resulting continuum and discrete mechanical problems are analyzed and the question of predicting correctly the direction of crack propagation is deemed as the main difficulty to be overcome in the discrete problem. It is proposed to use a crack tracking technique to attain the desired stability and convergence properties of the corresponding formulation. Numerical examples show that the resulting procedure is well-posed, stable and remarkably robust; the results obtained do not seem to suffer from spurious mesh-size or mesh-bias dependence.
Abstract
This paper describes a procedure for the solution of problems involving tensile cracking using the so-called smeared crack approach, that is, standard finite elements [...]
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On the orthogonal subgrid scale pressure stabilization of finite deformation J2 plasticity
C. Agelet de Saracibar, M. Chiumenti, Q. Valverde, M. Cervera

Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195 (9-12), pp. 1224-1251

Abstract
The use of stabilization methods is becoming an increasingly well-accepted technique due to their success in dealing with numerous numerical pathologies that arise in a variety of applications in computational mechanics. In this paper a multiscale finite element method technique to deal with pressure stabilization of nearly incompressibility problems in nonlinear solid mechanics at finite deformations is presented. A J2-flow theory plasticity model at finite deformations is considered. A mixed formulation involving pressure and displacement fields is used as starting point. Within the finite element discretization setting, continuous linear interpolation for both fields is considered. To overcome the Babuška–Brezzi stability condition, a multiscale stabilization method based on the orthogonal subgrid scale (OSGS) technique is introduced. A suitable nonlinear expression of the stabilization parameter is proposed. The main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements, which are easy to generate and, therefore, very convenient for practical industrial applications. Numerical results obtained using the OSGS stabilization technique are compared with results provided by the P1 standard Galerkin displacements linear triangular/tetrahedral element, P1/P1 standard mixed linear displacements/linear pressure triangular/tetrahedral element and Q1/P0 mixed bilinear/trilinear displacements/constant pressure quadrilateral/hexahedral element for 2D/3D nearly incompressible problems in the context of a nonlinear finite deformation J2 plasticity model.
Abstract
The use of stabilization methods is becoming an increasingly well-accepted technique due to their success in dealing with numerous numerical pathologies that arise in a variety [...]
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Mixed linear/linear simplicial elements for incompressible elasticity and plasticity
M. Cervera, M. Chiumenti, Q. Valverde, C. Agelet de Saracibar

Comput. Methods Appl. Mech. Engrg., (2003). Vol. 192 (49-50), pp. 5249-5263

Abstract
This paper exploits the concept of orthogonal sub-grid scales to stabilize the behaviour of mixed linear/linear simplicial elements (triangles and tetrahedra) in incompressible or nearly incompressible situations. Both incompressible elastic and J2-plastic constitutive behaviours have been considered. The different assumptions and approximations used to derive the method are exposed. Implementation and computational aspects are also discussed, showing that a robust application of the proposed formulation is feasible. Numerical examples show that the elements derived are free of volumetric locking and spurious oscillations of the pressure, and that the results obtained compare favourably with those obtained with the Q1P0 quadrilateral.
Abstract
This paper exploits the concept of orthogonal sub-grid scales to stabilize the behaviour of mixed linear/linear simplicial elements (triangles and tetrahedra) in incompressible [...]
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A stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations
M. Chiumenti, Q. Valverde, C. Agelet de Saracibar, M. Cervera

Comput. Methods Appl. Mech. Engrg., (2002). Vol. 191 (46), pp. 5253-5264

Abstract
In this paper a stabilized finite element method to deal with incompressibility in solid mechanics is presented. A mixed formulation involving pressure and displacement fields is used and a continuous linear interpolation is considered for both fields. To overcome the Babuška–Brezzi condition, a stabilization technique based on the orthogonal sub-scale method is introduced. The main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements, which are easy to generate for real industrial applications. Results are compared with standard Galerkin and Q1P0 mixed formulations for nearly incompressible problems in the context of linear elasticity.
Abstract
In this paper a stabilized finite element method to deal with incompressibility in solid mechanics is presented. A mixed formulation involving pressure and displacement fields [...]
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Mesh objective modeling of cracks using continuous linear strain and displacement interpolations
M. Cervera, M. Chiumenti, R. Codina

Int. J. Numer. Meth. Engng. (2011). Vol. 87 (10), pp. 962-987

Abstract
The paper addresses the problem of tensile and mixed‐mode cracking within the so‐called smeared crack approach. Because lack of point‐wise convergence on stresses is deemed as the main difficulty to be overcome in the discrete problem, a (stabilized) mixed formulation with continuous linear strain and displacement interpolations is used. The necessary convergence rate can be proved for such a formulation, at least in the linear problem. Two standard local isotropic Rankine damage models with strain‐softening, differing in the definition of the damage criteria, are used as discrete constitutive model. Numerical examples demonstrate the application of the proposed formulation using linear triangular P1P1 and bilinear quadrilateral Q1Q1 mixed elements. The results obtained do not suffer from spurious mesh‐bias dependence without the use of auxiliary tracking techniques.
Abstract
The paper addresses the problem of tensile and mixed‐mode cracking within the so‐called smeared crack approach. Because lack of point‐wise convergence on stresses is [...]
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A smeared‐embedded mesh‐corrected damage model for tensile cracking
M. Cervera

Int. J. Numer. Meth. Engng. (2008). Vol. 76 (12), pp. 1930-1954

Abstract
Traditional smeared orthotropic models display an unacceptable dependence of the solution on the alignment of the mesh, which usually manifests as stress locking. A solution for this drawback is proposed in this paper by adopting the concept of embedded inelastic strains, rather than displacement jumps, and by linking the structure of the inelastic strain to the geometry of the cracked element. The resulting model, applicable to linear 3‐noded triangles, is formulated as a non‐symmetric orthotropic local damage constitutive model, with the softening modulus regularized according to the material fracture energy and the element size. Analytical and numerical results show that this approach is effective in removing the locking problem as well as efficient from the computational point of view.
Abstract
Traditional smeared orthotropic models display an unacceptable dependence of the solution on the alignment of the mesh, which usually manifests as stress locking. A solution [...]
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Thermo‐mechanical analysis of industrial solidification processes
M. Cervera, C. Agelet de Saracibar, M. Chiumenti

Int. J. Numer. Meth. Engng. (1999). Vol. 46 (9), pp. 1575-1591

Abstract
The paper presents an up‐to‐date finite element numerical model for fully coupled thermo‐mechanical problems, focussing in the simulation of solidification processes of industrial metal parts. The proposed constitutive model is defined by a thermo‐visco‐elasto‐(visco)plastic free energy function which includes a contribution for thermal multiphase changes. Mechanical and thermal properties are assumed to be temperature‐dependent, and viscous‐like strains are introduced to account for the variation of the elastic moduli during the cooling process. The continuous transition between the initial fluid‐like and the final solid‐like behaviour of the part is modelled by considering separate viscous and elasto‐plastic responses as a function of the solid fraction. Thermo‐mechanical contact conditions between the mould and the part are specifically considered, assuming that the heat flux is a function of the normal pressure and the thermal and mechanical gaps. A fractional step method arising from an operator split of the governing equations is used to solve the non‐linear coupled system of equations, leading to a staggered product formula solution algorithm suitable for large‐scale computations. Representative simulations of industrial solidification processes are shown, and comparison of computed results using the proposed model with available experimental data is given.
Abstract
The paper presents an up‐to‐date finite element numerical model for fully coupled thermo‐mechanical problems, focussing in the simulation of solidification processes [...]
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Estudio de la distribución transitoria del gas en redes urbanas por el método de los elementos finitos
B. Suárez, E. Oñate

Anales de Ingeniería Mecánica (1984). Vol. 2 (1), pp. 59-68

Abstract
Se representa una formulación por elementos finitos que permite simular la distribución transitoria de presiones y caudales del gas en redes urbanas. Esta formulación, que parte de las ecuaciones básicas que proporciona la mecánica de fluidos para la circulación de un gas en régimen variable por conductos cilíndricos, utiliza elementos finitos unidimensionales parabólicos para discretizar los distintos tramos de la red y un esquema paso a paso de integración en el tiempo que supone una variación lineal de la presión del gas en cada intervalo de tiempo. La formulación se aplica al caso real de la red media presión de la ciudad de Barcelona utilizando algunos resultados experimentales para confirmar su eficiencia y aproximación.
Abstract
Se representa una formulación por elementos finitos que permite simular la distribución transitoria de presiones y caudales del gas en redes urbanas. Esta formulación, [...]
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Foreword: special issue on particles finite element method in multi-physics problems
S. Idelsohn

Comp. Part. Mech (2017). Vol. 4 (3), pp. 249-249

Abstract
Particle-based methods in which each material particle is followed in a Lagrangian manner have been used successfully in the last years for different applications. One of the latest evolution of particle-based methods is the Particle Finite Element Method (PFEM). The PFEM combines the particle precept with the FEM shape functions using an auxiliary FE mesh. This mesh may be quickly rebuilt at each time step (PFEM with moving mesh) or may be a fixed mesh (PFEM with fixed mesh). In the last case, the results from the Lagrangian particles are projected at each time iteration on a fixed mesh. The idea of combining FMs with moving particles was originally used in the so-called Particle in Cell method and later in an extension called the Material Point Method (MPM), which uses an FE background mesh. Despite that both PFEM and MPM employ a fixed FE mesh and a set of Lagrangian particles, there are important differences in the way the particles are employed; in the MPM, all computations are performed on the mesh, while in the PFEM, the aim is to calculate as much as possible on the particles, leaving small corrections to be performed on the mesh. Furthermore, the most important difference is that in PFEM, the particles do not represent a fixed amount of mass but rather material points that transport only intrinsic properties. This allows using a variable number of particles and therefore simplifying refinement. The PFEM has been successfully used to solve the Navier–Stokes equations and fluid–structure interaction problems as well as solid mechanics problems. The advantages of the PFEM concerning the tracking of internal interfaces have also been explored and used to solve multi-fluid flows. The possibility to use PFEM to solve nonlinear problems with large time-steps in order to obtain an accurate and fast solution was also successfully presented for the solution of the homogeneous incompressible Navier–Stokes equations. This new strategy was named PFEM second generation (PFEM-2). The enhanced PFEM-2 version to solve multi-phase problems, preserves the large time-step goodnesses of the single-phase strategy, also includes enrichment strategies to capture discontinuities in the pressure gradient, i.e., pressure kinks. This special issue is a collection of nine technical papers presenting the state-of-the-art in modeling and simulations of solid and fluid mechanics problems at different scales involving the Particle Finite Element Method as well in his original version (PFEM) as in his new upgrade (PFEM-2).
Abstract
Particle-based methods in which each material particle is followed in a Lagrangian manner have been used successfully in the last years for different applications. One [...]
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Assessment of a Lagrangian Incompressible Flow Code
R. Aubry, R. Lohner, E. Oñate, S. Idelsohn

American Institute of Aeronautics and Astronautics Paper (AIAA) (2007). 2007-0715

Abstract
An incompressible Finite Element Lagrangian code is presented and validated against classical experimental and numerical Eulerian results. The main distinction between an Eulerian and a Lagrangian approach is due to the convection of the mesh with the computed velocity. On one hand, the convective term is taken into account in the total derivative of the velocity, which greatly simplifies its numerical treatment. On the other hand, a constant remeshing must be performed to maintain a good element quality due to the large deformations undergone by the fluid. The classical cylinder and the thermally coupled cavity benchmarks have been chosen to perform a detailed comparison with an Eulerian code, FEFLO, and experimental results.
Abstract
An incompressible Finite Element Lagrangian code is presented and validated against classical experimental and numerical Eulerian results. The main distinction between an [...]
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A Finite Element Model for the Simulation of the UL-94 Burning Test
J. Marti, S. Idelsohn, E. Oñate

