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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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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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 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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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 using a fluid or a solid formulation of FSW processes with a 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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Computer Programming of free GUIs for the Analysis of the Behaviour of Marine Structures
J. Gutiérrez Romero, Z. B, J. García-Espinosa, M. Peyrau Rubio

Ships and Offshore Structures (2015). 11:5, 471-481 (preprint)

Abstract
This work presents the development of two free Graphical User Interfaces (GUI), called ''FASTLognoter'' and ''MorisonForm'', both focused on the analysis of the behaviour of offshore structures, especially of offshore wind turbines. The first one is related to the aeroelastic analysis of wind turbines, and the second is concerned with the seakeeping of marine structures. The development of these tools has been carried out using a powerful software called ''Lognoter''. This tool is free software for Knowledge Management in Technology (KMT), which integrates computer programming for allowing the development of GUIs. These GUIs give an open platform for conducting a parametric study of the structural and dynamic behaviour of marine structures. Their coupling permits the user to set a suitable way to evaluate new concepts in marine structures. Finally, an application for the intensive analysis of offshore wind turbines is shown.
Abstract
This work presents the development of two free Graphical User Interfaces (GUI), called ''FASTLognoter'' and ''MorisonForm'', both focused on [...]
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Desarrollo de un sistema de apoyo a la decisión para optimizar el comportamiento de barcos de vela
J. García-Espinosa, I. Ortigosa, A. Fernández

Rev. int. métodos numér. cálc. diseño ing. (2015). Vol. 31, (3)

Abstract
In this paper, the conception and design of a new monitoring system for a racing yachts rig is presented. The sensors developed are able to process the measured strain data, by applying artificial neural networks (ANN) algorithms, and then evaluate the load acting on an element and identify the direction of the action of that force. This way, it is possible to identify the actual operating conditions of the yacht rig. The required data for ANN training is generated from the results obtained from different finite element method (FEM) computational models of the device. Furthermore, during the design phase of the system, different experimental campaigns were carried out. The experimental tests were designed to serve as proof of concept, as well as to validate the different procedures used in the system development and application. The developed monitoring system is wireless, low-intrusive and easily adaptable to any yacht configuration. This work also presents the integration of the monitoring system into a coupled fluid-structure computation model for the sails and rig of a boat. The resulting system is an efficient tool for evaluating performance and decision support in the adjustment of a sailboat rig.
Abstract
In this paper, the conception and design of a new monitoring system for a racing yachts rig is presented. The sensors developed are able to process the measured strain data, [...]
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Accurate modelling of the elastic behavior a continuum with the Discrete Element Method
M. Celigueta, S. Latorre, F. Arrufat, E. Oñate

Computational Mechanics (2017). (prepint) Vol. 60 (6), pp. 997-1010

Abstract
The Discrete Element Method (DEM) has been used for modeling continua, like concrete or rocks. However, it requires a big calibration effort, even to capture just the linear elastic behavior of a continuum modelled via the classical force-displacement relationships at the contact interfaces between particles. In this work we propose a new way for computing the contact forces between discrete particles. The newly proposed forces take into account the surroundings of the contact, not just the contact itself. This brings in the missing terms that provide an accurate approximation to an elastic continuum, and avoids calibration of the DEM parameters for the purely linear elastic range.
Abstract
The Discrete Element Method (DEM) has been used for modeling continua, like concrete or rocks. However, it requires a big calibration effort, even to capture just the linear [...]
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An accurate FIC-FEM formulation for the 1D convection-diffusion-reaction equation
E. Oñate, J. Miquel, P. Nadukandi

Comput. Methods Appl. Mech. Engrg., (2016). Vol. 298() pp. 373-406 Vol. 298, pp. 373-406