Fire Technology (2018). Vol. 54 (6), pp. 1783–1805

Abstract
The tendency of the polymers to melt and drip when they are exposed to external heat source play a very important role in the ignition and the spread of fire. Numerical simulation is a promising methodology for predicting this behaviour. In this paper, a computational procedure that aims at analyzing the combustion, melting and flame spread of polymer is presented. The method models the polymer using a Lagrangian framework adopting the particle finite element method framework while the surrounding air is solved on a fixed Eulerian mesh. This approach allows to treat naturally the polymer shape deformations and to solve the thermo-mechanical problem in a staggered fashion. The problems are coupled using an embedded Dirichlet–Neumann scheme. A simple combustion model and a radiation modeling strategy are included in the air domain. With this strategy the burning of a polypropylene specimen under UL-94 vertical test conditions is simulated. Input parameters for the modelling (density, specific heat, conductivity and viscosity) and results for the validation of the numerical model has been obtained from different literature sources and by IMDEA burning a specimen of dimensions of 148×13×3.2mm3. Temperature measurements in the polymer have been recorder by means of three thermocouples exceeding the 1000 K. Simultaneously a digital camera was used to record the burning process. In addition, thermal decomposition of the material (Arrhenius coefficient A=7.14×1016 min−1 and activation energy E=240.67kJ/mol) as and changes in viscosity (μ) as a function of temperature were obtained. Finally, a good agreement between the experimental and the numerical can be seen in terms of shape of the polymer as well as in the temperature evolution inside the polymer.
Abstract
The tendency of the polymers to melt and drip when they are exposed to external heat source play a very important role in the ignition and the spread of fire. Numerical simulation [...]
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Modèle d'ordre hyper-réduit (HROM) global-local pour des problèmes thermiques non linéaires avec changements d'état irréversibles
A. Cosimo, A. Cardona, S. Idelsohn

C. R. Mecanique (2018). Vol. 346 (7), pp. 539-555

Abstract
Highly concentrated moving nonlinearities are extremely difficult to solve numerically. The Selective Laser Melting Additive Manufacturing process is a problem of this kind. A material global-local scheme is proposed, which consists in describing the neighbourhood of the heat source by a moving local domain while the material phase fractions are represented in a global domain. The equations of the non-linear thermal problem are defined on the local domain only, assuming that the local domain is large enough to capture the most important variations of the temperature field. Additionally, a Hyper-Reduced-Order Model (HROM) is proposed for the local domain problem. The performance is studied by solving a SLM problem taken from the literature.
Abstract
Highly concentrated moving nonlinearities are extremely difficult to solve numerically. The Selective Laser Melting Additive Manufacturing process [...]
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Reduced order models for thermally coupled low Mach flows
R. Reyes, R. Codina, J. Baiges, S. Idelsohn

Adv. Model. and Simul. in Eng. Sci. (2018). Vol. 5, art. 28

Abstract
In this paper we present a collection of techniques used to formulate a projection-based reduced order model (ROM) for zero Mach limit thermally coupled Navier–Stokes equations. The formulation derives from a standard proper orthogonal decomposition (POD) model reduction, and includes modifications to improve the drawbacks caused by the inherent non-linearity of the used Navier–Stokes equations: a hyper-ROM technique based on mesh coarsening; an implicit ROM subscales formulation based on a variational multi-scale (VMS) framework; and a Petrov–Galerkin projection necessary in the case of non-symmetric terms. At the end of the article, we test the proposed ROM formulation using 2D and 3D versions of the same example: a differentially heated cavity.
Abstract
In this paper we present a collection of techniques used to formulate a projection-based reduced order model (ROM) for zero Mach limit thermally coupled Navier–Stokes [...]
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On the issue that Finite Element discretizations violate, nodally, Clausius’s postulate of the second law of thermodynamics
A. Limache, S. Idelsohn

Adv. Model. and Simul. in Eng. Sci. (2016). Vol. 3, art 13

Abstract
Discretization processes leading to numerical schemes sometimes produce undesirable effects. One potentially serious problem is that a discretization may produce the loss of validity of some of the physical principles or mathematical properties originally present in the continuous equation. Such loss may lead to uncertain results such as numerical instabilities or unexpected non-physical solutions. As a consequence, the compatibility of a discrete formulation with respect to intrinsic physical principles might be essential for the success of a numerical scheme. This paper addresses such type of issue. Its main objective is to demonstrate that standard Finite Element discretizations of the heat conduction equation violate Clausius’s postulate of the second law of thermodynamics, at nodal level. The problem occurs because non-physical, reversed nodal heat-fluxes arise in such discretizations. Conditions for compatibility of discrete nodal heat-fluxes with respect to Clausius’s postulate are derived here and named discrete thermodynamic compatibility conditions (DTCC). Simple numerical examples are presented to show the undesirable consequences of such failure. It must be pointed out that such DTCCs have previously appeared in the context of the study of the conditions that make discrete solutions to satisfy the discrete maximum principle (DMP). However, the present article does not put attention on such mathematical principle but on the satisfaction of a fundamental physical one: the second law of thermodynamics. Of course, from the presented point of view, it is clear that the violation of such fundamental law will cause, among different problems, the violation of the DMP.
Abstract
Discretization processes leading to numerical schemes sometimes produce undesirable effects. One potentially serious problem is that a discretization may produce the loss [...]
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General treatment of essential boundary conditions in reduced order models for non-linear problems
A. Cosimo, A. Cardona, S. Idelsohn

Adv. Model. and Simul. in Eng. Sci. (2016). Vol. 3, art 7

Abstract
Inhomogeneous essential boundary conditions must be carefully treated in the formulation of Reduced Order Models (ROMs) for non-linear problems. In order to investigate this issue, two methods are analysed: one in which the boundary conditions are imposed in an strong way, and a second one in which a weak imposition of boundary conditions is made. The ideas presented in this work apply to the big realm of a posteriori ROMs. Nevertheless, an a posteriori hyper-reduction method is specifically considered in order to deal with the cost associated to the non-linearity of the problems. Applications to nonlinear transient heat conduction problems with temperature dependent thermophysical properties and time dependent essential boundary conditions are studied. However, the strategies introduced in this work are of general application.
Abstract
Inhomogeneous essential boundary conditions must be carefully treated in the formulation of Reduced Order Models (ROMs) for non-linear problems. In order to investigate this [...]
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A semi-analytical model for droplet dynamics on the GDL surface of a PEFC electrode
A. Jarauta, M. Secanell, J. Pons Prats, P. Ryzhakov, S. Idelsohn, E. Oñate

Int. J. Hydrogen Energy (2015). Vol. 40 (15), pp. 5375-5383

Abstract
Water management is one of the key factors in Proton Exchange Fuel Cell (PEFC) performance. The water produced within the fuel cell is evacuated through the gas channels, but at high current densities water can block the channel, thus limiting the current density generated in the fuel cell. A semi-analytical model of a water droplet emerging from a gas diffusion layer pore in a PEFC channel is developed. The transient model contains a detailed adhesion and drag force estimation model. Results show that the predicted values for both drag and surface tension force are higher than the results found in literature. The results for the detachment force are consistent with the experimental data available. Higher air velocity values lead to more deformation of the droplet and oscillation with lower frequency but higher amplitude. Similar effects have been identified when the liquid mass flow is increased, leading to faster detachment of the droplet.
Abstract
Water management is one of the key factors in Proton Exchange Fuel Cell (PEFC) performance. The water produced within the fuel cell is evacuated through the gas channels, [...]
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GPGPU implementation of the BFECC algorithm for pure advection equations
S. Costarelli, M. Storti, R. Paz, L. Dalcin, S. Idelsohn

Cluster computing (2014). Vol. 17 (2), pp. 243-254

Abstract
In the present work an implementation of the Back and Forth Error Compensation and Correction (BFECC) algorithm specially suited for running on General-Purpose Graphics Processing Units (GPGPUs) through Nvidia’s Compute Unified Device Architecture (CUDA) is analyzed in order to solve transient pure advection equations. The objective is to compare it to a previous explicit version used in a Navier-Stokes solver fully written in CUDA. It turns out that BFECC could be implemented with unconditional stable stability using Semi-Lagrangian time integration allowing larger time steps than Eulerian ones.
Abstract
In the present work an implementation of the Back and Forth Error Compensation and Correction (BFECC) algorithm specially suited for running on General-Purpose Graphics Processing [...]
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Evaluating the performance of the particle finite element method in parallel architectures
J. Gimenez, N. Nigro, S. Idelsohn

Comp. Part. Mech. (2014). Vol. 1 (1), pp. 103-116

Abstract
This paper presents a high performance implementation for the particle-mesh based method called particle finite element method two (PFEM-2). It consists of a material derivative based formulation of the equations with a hybrid spatial discretization which uses an Eulerian mesh and Lagrangian particles. The main aim of PFEM-2 is to solve transport equations as fast as possible keeping some level of accuracy. The method was found to be competitive with classical Eulerian alternatives for these targets, even in their range of optimal application. To evaluate the goodness of the method with large simulations, it is imperative to use of parallel environments. Parallel strategies for Finite Element Method have been widely studied and many libraries can be used to solve Eulerian stages of PFEM-2. However, Lagrangian stages, such as streamline integration, must be developed considering the parallel strategy selected. The main drawback of PFEM-2 is the large amount of memory needed, which limits its application to large problems with only one computer. Therefore, a distributed-memory implementation is urgently needed. Unlike a shared-memory approach, using domain decomposition the memory is automatically isolated, thus avoiding race conditions; however new issues appear due to data distribution over the processes. Thus, a domain decomposition strategy for both particle and mesh is adopted, which minimizes the communication between processes. Finally, performance analysis running over multicore and multinode architectures are presented. The Courant–Friedrichs–Lewy number used influences the efficiency of the parallelization and, in some cases, a weighted partitioning can be used to improve the speed-up. However the total cputime for cases presented is lower than that obtained when using classical Eulerian strategies.
Abstract
This paper presents a high performance implementation for the particle-mesh based method called particle finite element method two (PFEM-2). It consists of a material derivative [...]
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A compressible Lagrangian framework for modeling the fluid-structure interaction in the underwater implosion of an aluminum cylinder
K. Kamran, R. Rossi, E. Oñate, S. Idelsohn

Mathematical Models and Methods in Applied Sciences (2013). Vol. 23 (2), pp. 339–367

Abstract
We propose a fully Lagrangian monolithic system for the simulation of the underwater implosion of cylindrical aluminum containers. A variationally stabilized form of the Lagrangian shock hydrodynamics is exploited to deal with the ultrahigh compression shock waves that travel in both air and water domains. The aluminum cylinder, which separates the internal atmospheric-pressure air from the external high-pressure water, is modeled by a three-node rotation-free shell element. The cylinder undergoes fast transient deformations, large enough to produce self-contact along it. A novel elastic frictionless contact model is used to detect contact and compute the non-penetrating forces in the discretized domain between the mid-planes of the shell. Mesh quality in the vicinity of the cylinder is guaranteed by regenerating the mesh in the air and water domains when large displacements occur. A monolithic fluid–structure interaction (FSI) system is then solved. Two schemes are tested, implicit using the predictor/multi-corrector Bossak scheme, and explicit, using the forward Euler scheme. The results of the two simulations are compared with experimental data.
Abstract
We propose a fully Lagrangian monolithic system for the simulation of the underwater implosion of cylindrical aluminum containers. A variationally stabilized form of the Lagrangian [...]
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An assessment of the potential of PFEM-2 for solving long real-time industrial applications
J. Gimenez, D. Ramajo, S. Damián, N. Nigro, S. Idelsohn

Comp. Part. Mech. (2016). Vol. 4 (3), pp. 251-267

Abstract
The latest generation of the particle finite element method (PFEM-2) is a numerical method based on the Lagrangian formulation of the equations, which presents advantages in terms of robustness and efficiency over classical Eulerian methodologies when certain kind of flows are simulated, especially those where convection plays an important role. These situations are often encountered in real engineering problems, where very complex geometries and operating conditions require very large and long computations. The advantages that the parallelism introduced in the computational fluid dynamics making affordable computations with very fine spatial discretizations are well known. However, it is not possible to have the time parallelized, despite the effort that is being dedicated to use space–time formulations. In this sense, PFEM-2 adds a valuable feature in that its strong stability with little loss of accuracy provides an interesting way of satisfying the real-life computation needs. After having already demonstrated in previous publications its ability to achieve academic-based solutions with a good compromise between accuracy and efficiency, in this work, the method is revisited and employed to solve several nonacademic problems of technological interest, which fall into that category. Simulations concerning oil–water separation, waste-water treatment, metallurgical foundries, and safety assessment are presented. These cases are selected due to their particular requirements of long simulation times and or intensive interface treatment. Thus, large time-steps may be employed with PFEM-2 without compromising the accuracy and robustness of the simulation, as occurs with Eulerian alternatives, showing the potentiality of the methodology for solving not only academic tests but also real engineering problems.
Abstract
The latest generation of the particle finite element method (PFEM-2) is a numerical method based on the Lagrangian formulation of the equations, which presents advantages [...]
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Flow behaviour of negatively buoyant jets in immiscible ambient fluid
A. Geyer, J. Phillips, M. Mier-Torrecilla, S. Idelsohn, E. Oñate

Experiments in Fluids (2011). Vol 52 (1), pp. 261-257

Abstract
In this paper we investigate experimentally the injection of a negatively buoyant jet into a homogenous immiscible ambient fluid. Experiments are carried out by injecting a jet of dyed fresh water through a nozzle in the base of a cylindrical tank containing rapeseed oil. The fountain inlet flow rate and nozzle diameter were varied to cover a wide range of Richardson Ri(8 × 10−4 < Ri < 1.98), Reynolds Re (467 < Re < 5,928) and Weber We (2.40 < We < 308.56) numbers. Based on the Re, Ri and We values for the experiments, we have determined a regime map to define how these values may control the occurrence of the observed flow types. Whereas Ri plays a stronger role when determining the maximum penetration height, the effect of the Reynolds number is stronger predicting the flow behaviour for a specific nozzle diameter and injection velocity.
Abstract
In this paper we investigate experimentally the injection of a negatively buoyant jet into a homogenous immiscible ambient fluid. Experiments are carried out by injecting [...]
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Modeling bed erosion in free surface flows by the particle finite element method
E. Oñate, M. Celigueta, S. Idelsohn

Acta Geotechnica (2006). Vol. 1 (4), pp. 237-252

Abstract
We present a general formulation for modeling bed erosion in free surface flows using the particle finite element method (PFEM). The key feature of the PFEM is the use of an updated Lagrangian description to model the motion of nodes (particles) in domains containing fluid and solid subdomains. Nodes are viewed as material points (called particles) which can freely move and even separate from the fluid and solid subdomains representing, for instance, the effect of water drops or soil/rock particles. A mesh connects the nodes defining the discretized domain in the fluid and solid regions where the governing equations, expressed in an integral form, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the nonlinear transient coupled fluid-structure problem is described. The erosion mechanism is modeled by releasing the material adjacent to the bed surface according to the frictional work generated by the fluid shear stresses. The released bed material is subsequently transported by the fluid flow. Examples of application of the PFEM to solve a number of bed erosion problems involving large motions of the free surface and splashing of waves are presented.
Abstract
We present a general formulation for modeling bed erosion in free surface flows using the particle finite element method (PFEM). The key feature of the PFEM is the use of [...]
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Comparative accuracy and performance assessment of the finite point method in compressible flow problems
E. Ortega, E. Oñate, S. Idelsohn, R. Flores

Computers and Fluids (2014). Vol. 89, pp. 53-65

Abstract
A comparative assessment of the Finite Point Method (FPM) is presented. Using a wing-fuselage configuration under transonic inviscid flow conditions as reference test case, the performance of the FPM flow solver is compared with an equivalent edge-based Finite Element (FEM) implementation. Efficiency issues have discouraged practical application of meshless methods in the past. Thus, a simplification of the basic FPM technique is proposed in order to reduce the performance gap with respect to classical grid-based algorithms. A comparative evaluation of the accuracy, computational cost and parallel performance of the meshless implementation is carried out with the objective to assess the level of maturity of the technique and identify improvements still required to tackle practical applications. The results obtained show accuracy and performance of the core algorithm comparable to a conventional FEM implementation, thus removing a major obstacle for further developments of the FPM.
Abstract
A comparative assessment of the Finite Point Method (FPM) is presented. Using a wing-fuselage configuration under transonic inviscid flow conditions as reference test case, [...]
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A portable OpenCL-based unstructured edge-based finite element Navier–Stokes solver on graphics hardware
R. Rossi, F. Mossaiby, S. Idelsohn

Computers & Fluids (2013). Vol. 81, pp. 134-144

Abstract
The rise of GPUs in modern high-performance systems increases the interest in porting portion of codes to such hardware. The current paper aims to explore the performance of a portable state-of-the-art FE solver on GPU accelerators. Performance evaluation is done by comparing with an existing highly-optimized OpenMP version of the solver. Code portability is ensured by writing the program using the OpenCL 1.1 specifications, while performance portability is sought through an optimization step performed at the beginning of the calculations to find out the optimal parameter set for the solver. The results show that the new implementation can be several times faster than the OpenMP version.
Abstract
The rise of GPUs in modern high-performance systems increases the interest in porting portion of codes to such hardware. The current paper aims to explore the performance [...]
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Migration of a generic multi-physics framework to HPC environments
P. Dadvand, R. Rossi, M. Gil, X. Martorell, J. Cotela, E. Juanpere, S. Idelsohn, E. Oñate

Computers and Fluids (2013). Vol. 80, pp. 301-309

Abstract
Creating a highly parallelizable code is a challenge specially for Distributed Memory Machines (DMMs). Moreover, algorithms and data structures suitable for these platforms can be very different from the ones used in serial code. For this reason, many programmers in the field prefer to start their own code from scratch. However, for an already existing framework supported by a long-time expertise the idea of transformation becomes attractive in order to reuse the effort done during years of development. In this presentation we explain how a relatively complex framework but with modular structure can be prepared for high performance computing with minimum modification. Kratos Multi-Physics is an open source generic multi-disciplinary platform for solution of coupled problems consist of fluid, structure, thermal and electromagnetic fields. The parallelization of this framework is performed with objective of enforcing the less possible changes to its different solver modules and encapsulate the changes as much as possible in its common kernel. This objective is achieved thanks to the Kratos design and also innovative way of dealing with data transfers for a multi-disciplinary code. This work is completed by the migration of the framework from the 86× architecture to the Marenostrum Supercomputing platform. The migration has been verified by a set of benchmarks which show high scalability, from which we present the Telescope problem in this paper.
Abstract
Creating a highly parallelizable code is a challenge specially for Distributed Memory Machines (DMMs). Moreover, algorithms and data structures suitable for these platforms [...]
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Parallel adaptive mesh refinement for incompressible flow problems
R. Rossi, J. Cotela, N. Lafontaine, P. Dadvand, S. Idelsohn

Computers and Fluids (2013). Vol. 80, pp. 342-355

Abstract
The present article describes a simple element-driven strategy for the conforming refinement of simplicial finite element meshes in a distributed environment. The proposed algorithm is effective both for local adaptive refinement and for the division of all the elements within an existing mesh. We aim to provide sufficient detail to allow the practical implementation of the algorithm, which can be coded with minimal effort provided that a distributed linear algebra library is available. The proposed refinement strategy is composed of three basic components: a global splitting strategy, an elemental splitting procedure and an error estimation technique, which are combined so to guarantee obtaining a conformant refined mesh. A number of benchmark examples show the capabilities of the proposed method. Error is estimated for the incompressible fluid-flow benchmarks using a novel indicator based on the computation of the sub-scale velocity.
Abstract
The present article describes a simple element-driven strategy for the conforming refinement of simplicial finite element meshes in a distributed environment. The proposed [...]
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A FFT preconditioning technique for the solution of incompressible flow on GPUs
M. Storti, R. Paz, L. Dalcin, S. Costarelli, S. Idelsohn

Computers and Fluids (2013). Vol. 74, pp. 44-57

Abstract
Graphic processing units have received much attention in last years. Compute-intensive algorithms operating on multidimensional arrays that have nearest neighbor dependency and/or exploit data locality can achieve massive speedups. Simulation of problems modeled by time-dependent Partial Differential Equations by using explicit time-stepping methods on structured grids is an instance of such GPU-friendly algorithms. Solvers for transient incompressible fluid flow cannot be developed in a fully explicit manner due to the incompressibility constraint. Segregated algorithms like the fractional step method require the solution of a Poisson problem for the pressure field at each time level. This stage is usually the most time-consuming one. This work discuss a solver for the pressure problem in applications using immersed boundary techniques in order to account for moving solid bodies. This solver is based on standard Conjugate Gradients iterations and depends on the availability of a fast Poisson solver on the whole domain to define a preconditioner. We provide a theoretical and numerical evidence on the advantages of our approach versus classical techniques based on fixed point iterations such as the Iterated Orthogonal Projection method.
Abstract
Graphic processing units have received much attention in last years. Compute-intensive algorithms operating on multidimensional arrays that have nearest neighbor dependency [...]
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The ALE/Lagrangian Particle Finite Element Method: A new approach to computation of free-surface flows and fluid–object interactions
F. Del Pin, S. Idelsohn, E. Oñate, R. Aubry

Computers and Fluids (2007). Vol. 36 (1), pp. 27-38

Abstract
The Particle Finite Element Method (PFEM) is a well established numerical method [Aubry R, Idelsohn SR, Oñate E, Particle finite element method in fluid mechanics including thermal convection–diffusion, Comput Struct 2004;83:1459–75; Idelsohn S, Oñate E, Del Pin F, A Lagrangian meshless finite element method applied to fluid–structure interaction problems, Comput Struct 2003;81:655–71; Idelsohn SR, Oñate E, Del Pin F, The particle finite element method a powerful tool to solve incompressible flows with free-surfaces and breaking waves, Int J Num Methods Eng 2004;61:964–84] where critical parts of the continuum are discretized into particles. The nodes treated as particles transport their momentum and physical properties in a Lagrangian way while the rest of the nodes may move in an Arbitrary Lagrangian–Eulerian (ALE) frame. In order to solve the governing equations that represent the continuum, the particles are connected by means of a Delaunay Triangulation [Idelsohn SR, Oñate E, Calvo N, Del Pin F, The meshless finite element method, Int J Num Methods Eng 2003;58(4)]. The resulting partition is a mesh where the Finite Element Method is applied to solve the equations of motion. The application of a fully Lagrangian formulation on the particles provides a natural and simple way to track free surfaces as well as to compute contacts in an accurate and robust fashion. Furthermore, the usage of an ALE formulation allows large mesh deformation with larger time steps than the full Lagrangian scheme.
Abstract
The Particle Finite Element Method (PFEM) is a well established numerical method [Aubry R, Idelsohn SR, Oñate E, Particle finite element method in fluid mechanics [...]
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A multiresolution strategy for solving landslides using the Particle Finite Element Method
P. Becker, S. Idelsohn

Acta Geotechnica (2016). Vol. 11 (3), pp. 643-657

Abstract
We present an approach for the simulation of landslides using the Particle Finite Element Method of the second generation. In this work, the multiphase nature (granular phase and water) of the phenomenon is considered in a staggered fashion using a single, indeformable Finite Element mesh. A fractional step and a monolithic strategy are used for the water flow and granular phase, respectively. In this way, the maximum accuracy with minimal computational times is reached. The method is completed by adding the interaction terms due to drag and pressure forces, together with a moving mesh strategy to reduce the size of the computational domain.
Abstract
We present an approach for the simulation of landslides using the Particle Finite Element Method of the second generation. In this work, the multiphase nature (granular phase [...]
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Numerical Simulation of the 3D Laminar Viscous Flow on a Horizontal-axis Wind Turbine Blade
R. Prado, M. Storti, S. Idelsohn

Int. J. Computational Fluid Dynamics (2002). Vol. 16 (4), pp. 283-295

Abstract
The aim of this paper is to describe the methodology followed in order to determine the viscous effects of a uniform wind on the blades of small horizontal-axis wind turbines that rotate at a constant angular speed. The numerical calculation of the development of the three-dimensional boundary layer on the surface of the blades is carried out under laminar conditions and considering flow rotation, airfoil curvature and blade twist effects. The adopted geometry for the twisted blades is given by cambered thin blade sections conformed by circular are airfoils with constant chords. The blade is working under stationary conditions at a given tip speed ratio, so that an extensive laminar boundary layer without flow separation is expected. The boundary layer growth is determined on a non-orthogonal curvilinear coordinate system related to the geometry of the blade surface. Since the thickness of the boundary layer grows from the leading edge of the blade and also from the tip to the blade root, a domain transformation is proposed in order to solve the discretized equations in a regular computational 3D domain. The non-linear system of partial differential coupled equations that governs the boundary layer development is numerically solved applying a finite difference technique using the Krause zig-zag scheme. The resulting coupled equations of motion are linearized, leading to a tridiagonal system of equations that is iteratively solved for the velocity components inside the viscous layer applying the Thomas algorithm, procedure that allows the subsequent numerical determination of the shear stress distribution on the blade surface.
Abstract
The aim of this paper is to describe the methodology followed in order to determine the viscous effects of a uniform wind on the blades of small horizontal-axis wind turbines [...]
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An unstructured grid-based, parallel free surface solver
R. Löhner, C. Yang, E. Oñate, S. Idelsohn

Applied Numerical Mathematics (1999). Vol. 31 (3), pp. 271-293

Abstract
An unstructured grid-based, parallel-free surface solver is presented. The overall scheme combines a finite-element, equal-order, projection-type 3-D incompressible flow solver with a finite element, 2-D advection equation solver for the free surface equation. For steady-state applications, the mesh is not moved every timestep, in order to reduce the cost of geometry recalculations and surface repositioning. A number of modifications required for efficient processing on shared-memory, cache-based parallel machines are discussed, and timings are shown that indicate scalability to a modest number of processors. The results show good quantitative comparison with experiments and the results of other techniques. The present combination of unstructured grids (enhanced geometrical flexibility) and good parallel performance (rapid turnaround) should make the present approach attractive to hydrodynamic design simulations.
Abstract
An unstructured grid-based, parallel-free surface solver is presented. The overall scheme combines a finite-element, equal-order, projection-type 3-D incompressible flow solver [...]
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A second-order in time and space particle-based method to solve flow problems on arbitrary meshes
J. Gimenez, H. Aguerre, S. Idelsohn, N. Nigro

Journal of Computational Physics (2018). Vol. 380, pp. 295-310

Abstract
This work presents a novel proposal of a second-order accurate (in time and space) particle-based method for solving transport equations including incompressible flows problems within a mixed Lagrangian–Eulerian formulation. This methodology consists of a symmetrical operator splitting, the use of high-order operators to transfer data between the particles and the background mesh, and an improved version of the eXplicit Integration Following the Streamlines (X–IVS) method. In the case of incompressible flows, a large time-step iterative solver is employed where the momentum equation is split to improve the numerical approximation of the convective term. New interpolation and projection operators are evaluated and quadratically accurate solutions of scalar transport tests are presented. Then, incompressible flow problems are solved where the rate of convergence of the method is assessed using both structured and unstructured background grids. The method is implemented in the open source platform OpenFOAM®allowing employing arbitrary meshes and obtaining reliable computing time comparisons with standardized solvers. The results obtained reveal that the current method is able to obtain a lower level of error than a fast Eulerian alternative, without increasing the total computing time.
Abstract
This work presents a novel proposal of a second-order accurate (in time and space) particle-based method for solving transport equations including incompressible [...]
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Algebraic Discrete Nonlocal (DNL) Absorbing Boundary Condition for the Ship Wave Resistance Problem
M. Storti, J. D'ELIA, S. Idelsohn

Journal of Computational Physics (1998). Vol. 146 (2), pp 570-602

Abstract
An absorbing boundary condition for the ship wave resistance problem is presented. In contrast to the Dawson-like methods, it avoids the use of numerical viscosities in the discretization, so that a centered scheme can be used for the free surface operator. The absorbing boundary condition is “completely absorbing,” in the sense that the solution is independent of the position of the downstream boundary and is derived from straightforward analysis of the resulting constant-coefficients difference equations, assuming that the mesh is 1D-structured (in the longitudinal direction) and requires the eigen-decomposition of a matrix one dimension lower than the system matrix. The use of a centered scheme for the free surface operator allows a full finite element discretization. The drag is computed by a momentum flux balance. This method is more accurate and guarantees positive resistances.
Abstract
An absorbing boundary condition for the ship wave resistance problem is presented. In contrast to the Dawson-like methods, it avoids the use of numerical viscosities in the [...]
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An improved enrichment method for weak discontinuities for thermal problems
J. Marti, E. Ortega, S. Idelsohn

Int. J. of Num. Meths. for Heat and Fluid Flow (2017). Vol. 27 (8), pp.1748-1764

Abstract
Purpose The purpose of this paper is to propose a new elemental enrichment technique to improve the accuracy of the simulations of thermal problems containing weak discontinuities. Design/methodology/approach The enrichment is introduced in the elements cut by the materials interface by means of adding additional shape functions. The weak form of the problem is obtained using Galerkin approach and subsequently integrating the diffusion term by parts. To enforce the continuity of the fluxes in the “cut” elements, a contour integral must be added. These contour integrals named here the “inter-elemental heat fluxes” are usually neglected in the existing enrichment approaches. The proposed approach takes these fluxes into account. Findings It has been shown that the inter-elemental heat fluxes cannot be generally neglected and must be included. The corresponding method can be easily implemented in any existing finite element method (FEM) code, as the new degrees of freedom corresponding to the enrichment are local to the elements. This allows for their static condensation, thus not affecting the size and structure of the global system of governing equations. The resulting elements have exactly the same number of unknowns as the non-enriched finite element (FE). Originality/value It is the first work where the necessity of including inter-elemental heat fluxes has been demonstrated. Moreover, numerical tests solved have proven the importance of these findings. It has been shown that the proposed enrichment leads to an improved accuracy in comparison with the former approaches where inter-elemental heat fluxes were neglected.
Abstract
Purpose The purpose of this paper is to propose a new elemental enrichment technique to improve the accuracy of the simulations of thermal problems [...]
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Variational Framework for FIC Formulations in Continuum Mechanics: High Order Tensor-Derivative Transformations and Invariants
C. Felippa, E. Oñate, S. Idelsohn

Archives of Comp. Meths. Engng. (2017). Vol. 25 (4), pp. 919–963

Abstract
This is part of an article series on a variational framework for continuum mechanics based on the Finite Increment Calculus (FIC). The formulation utilizes high order derivatives of the classical fields of continuum mechanics integrated over control regions to construct stabilizing modification terms. Fields may include displacements, body forces, strains, stresses, pressure and volumetric strains. To support observer-invariant FIC formulations, we have catalogued field transformation equations as well as sets of linear and quadratic invariants of fields and of their derivatives up to appropriate order. Attention is focused on the two-dimensional case of a body in plane strain under the drilling-rotation transformation group. Results are presented for displacement and body-force derivatives of orders up to 4, and for stress, strain, pressure and volumetric strain derivatives of order up to 3. The material assembled here is self-contained because this catalog is believed to be useful beyond FIC applications; for example gradient-based, nonlocal constitutive models of multiscale mechanics and physics that involve finite characteristic dimensions analogous to FIC steplengths.
Abstract
This is part of an article series on a variational framework for continuum mechanics based on the Finite Increment Calculus (FIC). The formulation utilizes high order derivatives [...]
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Multifluid flows with weak and strong discontinuous interfaces using an elemental enriched space
S. Idelsohn, J. Gimenez, N. Nigro

Int. J. Numer. Meth. Fluids (2018). Vol. 86 (12), pp. 750–769

Abstract
In a previous paper, the authors presented an elemental enriched space to be used in a finite‐element framework (EFEM) capable of reproducing kinks and jumps in an unknown function using a fixed mesh in which the jumps and kinks do not coincide with the interelement boundaries. In this previous publication, only scalar transport problems were solved (thermal problems). In the present work, these ideas are generalized to vectorial unknowns, in particular, the incompressible Navier‐Stokes equations for multifluid flows presenting internal moving interfaces. The advantage of the EFEM compared with global enrichment is the significant reduction in computing time when the internal interface is moving. In the EFEM, the matrix to be solved at each time step has not only the same amount of degrees of freedom (DOFs) but also the same connectivity between the DOFs. This frozen matrix graph enormously improves the efficiency of the solver. Another characteristic of the elemental enriched space presented here is that it allows a linear variation of the jump, thus improving the convergence rate, compared with other enriched spaces that have a constant variation of the jump. Furthermore, the implementation in any existing finite‐element code is extremely easy with the version presented here because the new shape functions are based on the usual finite‐element method shape functions for triangles or tetrahedrals, and once the internal DOFs are statically condensed, the resulting elements have exactly the same number of unknowns as the nonenriched finite elements.
Abstract
In a previous paper, the authors presented an elemental enriched space to be used in a finite‐element framework (EFEM) capable of reproducing kinks and jumps in an unknown [...]
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Analysis of multifluid flows with large time steps using the particle finite element method
S. Idelsohn, J. Marti, P. Becker, E. Oñate

Int. J. Numer. Meth. Fluids (2014). Vol. 75 (9), pp. 621-644

Abstract
Multifluids are those fluids in which their physical properties (viscosity or density) vary internally and abruptly forming internal interfaces that introduce a large nonlinearity in the Navier–Stokes equations. For this reason, standard numerical methods require very small time steps in order to solve accurately the internal interface position. In a previous paper, the authors developed a particle‐based method (named particle finite element method (PFEM)) based on a Lagrangian formulation and FEM for solving the fluid mechanics equations for multifluids. PFEM was capable of achieving accurate results, but the limitation of small time steps was still present. In this work, a new strategy concerning the time integration for the analysis of multifluids is developed allowing time steps one order of magnitude larger than the previous method. The advantage of using a Lagrangian solution with PFEM is shown in several examples. All kind of heterogeneous fluids (with different densities or viscosities), multiphase flows with internal interfaces, breaking waves, and fluid separation may be easily solved with this methodology without the need of small time steps.
Abstract
Multifluids are those fluids in which their physical properties (viscosity or density) vary internally and abruptly forming internal interfaces that introduce a large nonlinearity [...]
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Application of the finite point method to high‐Reynolds number compressible flow problems
R. Ortega, E. Oñate, S. Idelsohn, R. Flores

Int. J. Numer. Meth. Fluids (2014). Vol. 74 (10), pp. 732-748

Abstract
In this work, the finite point method is applied to the solution of high‐Reynolds compressible viscous flows. The aim is to explore this important field of applications focusing on two main aspects: the easiness and automation of the meshless discretization of viscous layers and the construction of a robust numerical approximation in the highly stretched clouds of points resulting in such domain areas. The flow solution scheme adopts an upwind‐biased scheme to solve the averaged Navier–Stokes equations in conjunction with an algebraic turbulence model. The numerical applications presented involve different attached boundary layer flows and are intended to show the performance of the numerical technique. The results obtained are satisfactory and indicative of the possibilities to extend the present meshless technique to more complex flow problems.
Abstract
In this work, the finite point method is applied to the solution of high‐Reynolds compressible viscous flows. The aim is to explore this important field of applications [...]
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A meshless finite point method for three‐dimensional analysis of compressible flow problems involving moving boundaries and adaptivity
R. Ortega, E. Oñate, S. Idelsohn, R. Flores

Int. J. Numer. Meth. Fluids (2013). Vol. 73 (4), pp. 323-343

Abstract
A finite point method for solving compressible flow problems involving moving boundaries and adaptivity is presented. The numerical methodology is based on an upwind‐biased discretization of the Euler equations, written in arbitrary Lagrangian–Eulerian form and integrated in time by means of a dual‐time steeping technique. In order to exploit the meshless potential of the method, a domain deformation approach based on the spring network analogy is implemented, and h‐adaptivity is also employed in the computations. Typical movable boundary problems in transonic flow regime are solved to assess the performance of the proposed technique. In addition, an application to a fluid–structure interaction problem involving static aeroelasticity illustrates the capability of the method to deal with practical engineering analyses. The computational cost and multi‐core performance of the proposed technique is also discussed through the examples provided.
Abstract
A finite point method for solving compressible flow problems involving moving boundaries and adaptivity is presented. The numerical methodology is based on an upwind‐biased [...]
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Explicit reduced‐order models for the stabilized finite element approximation of the incompressible Navier–Stokes equations
J. Baiges, R. Codina, S. Idelsohn

Int. J. Numer. Meth. Fluids (2013). Vol. 72 (12), pp. 1219-1243

Abstract
In this paper, we present an explicit formulation for reduced‐order models of the stabilized finite element approximation of the incompressible Navier–Stokes equations. The basic idea is to build a reduced‐order model based on a proper orthogonal decomposition and a Galerkin projection and treat all the terms in an explicit way in the time integration scheme, including the pressure. This is possible because the reduced model snapshots do already fulfill the continuity equation. The pressure field is automatically recovered from the reduced‐order basis and solution coefficients. The main advantage of this explicit treatment of the incompressible Navier–Stokes equations is that it allows for the easy use of hyper‐reduced order models, because only the right‐hand side vector needs to be recovered by means of a gappy data reconstruction procedure. A method for choosing the optimal set of sampling points at the discrete level in the gappy procedure is also presented. Numerical examples show the performance of the proposed strategy
Abstract
In this paper, we present an explicit formulation for reduced‐order models of the stabilized finite element approximation of the incompressible Navier–Stokes equations. [...]
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A new enrichment space for the treatment of discontinuous pressures in multi‐fluid flows
R. Ausas, G. Buscaglia, S. Idelsohn

Int. J. Numer. Meth. Fluids (2011). Vol. 70 (7), pp. 829-850

Abstract
In this work, a new enrichment space to accommodate jumps in the pressure field at immersed interfaces in finite element formulations, is proposed. The new enrichment adds two degrees of freedom per element that can be eliminated by means of static condensation. The new space is tested and compared with the classical P1 space and to the space proposed by Ausas et al (Comp. Meth. Appl. Mech. Eng., Vol. 199, 1019–1031, 2010) in several problems involving jumps in the viscosity and/or the presence of singular forces at interfaces not conforming with the element edges. The combination of this enrichment space with another enrichment that accommodates discontinuities in the pressure gradient has also been explored, exhibiting excellent results in problems involving jumps in the density or the volume forces.
Abstract
In this work, a new enrichment space to accommodate jumps in the pressure field at immersed interfaces in finite element formulations, is proposed. The new enrichment adds [...]
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Numerical simulations of negatively buoyant jets in an immiscible fluid using the Particle Finite Element Method
M. Mier-Torrecilla, A. Geyer, J. Phillips, S. Idelsohn, E. Oñate

Int. J. Numer. Meth. Fluids (2011). Vol. 69 (5), pp. 1016-1030

Abstract
Negatively buoyant jets consist in a dense fluid injected vertically upward into a lighter ambient fluid. The numerical simulation of this kind of buoyancy‐driven flows is challenging as it involves multiple fluids with different physical properties. In the case of immiscible fluids, it requires, in addition, to track the motion of the interface between fluids and accurately represent the discontinuities of the flow variables. In this paper, we investigate numerically the injection of a negatively buoyant jet into a homogenous immiscible ambient fluid using the Particle Finite Element Method and compare the two‐dimensional numerical results with experiments on the injection of a jet of dyed water through a nozzle in the base of a cylindrical tank containing rapeseed oil. In both simulations and experiments, the fountain inlet flow velocity and nozzle diameter have been varied to cover a wide range of Froude Fr and Reynolds Re numbers ( 0.1 < Fr < 30, 8 < Re < 1350), reproducing both weak and strong laminar fountains. The flow behaviors observed for the different numerical simulations fit in the regime map based on the Re and Fr values of the experiments, and the maximum fountain height is in good agreement with the experimental observations, suggesting that particle finite element method is a useful tool for the study of immiscible two‐fluid systems.
Abstract
Negatively buoyant jets consist in a dense fluid injected vertically upward into a lighter ambient fluid. The numerical simulation of this kind of buoyancy‐driven flows [...]
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A family of residual‐based stabilized finite element methods for Stokes flows
E. Oñate, P. Nadukandi, S. Idelsohn, J. García-Espinosa, C. Felippa

Int. J. Numer. Meth. Fluids (2010). Vol. 65 (1-3), pp. 106-134

Abstract
We present a collection of stabilized finite element (FE) methods derived via first‐ and second‐order finite calculus (FIC) procedures. It is shown that several well known existing stabilized FE methods such as the penalty technique, the Galerkin Least Square (GLS) method, the Pressure Gradient Projection (PGP) method and the orthogonal sub‐scales (OSS) method are recovered from the general residual‐based FIC stabilized form. A new family of stabilized Pressure Laplacian Stabilization (PLS) FE methods with consistent nonlinear forms of the stabilization parameters are derived. The distinct feature of the family of PLS methods is that they are residual‐based, i.e. the stabilization terms depend on the discrete residuals of the momentum and/or the incompressibility equations. The advantages and disadvantages of the different stabilization techniques are discussed and several examples of application are presented.
Abstract
We present a collection of stabilized finite element (FE) methods derived via first‐ and second‐order finite calculus (FIC) procedures. It is shown that several well known [...]
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A finite point method for adaptive three‐dimensional compressible flow calculations
E. Ortega, E. Oñate, S. Idelsohn

Int. J. Numer. Meth. Fluids (2008). Vol. 60 (9), pp. 937-971

Abstract
The finite point method (FPM) is a meshless technique, which is based on both, a weighted least‐squares numerical approximation on local clouds of points and a collocation technique which allows obtaining the discrete system of equations. The research work we present is part of a broader investigation into the capabilities of the FPM to deal with 3D applications concerning real compressible fluid flow problems. In the first part of this work, the upwind‐biased scheme employed for solving the flow equations is described. Secondly, with the aim of exploiting the meshless capabilities, an h‐adaptive methodology for 2D and 3D compressible flow calculations is developed. This adaptive technique applies a solution‐based indicator in order to identify local clouds where new points should be inserted in or existing points could be safely removed from the computational domain. The flow solver and the adaptive procedure have been evaluated and the results are encouraging. Several numerical examples are provided in order to illustrate the good performance of the numerical methods presented.
Abstract
The finite point method (FPM) is a meshless technique, which is based on both, a weighted least‐squares numerical approximation on local clouds of points and a collocation [...]
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The violation of objectivity in Laplace formulations of the Navier–Stokes equations
A. Limache, S. Idelsohn, R. Rossi, E. Oñate

Int. J. Numer. Meth. Fluids (2007). Vol. 54 (6-8), pp. 639-664

Abstract
The Navier–Stokes equations written in Laplace form are often the starting point of many numerical methods for the simulation of viscous flows. Imposing the natural boundary conditions of the Laplace form or neglecting the viscous contributions on free surfaces are traditionally considered reasonable and harmless assumptions. With these boundary conditions any formulation derived from integral methods (like finite elements or finite volumes) recovers the pure Laplacian aspect of the strong form of the equations. This approach has also the advantage of being convenient in terms of computational effort and, as a consequence, it is used extensively. However, we have recently discovered that these resulting Laplacian formulations violate a basic axiom of continuum mechanics: the principle of objectivity. In the present article we give an accurate account about these topics. We also show that unexpected differences may sometimes arise between Laplace discretizations and divergence discretizations.
Abstract
The Navier–Stokes equations written in Laplace form are often the starting point of many numerical methods for the simulation of viscous flows. Imposing the natural [...]
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Predicción de fracturas en estructuras de hormigón combinando los métodos de elementos finitos y de elementos discretos
F. Zarate, E. Oñate

Hormigón y Acero (2018). (prepint) 69, Supl 1, pp. 53-69

Abstract
This paper presents the basic concepts and application of the strategy that combines finite element methods (FEM) and discrete elements (DEM)for the study of the propagation of fractures in concrete structures. The calculation of the structure, modeled as a continuum, begins with the FEMand the DEM is used to start and grow the cracks that may appear in the structure. This methodology has been proposed by the authors in two andthree dimensions. Recently, the use of one-dimensional steel elements embedded in the continuum has been added to model the reinforcement inconcrete structures. The work presents different examples of application to the study of the breakage of parts and structures of concrete in massand armed, as well as the multiple breakage of a historic structure of masonry due to an earthquake.
Abstract
This paper presents the basic concepts and application of the strategy that combines finite element methods (FEM) and discrete elements (DEM)for the study of the propagation [...]
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A fast and accurate method to solve the incompressible Navier‐Stokes equations
S. Idelsohn, N. Nigro, J. Gimenez, R. Rossi, J. Marti

Engineering Computations (2013). Vol. 30 (2), pp. 197-222

Abstract
Purpose – The purpose of this paper is to highlight the possibilities of a novel Lagrangian formulation in dealing with the solution of the incompressible Navier‐Stokes equations with very large time steps. Design/methodology/approach – The design of the paper is based on introducing the origin of this novel numerical method, originally inspired on the Particle Finite Element Method (PFEM), summarizing the previously published theory in its moving mesh version. Afterwards its extension to fixed mesh version is introduced, showing some details about the implementation. Findings – The authors have found that even though this method was originally designed to deal with heterogeneous or free‐surface flows, it can be competitive with Eulerian alternatives, even in their range of optimal application in terms of accuracy, with an interesting robustness allowing to use large time steps in a stable way. Originality/value – With this objective in mind, the authors have chosen a number of benchmark examples and have proved that the proposed algorithm provides results which compare favourably, both in terms of solution time and accuracy achieved, with alternative approaches, implemented in in‐house and commercial codes.
Abstract
Purpose – The purpose of this paper is to highlight the possibilities of a novel Lagrangian formulation in dealing with the solution [...]
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Smoothed surface gradients for panel methods
J. D'Elía, M. Storti, S. Idelsohn

Advances in Engineering Software (2000). Vol. 31 (5), pp. 339-346

Abstract
A weak form to compute the dipolar and monopolar surface gradients, related to a low-order panel method, is shown. The flow problem is formulated by means of a three-dimensional potential model and the discretization is based on Morino's formulation for the perturbation velocity potential. On the body surface, this representation reduces to a boundary integral equation with the source (or monopolar) and the doublet (or dipolar) densities. The first of the two is found by application of the boundary flow condition, and the second one is the unknown over the body surface. A lower panel method is used for the analytic integrations of both the monopolar and dipolar influence coefficients. The surface velocity field is computed after solving the linear system, with a strong and a weak form of the Stokes theorem, which is oriented to fairly non-structured panel meshes. The proposed method is validated by comparing the numerical results with analytical ones for an isolated sphere and includes a prediction over a car-like configuration.
Abstract
A weak form to compute the dipolar and monopolar surface gradients, related to a low-order panel method, is shown. The flow problem is formulated by means of a three-dimensional [...]
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A closed form for low-order panel methods
J. D'Elía, M. Storti, S. Idelsohn

Advances in Engineering Software (2000). Vol. 31 (5), pp. 347-353

Abstract
A closed form for the computation of the dipolar and monopolar influence coefficients related to a low-order panel method is shown. The flow problem is formulated by means of a three-dimensional potential model; the method of discretization is based on the Morino formulation for the perturbation velocity potential. On the body surface this representation reduces to an integral equation with the source (or monopolar) and the doublet (or dipolar) densities. The former is found by application of the boundary condition, and the latter is the unknown over the surface of the body. The lower panel method is used for the analytical integrations of the monopolar and dipolar influence coefficients, with special attention to avoid a logarithmic singularity in the monopolar matrix when flat fairly structured meshes that are common in ship-wave calculations are used.
Abstract
A closed form for the computation of the dipolar and monopolar influence coefficients related to a low-order panel method is shown. The flow problem is formulated by means [...]
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An unstructured finite element solver for ship hydrodynamics problems
J. García-Espinosa, E. Oñate

J. Appl. Mech (2003). Vol. 70 (1), pp. 18-26

Abstract
A stabilized semi-implicit fractional step algorithm based on the finite element method for solving ship wave problems using unstructured meshes is presented. The stabilized governing equations for the viscous incompressible fluid and the free surface are derived at a differential level via a finite calculus procedure. This allows us to obtain a stabilized numerical solution scheme. Some particular aspects of the problem solution, such as the mesh updating procedure and the transom stern treatment, are presented. Examples of the efficiency of the semi-implicit algorithm for the analysis of ship hydrodynamics problems are presented.
Abstract
A stabilized semi-implicit fractional step algorithm based on the finite element method for solving ship wave problems using unstructured meshes is presented. The stabilized [...]
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Fast fluid–structure interaction simulations using a displacement-based finite element model equipped with an explicit streamline integration prediction
P. Ryzhakov, J. Miquel, S. Idelsohn, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2017). Vol. 315, pp. 1080-1097

Abstract
We propose here a displacement-based updated Lagrangian fluid model developed to facilitate a monolithic coupling with a wide range of structural elements described in terms of displacements. The novelty of the model consists in the use of the explicit streamline integration for predicting the end-of-step configuration of the fluid domain. It is shown that this prediction considerably alleviates the time step size restrictions faced by the former Lagrangian models due to the possibility of an element inversion within one time step. The method is validated and compared with conventional approaches using three numerical examples. Time step size and corresponding Courant numbers leading to optimal behavior in terms of computational efficiency are identified.
Abstract
We propose here a displacement-based updated Lagrangian fluid model developed to facilitate a monolithic coupling with a wide range of structural elements [...]
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OpenCL‐based implementation of an unstructured edge‐based finite element convection‐diffusion solver on graphics hardware
F. Mossaiby, R. Rossi, P. Dadvand, S. Idelsohn

Int. J. Numer. Meth. Engng. (2012). Vol. 89 (13), pp. 1635-1651

Abstract
The solution of problems in computational fluid dynamics (CFD) represents a classical field for the application of advanced numerical methods. Many different approaches were developed over the years to address CFD applications. Good examples are finite volumes, finite differences (FD), and finite elements (FE) but also newer approaches such as the lattice‐Boltzmann (LB), smooth particle hydrodynamics or the particle finite element method. FD and LB methods on regular grids are known to be superior in terms of raw computing speed, but using such regular discretization represents an important limitation in dealing with complex geometries. Here, we concentrate on unstructured approaches which are less common in the GPU world. We employ a nonstandard FE approach which leverages an optimized edge‐based data structure allowing a highly parallel implementation. Such technique is applied to the ‘convection‐diffusion’ problem, which is often considered as a first step towards CFD because of similarities to the nonconservative form of the Navier–Stokes equations. In this regard, an existing highly optimized parallel OpenMP solver is ported to graphics hardware based on the OpenCL platform. The optimizations performed are discussed in detail. A number of benchmarks prove that the GPU‐accelerated OpenCL code consistently outperforms the OpenMP version.
Abstract
The solution of problems in computational fluid dynamics (CFD) represents a classical field for the application of advanced numerical methods. Many different approaches were [...]
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A finite point method in computational mechancis. Applications to convective transport and fluid flow.
E. Oñate, S. Idelsohn, O. Zienkiewicz, R. Taylor

Int. J. Numer. Meth. Engng. (1996). Vol. 39 (22), pp. 3839-3866

Abstract
The paper presents a fully meshless procedure fo solving partial differential equations. The approach termed generically the ‘finite point method’ is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals. Some examples showing the accuracy of the method for solution of adjoint and non‐self adjoint equations typical of convective‐diffusive transport and also to the analysis of compressible fluid mechanics problem are presented.
Abstract
The paper presents a fully meshless procedure fo solving partial differential equations. The approach termed generically the ‘finite point method’ is based on [...]
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Global–Local ROM for the solution of parabolic problems with highly concentrated moving sources
A. Cosimo, A. Cardona, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2017). Vol. 326, pp. 739-756

Abstract
Problems characterised by steep moving gradients are challenging for any numerical technique and even more for the successful formulation of Reduced Order Models (ROMs). The aim of this work is to study the numerical solution of problems with steep moving gradients, by placing the focus on parabolic problems with highly concentrated moving sources. More specifically, a Global–Local scheme well-suited for reduction methods is formulated. With this Global–Localscheme, the local nature of the steep moving gradients is exploited by modelling the neighbourhood of the heat source with a moving local domain. This domain is coupled to the global domain without requiring any re-mesh and preserving the meshes of both domains during the whole simulation. Then, a ROM based on the Proper Orthogonal Decomposition (POD) technique is developed for the moving local domain. The proposed technique establishes a valid approach for tackling the non-separability of the space and time dimensions of these problems. In order to assess the numerical performance of the proposed numerical techniques, several evaluation tests are performed.
Abstract
Problems characterised by steep moving gradients are challenging for any numerical technique and even more for the successful formulation of Reduced Order Models (ROMs). [...]
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An embedded strategy for the analysis of fluid structure interaction problems
S. Costarelli, L. Garelli, M. Cruchaga, M. Storti, R. Ausensi, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2016). Vol. 300, pp. 106-128

Abstract
A Navier–Stokes solver based on Cartesian structured finite volume discretization with embedded bodies is presented. Fluid structure interaction with solid bodies is performed with an explicit partitioned strategy. The Navier–Stokes equations are solved in the whole domain via a Semi-Implicit Method for Pressure Linked Equations (SIMPLE) using a colocated finite volume scheme, stabilized via the Rhie–Chow discretization. As uniform Cartesian grids are used, the solid interface usually do not coincide with the mesh, and then a second order Immersed Boundary Method is proposed, in order to avoid the loss of precision due to the staircase representation of the surface. This fact also affects the computation of fluid forceson the solid wall and, accordingly, the results in the fluid–structure analysis. In the present work, first and second order approximations for computing the fluid forces at the interface are studied and compared. The solver is specially oriented to General Purpose Graphic Processing Units (GPGPU) hardware and the efficiency is discussed. Moreover, a novel submerged buoy experiment is also reported. The experiment consists of a sphere with positive buoyancy fully submerged in a cubic tank, subject to harmonic displacements imposed by a shake table. The sphere is attached to the bottom of the tank with a string. The position of the buoy is determined from video records with a Motion Capture algorithm. The obtained amplitude and phase curves allow a precise determination of the added mass and drag forces. Due to this aspect the experimental data can be of interest for comparison with other fluid–structure interaction codes. Finally, the numerical results are compared with the experiments, and allow the confirmation of the numerically predicted drag and added mass of the body.
Abstract
A Navier–Stokes solver based on Cartesian structured finite volume discretization with embedded bodies is presented. Fluid structure interaction with [...]
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Reduced-order subscales for POD models
J. Baiges, R. Codina, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2015). Vol. 291; pp. 173-196

Abstract
In this work the Reduced-Order Subscales for Proper Orthogonal Decomposition models are presented. The basic idea consists in splitting the full-order solution into the part which can be captured by the reduced-order model and the part which cannot, the subscales, for which a model is required. The proposed model for the subscales is defined as a linear function of the solution of the reduced-order model. The coefficients of this linear function are obtained by comparing the solution of the full-order model with the solution of the reduced-order model for the same initial conditions, which, for convenience, are evaluated in the snapshots used to train the original reduced-order-model. The difference between both solutions are the subscales, for which a model can be built using a least-squares procedure. The subscales are then introduced as a correction in the reduced-order model, resulting in an important improvement in accuracy. The enhanced reduced-order model is tested in several numerical examples. These practical cases show that the use of the subscales leads to more accurate solutions, successfully corrects errors introduced by hyper-reduction, and allows to solve complex flow problems using a reduced number of degrees of freedom.
Abstract
In this work the Reduced-Order Subscales for Proper Orthogonal Decomposition models are presented. The basic idea consists in splitting the full-order solution into the part [...]
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Improving the k-compressibility of Hyper Reduced Order Models with moving sources: Applications to welding and phase change problems
A. Cosimo, A. Cardona, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2014). Vol. 274, pp. 237-263

Abstract
The simulation of engineering problems is quite often a complex task that can be time consuming. In this context, the use of Hyper Reduced Order Models (HROMs) is a promising alternative for real-time simulations. In this work, we study the design of HROMs for non-linear problems with a moving source. Applications to nonlinear phase change problems with temperature dependent thermophysical properties are particularly considered; however, the techniques developed can be applied in other fields as well. A basic assumption in the design of HROMs is that the quantities that will be hyper-reduced are k-compressible in a certain basis in the sense that these quantities have at most k non-zero significant entries when expressed in terms of that basis. To reach the computational speed required for a real-time application, k must be small. This work examines different strategies for addressing hyper-reduction of the nonlinear terms with the objective of obtaining k-compressible signals with a notably small k. To improve performance and robustness, it is proposed that the different contributing terms to the residual are separately hyper-reduced. Additionally, the use of moving reference frames is proposed to simulate and hyper-reduce cases that contain moving heat sources. Two application examples are presented: the solidification of a cube in which no heat source is present and the welding of a tube in which the problem posed by a moving heat source is analysed.
Abstract
The simulation of engineering problems is quite often a complex task that can be time consuming. In this context, the use of Hyper Reduced Order Models (HROMs) is a promising [...]
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A domain decomposition strategy for reduced order models. Application to the incompressible Navier–Stokes equations
J. Baiges, R. Codina, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2013). Vol. 267, pp. 23-42

Abstract
In this work, a domain decomposition strategy for non-linear hyper-reduced-order models is presented. The basic idea consists of restricting the reduced-order basis functions to the nodes belonging to each of the subdomains into which the physical domain is partitioned. An extension of the proposed domain decomposition strategy to a hybrid full-order/reduced-order model is then described. The general domain decomposition approach is particularized for the reduced-order finite element approximation of the incompressible Navier–Stokes equations with hyper-reduction. When solving the reduced incompressible Navier–Stokes equations, instabilities in the form of large gradients of the recovered reduced-order unknown at the subdomain interfaces may appear, which is the motivation for the design of additional stability terms giving rise to penalty matrices. Numerical examples illustrate the behavior of the proposed method for the simulation of the reduced-order systems, showing the capability of the approach to adapt to configurations which are not present in the original snapshot set.
Abstract
In this work, a domain decomposition strategy for non-linear hyper-reduced-order models is presented. The basic idea consists of restricting the reduced-order basis functions [...]
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Una formulación para el estudio, por el método de los elementos finitos, de la deformación de tuberías marinas durante su instalación
J. Oliver, E. Oñate

Revista de Obras Públicas (1983). Vol. 130 (3218), pp. 747-763

Abstract
La ejecución de emisarios submarinos para saneamiento y la instalación de tuberías para transporte de productos petrolíferos son ejemplos de la necesidad de conocer los esfuerzos y deformaciones que se producen en el tendido de tuberías submarinas, a cuyo estudio, mediante elementos finitos en diversas condiciones de instalación, se dedica este artículo, que permite la obtención de ábacos de cálculo o formulas sencillas aplicables en los distintos casos.
Abstract
La ejecución de emisarios submarinos para saneamiento y la instalación de tuberías para transporte de productos petrolíferos son ejemplos de la [...]
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A coupled fluid FEM-DEM technique for predicting blasting operations in tunnels
F. Zarate, J. Gonzalez, J. Miquel, R. Lohner, E. Oñate

Underground Space (2018). (prepint)

Abstract
We present recent developments in the coupling of the finite element method (FEM) and the discrete element method (DEM) for analysis of rock blasting operations in tunnels. The coupled FEM-DEM technique has proven to be an efficient procedure for predicting the multi-fracture of rock induced by the loads generated in blasting situations. The coupled FEM-DEM procedure is applied in the tunnel construction, as well as to gas pressure blasting pyrotechnics situations to break rock for excavation of the tunnel front. In the latter case the effect of gas explosion is modelled by solving with the FEM the equations of gas dynamics in the analysis domain. The effect of the gas forces in the underlying rock mass is modelled via an embedded fluid-structure interaction method. The efficiency of the coupled FEM-DEM technique is demonstrated in several examples of fracture tests and rock blasting problems related to tunnel engineering. The examples presented show that the combination of the DEM with simple 3-noded linear triangular elements (for 2D problems) correctly captures the onset of fractures and their evolution accounting for the penetration of the gas in the failure domain [[#cite-1|[1,2]]].
Abstract
We present recent developments in the coupling of the finite element method (FEM) and the discrete element method (DEM) for analysis of rock blasting operations in tunnels. [...]
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Pulse fracture simulation in shale rock reservoirs. DEM and FEM-DEM approaches
J. Gonzalez, F. Zarate, E. Oñate

Comp. Part. Mech (2018). (prepint) Vol. 5 (3), pp. 355-373

Abstract
In this paper we analyze the capabilities of two numerical techniques based on DEM and FEM-DEM approaches for the simulation of fracture in shale rock caused by a pulse of pressure. We have studied the evolution of fracture in several fracture scenarios related to the initial stress state in the soil or the pressure pulse peak. Fracture length and type of failure have been taken as reference for validating the models. The results obtained show a good approximation to FEM results from the literature.
Abstract
In this paper we analyze the capabilities of two numerical techniques based on DEM and FEM-DEM approaches for the simulation of fracture in shale rock caused by a pulse of [...]
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A three dimensional FEM-DEM technique for predicting the evolution of fracture in geomaterials and concrete
F. Zarate, A. Cornejo Velázquez, E. Oñate

Comp. Part. Mech (2018). (prepint) Vol. 5 (3) , pp. 411-420

Abstract
This paper extends to three dimensions (3D) the computational technique developed by the authors in 2D for predicting the onset and evolution of fracture in a finite element mesh in a simple manner based on combining the finite element method (FEM) and the discrete element method (DEM) approach Zarate2D. Once a crack is detected at an element edge, discrete elements are generated at the adjacent element vertexes and a simple DEM mechanism is considered in order to follow the evolution of the crack. The combination of the DEM with simple 4-noded linear tetrahedron elements correctly captures the onset of fracture and its evolution, as shown in several 3D examples of application.
Abstract
This paper extends to three dimensions (3D) the computational technique developed by the authors in 2D for predicting the onset and evolution of fracture in a finite element [...]
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The challenge of mass conservation in the solution of free‐surface flows with the fractional‐step method: Problems and solutions
S. Idelsohn, E. Oñate

Int. J. Numer. Meth. Biomed. Engng (2010). Vol. 26 (10), pp. 1313-1330

Abstract
The purpose of this paper is to put in evidence that the fractional‐step method (FSM) used to solve the incompressible transient Euler and Navier–Stokes equations for free‐surface flows has a problem inherent to the method that may produce unacceptable variations of the domain volume. A simple modification of the free‐surface boundary term is introduced in order to reduce considerably the volume loss and preserve the computational advantages of the FSM.
Abstract
The purpose of this paper is to put in evidence that the fractional‐step method (FSM) used to solve the incompressible transient Euler and Navier–Stokes equations [...]
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A continuum mechanics model for mechanical fatigue analysis
S. Oller, O. Salomon, E. Oñate

Computational Materials Science (2005). Vol. 32 (2), pp. 175-195

Abstract
In this paper, a thermo-mechanical constitutive model for the predictions of fatigue in structures using the finite element method is formulated. The model is based on the damage mechanics of the continuous medium and allows the treatment in a unified way of coupled phenomena such as fatigue with damage, plasticity, viscosity and temperature effects. Basically it is gotten sensitive models to cyclic loads starting from classical non-linear constitutive formulations incorporating the special variable influenced by the characteristics of the cyclic load. A formulation based on the theories of damage and plasticity is developed. The necessary modifications of these theories are outlined in order to include the fatigue phenomena. A brief description of the finite element implementation is given. Finally, results of the performance of the proposed model are shown through the simple fatigue test and the fatigue analysis of an aluminium engine alternator support.
Abstract
In this paper, a thermo-mechanical constitutive model for the predictions of fatigue in structures using the finite element method is formulated. The model is based on the [...]
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A Lagrangian Panel Method in the Time Domain for Moving Free-surface Potential Flows
J. D'ELIA, M. Storti, E. Oñate, S. Idelsohn

Int. J. Computational Fluid Dynamics (2002). Vol. 16 (4), pp. 263-275

Abstract
A Lagrangian-type panel method in the time domain is proposed for potential flows with a moving free surface. After a spatial semi-discretization with a low-order scheme, the instantaneous velocity-potential and normal displacement on the moving free surface are obtained by means of a time-marching scheme. The kinematic and dynamic boundary conditions at the free surface are non-linear restrictions over the related Ordinary Differential Equation (ODE) system and, in order to handle them, an alternative Steklov-Poincaré operator technique is proposed. The method is applied to sloshing like flow problems.
Abstract
A Lagrangian-type panel method in the time domain is proposed for potential flows with a moving free surface. After a spatial semi-discretization with a low-order scheme, [...]
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A finite element formulation for the analysis of marine pipelines during laying operations
J. Oliver, E. Oñate

Journal of Pipelines (1985). Vol. 5 (1), pp. 15-35

Abstract
In this paper a finite element formulation for the deformation analysis of submarine pipelines during laying operations is presented. The formation allows for large displacement/rotations and the effect of nonconservative water loads. An iterative procedure to deal with the changing boundary conditions at the seafloor is also presented. Numerical results for two pipeline laying cases, obtained using three noded isoparametrical one-dimensional curved elements, are given.
Abstract
In this paper a finite element formulation for the deformation analysis of submarine pipelines during laying operations is presented. The formation allows for large displacement/rotations [...]
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A finite point method for incompressible flow problems
E. Oñate, C. Sacco, S. Idelsohn

Computing and Visualization in Science (2000). Vol. 3 (1), pp. 67-75

Abstract
A stabilized finite point method (FPM) for the meshless analysis of incompressible fluid flow problems is presented. The stabilization approach is based in the finite increment calculus (FIC) procedure developed by Oñate [14]. An enhanced fractional step procedure allowing the semi-implicit numerical solution of incompressible fluids using the FPM is described. Examples of application of the stabilized FPM to the solution of two incompressible flow problems are presented.
Abstract
A stabilized finite point method (FPM) for the meshless analysis of incompressible fluid flow problems is presented. The stabilization approach is based in the finite increment [...]
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A methodology for adaptive mesh refinement in optimum shape design problems
G. Bugeda, E. Oñate

Computing Systems in Engineering (1994). Vol. 5 (1), pp. 91-102

Abstract
This work presents a methodology based on the use of adaptive mesh refinement (AMR) techniques in the context of shape optimization problems analyzed by the Finite Element Method (FEM). A suitable and very general technique for the parametrization of the optimization problem using B-splines to define the boundary is first presented. Then, mesh generation using the advancing front method, the error estimation and the mesh refinement criteria are dealt with in the context of a shape optimization problems. In particular, the sensitivities of the different ingredients ruling the problem (B-splines, finite element mesh, design behaviour, and error estimator) are studied in detail. The sensitivities of the finite element mesh coordinates and the error estimator allow their projection from one design to the next, giving an “a priori knowledge” of the error distribution on the new design. This allows to build up a finite element mesh for the new design with a specified and controlled level of error. The robustness and reliability of the proposed methodology is checked out with some 2D examples.
Abstract
This work presents a methodology based on the use of adaptive mesh refinement (AMR) techniques in the context of shape optimization problems analyzed by the Finite Element [...]
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Reliability estimation of the sheet stamping process using support vector machines
J. Hurtado, F. Zarate, E. Oñate

Int. J. of Vehicle Design (2005). Vol. 39 (1-2), pp. 110–124

Abstract
An important concern in sheet stamping is the risk of obtaining brittle final products that can be affected by fracture. Monte Carlo simulations presented herein show that this is governed by two main factors, namely static and dynamic friction coefficients. Whereas the latter correlates in a non-linear manner with minimum and maximum end thickness, the relationship of these design parameters to the former exhibits a bifurcation that is typical of highly non-linear phenomena, in which there is a sensitivity to small perturbations of the input values (chaos). In order to estimate the reliability of the process (i.e., the probability of obtaining brittle products due to low minimum and maximum thicknesses) with a reduced number of Monte Carlo runs, it is proposed to assimilate the problem to a pattern recognition task, due to the existence of two classes, namely robust and brittle. Among many pattern recognition algorithms that are useful to this end, use is made of support vector machines, as this incorporates the powerful tool of class margins that allow a drastic reduction of the number of simulations.
Abstract
An important concern in sheet stamping is the risk of obtaining brittle final products that can be affected by fracture. Monte Carlo simulations presented herein show that [...]
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A viscous shell formulation for the analysis of thin sheet metal forming
E. Oñate, O. Zienkiewicz

Int. J. Mechanical Sciences (1983). Vol. 25 (5), pp. 305-335

Abstract
A finite element method to analyse large plastic deformations of thin sheets of metal is presented. The formulation is based on an extension of the general viscoplastic flow theory for continuum problems to deal with thin shells. Axisymmetric situations are considered first and here the simple two noded reduced integration element is used. Numerical results for the stretch forming and deep drawing of circular sheets are presented and comparison with experimental results is made. The second part of the paper deals with the deformation of sheets of arbitrary shape. The general viscous shell element is derived from the standard reduced integration, “thick shell element. Numerical results for simple 3-D sheet forming problems are given.
Abstract
A finite element method to analyse large plastic deformations of thin sheets of metal is presented. The formulation is based on an extension of the general viscoplastic flow [...]
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Numerical analysis of stereolithography processes using the finite element method
G. Bugeda, M. Cervera, G. Lombera, E. Oñate

Rapid Prototyping Journal (1995). Vol. 1 (2), pp. 13-23

Abstract
Stereolithography (SLA) is one of the most important techniques used in rapid prototyping processes. It has a great industrial interest because it allows for dramatic time savings with respect to traditional manufacturing processes. One of the main sources of error in the final dimensions of the prototype is the curl distortion effect owing to the shrinkage of the resin during the SLA process. Presents a study of the influence of different constructive and numerical parameters in the curl distortion, an analysis which was made using the computer code stereolithography analysis program, developed to model SLA processes using the finite element method. Also briefly presents this code.
Abstract
Stereolithography (SLA) is one of the most important techniques used in rapid prototyping processes. It has a great industrial interest because it allows for dramatic time [...]
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Fatigue analysis of materials and structures using a continuum damage model
O. Salomon, S. Oller, E. Oñate

International Journal of Forming Processes (2002). Vol. 5 (2-3-4), pp. 493-503

Abstract
The scatter in the fatigue life of the metallic structures seems to be mainly caused by internal defects of the material (porosity, inclusions as oxide films and carbon layers, grain boundaries, etc.). As discontinuities in geometry, defects cause stress concentration and are therefore prone to fatigue crack initiation. Here, a fatigue model based in continuum mechanic with its general expressions for the elasto-plastic-damage constitutive equations, previously developed by the authors, is extended to include the effects of material internal defects. In this stress life approach the material is considered to be non-homogenous. The material strength is randomly assigned and Stress-Nº of cycles curves are scaled down according to material strength of each point. Limit values for material strength are based on experimental tests of samples with different degree of porosity.
Abstract
The scatter in the fatigue life of the metallic structures seems to be mainly caused by internal defects of the material (porosity, inclusions as oxide films and carbon layers, [...]
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Finite element nonlinear analysis of concrete structures using a “plastic-damage model”
S. Oller, E. Oñate, J. Oliver, J. Lubliner

Engineering Fracture Mechanics (1990). Vol. 35 (1-2-3), pp. 219-231

Abstract
In this paper a plastic damage model for nonlinear finite element analysis of concrete is presented. The model is based on standard plasticity theory for frictional materials. Details of the expressions of a new yield function proposed and of the evolution laws of the model parameters are given. The model allows to include elastic and plastic stiffness degradation effects. This is also discussed in the paper together with the problem of mesh objectivity, and the a posteriori determination of cracks. Finally, one example of application which shows the accuracy of the model is also given.
Abstract
In this paper a plastic damage model for nonlinear finite element analysis of concrete is presented. The model is based on standard plasticity theory for frictional [...]
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A computational model for progressive cracking in large dams due to the swelling of concrete
M. Cervera, J. Oliver, E. Herrero, E. Oñate

Engineering Fracture Mechanics (1990). Vol. 35 (1-3), pp. 573-585

Abstract
The paper presents a computational model for the analysis of large concrete gravity dams subjected to severe damage due to internal actions. It has been observed in several operating concrete dams that the combined effects of water intrusion and concrete expansion produce a time-advancing deteriorating process that may endanger the global stability of the construction. The present study was undertaken to simulate numerically the observed phenomena and to enable to predict future developments. Tensile cracking of the concrete is modelled using an elasticfracturing constitutive model. The model is able to simulate in a realistic manner the phenomena of primary and secondary crack initiation, elastic degradation, crack closing and reopening. The triggering of the volumetric expansion due to water intrusion is linked to the onset of cracking at each point, assuming that water enters the dam mostly through the cracks. Temperature and pore-water pressure effects are included using assumed distributions based on available field data. Construction joints are modelled using a frictional joint element, although a “constitutive alternative” is outlined. Close surveillance of the behaviour of a dam that presented this sort of problem was used to calibrate the numerical model and to confirm the obtained results.
Abstract
The paper presents a computational model for the analysis of large concrete gravity dams subjected to severe damage due to internal actions. It has been observed in several [...]
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Numerical aerodynamic analysis of large buildings using a finite element model with application to a telescope building
R. Codina, C. Morton, E. Oñate, O. Soto

Int. J. of Num. Meths. for Heat and Fluid Flow (2000). Vol. 10 (5-6), pp. 616-633

Abstract
Presents a numerical strategy for the aerodynamic analysis of large buildings, with an application to the simulation of the air flow within a telescope building. The finite element formulation is presented first, and then the methodology followed to obtain significant data from the calculations is described. The quality of the ventilation of the building is defined by the average residence times, and the feasibility of this ventilation by the actions created on the instruments and the general flow pattern.
Abstract
Presents a numerical strategy for the aerodynamic analysis of large buildings, with an application to the simulation of the air flow within a telescope building. The finite [...]
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Mould filling simulation using finite elements
R. Codina, U. Schäfer, E. Oñate

Int. J. of Num. Meths. for Heat and Fluid Flow (1994). Vol. 4 (1), pp. 291-310

Abstract
In this paper we consider several aspects related to the application of the pseudo‐concentration techniques to the simulation of mould filling processes. We discuss, in particular, the smoothing of the front when finite elements with interior nodes are employed and the evacuation of air through the introduction of temporary free wall nodes. The basic numerical techniques to solve the incompressible Navier—Stokes equations are also briefly described. The main features of the numerical model are the use of div‐stable velocity—pressure interpolations with discontinuous pressures, the elimination of the pressure via an iterative penalty formulation, the use of the SUPG approach to deal with convection‐dominated problems and the temporal integration using the generalized trapezoidal rule. At the end of the paper we present some numerical results obtained for a two‐dimensional test problem showing the ability of the method to capture complicated flow patterns.
Abstract
In this paper we consider several aspects related to the application of the pseudo‐concentration techniques to the simulation of mould filling processes. We discuss, in [...]
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Analysis of bridges by the finite strip method
E. Oñate

Hormigón y Acero (1977). Vol. 124, pp. 53-85

Abstract
Se presenta el análisis general de estructuras formadas por un ensamblaje de placas y vigas y con sección transversal constante, mediante una combinación de elementos finitos transversalmente y series de Fourier en dirección longitudinal. Se ha tenido en cuenta en el análisis el efecto de la deformación transversal debida al esfuerzo cortante, que puede ser importante si los espesores de los componentes que forman la estructura son considerables. Debido a la generalidad del análisis se evita la dificultad de tener que establecer hipótesis simplificadoras para idealizar la estructura, a veces lejos de la realidad, como ocurre en el análisis clásico mediante las teorías de Guyon-Massonet o la de la losa ortótropa. Asimismo permite el estudio de estructuras complejas, como puentes con sección transversal tipo cajón, etc., resultado ser uno de los métodos más versátiles y económicos para el análisis de puentes de los más diversos tipos. Al final del estudio se analizan diversas estructuras tipo puente, comparándose los resultados obtenidos aplicando el método de la banda finita, el método de los elementos finitos y el método del prisma finito.
Abstract
Se presenta el análisis general de estructuras formadas por un ensamblaje de placas y vigas y con sección transversal constante, mediante una combinación [...]
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Wrinkling and folding analysis of elastic membranes using an enhanced rotation-free thin shell triangular element
F. Flores, E. Oñate

Finite Elements in Analysis and Design (2011). Vol. 47 (9), pp. 982-990

Abstract
This paper presents a formulation for analysis of thin elastic membranes using a rotation-free shell element within an explicit time integration strategy. The applications presented are isotropic/anisotropic rectangular membranes under shear forces and fabric drapes falling over a pedestal. Results are compared with other numerical results existing in the literature.
Abstract
This paper presents a formulation for analysis of thin elastic membranes using a rotation-free shell element within an explicit time integration strategy. The applications [...]
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Advancing front techniques for filling space with arbitrary separated objects
R. Löhner, E. Oñate

Finite Elements in Analysis and Design (2010). Vol. 46 (1-2), pp. 140-151

Abstract
A review is given of advancing front techniques for filling space with arbitrary separated objects. Over the last decade, these techniques have reached a considerable degree of maturity and are being used to generate clouds of points for SPH and FPM simulations, as well as spheres, ellipsoids, objects defined by a collection of spheres or polyhedral objects for DEM simulations. Algorithmic as well as implementational aspects are discussed. Techniques to obtain maximum packing, such as closest object placement (during generation) and move/enlarge (after generation) are also considered. Several examples are included that demonstrate the capabilities developed.
Abstract
A review is given of advancing front techniques for filling space with arbitrary separated objects. Over the last decade, these techniques have reached a considerable degree [...]
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Nonlinear finite element analysis of orthotropic and prestressed membrane structures
J. Valdes-Vazquez, J. Canet, E. Oñate

Finite Elements in Analysis and Design (2009). Vol. 45 (6-7), pp. 395-405

Abstract
A new methodology for the geometrically nonlinear analysis of orthotropic membrane structures using triangular finite elements is presented. The approach is based on writing the constitutive equations in the principal fiber orientation of the material. A direct consequence of the fiber orientation strategy is the possibility to analyze initially out-of-plane prestressed membrane structures. An algorithm to model wrinkling behavior is also described. Examples of application to a number of membrane structures are presented.
Abstract
A new methodology for the geometrically nonlinear analysis of orthotropic membrane structures using triangular finite elements is presented. The approach is based on writing [...]
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Advances in FE explicit formulation for simulation of metalforming processes
J. Rojek, O. Zienkiewicz, E. Oñate, E. Postek

Journal of Materials Processing Technology (2001). Vol. 119, pp. 41-47

Abstract
This paper presents some advances of finite element explicit formulation for simulation of metal forming processes. Because of their computational efficiency, finite element programs based on the explicit dynamic formulation proved to be a very attractive tool for the simulation of metal forming processes. The use of explicit programs in the sheet forming simulation is quite common, the possibilities of these codes in bulk forming simulation in our opinion are still not exploited sufficiently. In our paper, we will consider aspects of bulk forming simulation. We will present new formulations and algorithms developed for bulk metal forming within the explicit formulation. An extension of a finite element code for the thermomechanical coupled analysis is discussed. A new thermomechanical constitutive model developed by the authors and implemented in the program is presented. A new formulation based on the so-called split algorithm allows us to use linear triangular and tetrahedral elements in the analysis of large plastic deformations characteristic to forming processes. Linear triangles and tetrahedra have many advantages over quadrilateral and hexahedral elements. Linear triangles and tetrahedra based on the standard formulations exhibit volumetric locking and are not suitable for large plastic strain simulation. The new formulation allows to overcome this difficulty. New formulations and algorithms have been implemented in the finite element code Stampack developed at the International Centre for Numerical Methods in Engineering in Barcelona. Numerical examples illustrate some of the possibilities of the finite element code developed and validate new algorithms.
Abstract
This paper presents some advances of finite element explicit formulation for simulation of metal forming processes. Because of their computational efficiency, finite element [...]
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Application of explicit FE codes to simulation of sheet and bulk metal forming processes
J. Rojek, E. Oñate, E. Postek

Journal of Materials Processing Technology (1998). Vols. 80-81, pp. 620-627

Abstract
This paper presents the application of an explicit dynamic finite element code for simulation of metal forming processes, of both sheet and bulk forming. The experiences reported here have been gained during the development and use of our own explicit program Stampack. An original formulation of a triangular shell element without rotational degrees of freedom is reviewed combining the explicit sheet forming simulation with the implicit springback analysis as well as the parallelization of the explicit program described. An extension of a finite element code for coupled thermomechanical analysis is discussed. A new thermomechanical constitutive model developed by the authors and implemented in the program is presented. Numerical examples illustrate some of the possibilities of the finite element code developed.
Abstract
This paper presents the application of an explicit dynamic finite element code for simulation of metal forming processes, of both sheet and bulk forming. The experiences [...]
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Industrial applications of sheet stamping simulation using new finite element models
J. Rojek, J. Jovicevic, E. Oñate

Journal of Materials Processing Technology (1996). Vol. 60 (1-4), pp. 243-247

Abstract
The paper is aimed to present industrial applications of sheet stamping simulation using new finite element formulations developed in the International Center for Numerical Methods in Engineering in Barcelona. Theoretical formulation is briefly reviewed. Both continuum and shell elements have been considered. The new shell elements developed are based on a geometrically exact shell model treating the shell as one-director Cosserat surface. The formulation of the continuum elements employs the multiplicative decomposition of the deformation gradient tensor into its elastic and plastic parts. The new finite element models have been implemented in the in-house explicit dynamic code STAMPACK. A number of practical problems of sheet metalforming have been solved with the program. Some of the problems, namely stamping of a kitchen sink, hydraulic forming of an aeronautical part and stamping of a food can, have been presented in the paper. The examples give an idea of practical information that can be obtained from the computer simulation of a forming process. The results confirm a good behaviour of the formulation and program used in the industrial applications.
Abstract
The paper is aimed to present industrial applications of sheet stamping simulation using new finite element formulations developed in the International Center for Numerical [...]
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NUMISTAMP: a research project for assessment of finite-element models for stamping processes
E. Oñate, J. Rojek, C. Garino

Journal of Materials Processing Technology (1995). Vol. 50 (1-4), pp. 17-38

Abstract
This paper describes the objectives and current status of the research project NUMISTAMP currently under development at the International Center for Numerical Methods in Engineering of (CIMNE) located in Barcelona, Spain. The aim of this project is the assesment of different finite element models for simulation of sheet stamping processes. The models currently analyzed include: quasistatic viscoplastic flow and elastoplastic solid models and explicit dynamic models. Both shell and continuum elements are considered in most of these cases. The paper presents an overview of the basic features of the different models. Examples of application including some benchmark test cases proposed at NUMISHEET are also presented.
Abstract
This paper describes the objectives and current status of the research project NUMISTAMP currently under development at the International Center for Numerical Methods in Engineering [...]
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