Abstract
In this paper we present an accurate stabilized FIC-FEM formulation for the 1D advection-diffusion-reaction equation in the exponential and propagation regimes using two stabilization parameters. Both the steady-state and transient solutions are considered. The stabilized formulation is based on the standard Galerkin FEM solution of the governing differential equations derived via the Finite Increment Calculus (FIC) method. The steady-state problem is considered first. The optimal value of the two stabilization parameters ensuring an exact (nodal) FEM solution using uniform meshes of linear 2-noded elements is obtained. In the absence of the absorption term the formulation simplifies to the standard one-parameter Petrov-Galerkin method for the advection-diffusion problem. For the diffusion-reaction case one stabilization parameter is just needed and the diffusion-type stabilization term is identical to that obtained by Felippa and O˜ nate [16] using a variational FIC approach. A procedure for computing the stabilization parameters for the transient problem is proposed. The accuracy of the new FIC-FEM formulation is demonstrated in the solution of steady-state and transient 1D advection-diffusion-radiation problems for a the range of physical parameters and boundary conditions. Finally we outline the procedure to extend the 1D FIC-FEM formulation to multidimensions.
Abstract
In this paper we present an accurate stabilized FIC-FEM formulation for the 1D advection-diffusion-reaction equation in the exponential and propagation regimes using two stabilization [...]
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Accurate FIC-FEM formulation for the multidimensional steady-state advection diffusion–absorption equation
E. Oñate, P. Nadukandi, J. Miquel

Comput. Methods Appl. Mech. Engrg., (2017). Vol. 327, pp. 352-368

Abstract
In this paper we present an accurate stabilized FIC-FEM formulation for the multidimensional steady-state advection-diffusion-absorption equation. The stabilized formulation is based on the Galerkin FEM solution of the governing differential equations derived via the Finite Increment Calculus (FIC) method using two stabilization parameters. The value of the two stabilization parameters ensuring an accurate nodal FEM solution using uniform meshes of linear elements is obtained from the optimal values for the 1D problem. The accuracy of the new FIC-FEM formulation is demonstrated in the solution of 2D steadystate advection-diffusion-absorption problems for a range of physical parameters and boundary conditions.
Abstract
In this paper we present an accurate stabilized FIC-FEM formulation for the multidimensional steady-state advection-diffusion-absorption equation. The stabilized formulation [...]
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Unified Lagrangian formulation for solid and fluid mechanics and FSI problems
A. Franci, E. Oñate, J. Carbonell

Comput. Methods Appl. Mech. Engrg., (2016). Vol. 107(11) pp. 970-990 (preprint) Vol. 298, pp. 520-547

Abstract
We present a Lagrangian monolithic strategy for solving fluid-structure interaction (FSI) problems. The formulation is called Unified because fluids and solids are solved using the same solution scheme and unknown variables. The method is based on a mixed velocity-pressure formulation. Each time step increment is solved via an iterative partitioned two-step procedure. The Particle Finite Element Method (PFEM) is used for solving the fluid parts of the domain, while for the solid ones the Finite Element Method (FEM) is employed. Both velocity and pressure fields are interpolated using linear shape functions. For quasiincompressible materials, the solution scheme is stabilized via the Finite Calculus (FIC) method. The stabilized elements for quasi-incompressible hypoelastic solids and Newtonian fluids are called VPS/S-element and VPS/F-element, respectively. Other two non-stabilized elements are derived for hypoelastic solids. One is based on a Velocity formulation (V-element) and the other on a mixed Velocity-Pressure scheme (VP-element). The algorithms for coupling the solid elements with the VPS/F fluid element are explained in detail. The Unified formulation is validated by solving benchmark FSI problems and by comparing the numerical solution to the ones published in the literature.
Abstract
We present a Lagrangian monolithic strategy for solving fluid-structure interaction (FSI) problems. The formulation is called Unified because fluids and solids are solved [...]
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Computation of the stabilization parameter for the finite element solution of advective–diffusive problems
E. Oñate, J. García-Espinosa, S. Idelsohn

Int. J. of Num. Meths. in Fluid (1997). Vol. 25, pp. 1387-1407;

Abstract
In a previous paper a general procedure for deriving stabilized finite element schemes for advective type problems based on invoking higher order balance laws over finite size domains was presented. This provides an expression for the element stabilization parameter in terms of the solution residual and its first derivatives in a kind of iterative or adaptative manner. Details of the application of this procedure to 1D and 2D advective- diffusive problems are given. Some examples of applications showing the potential of the new approach are presented.
Abstract
In a previous paper a general procedure for deriving stabilized finite element schemes for advective type problems based on invoking higher order balance laws over finite [...]
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A FEM-DEM technique for studying the motion of particles in non-Newtonian fluids. Application to the transport of drill cuttings in wellbores
M. Celigueta, K. Deshpande, S. Latorre, E. Oñate

Comp. Part. Mech (2016). Vol. 3(2) pp. 263-276 Vol. 30 (2), pp. 263-276

Abstract
We present a procedure for coupling the finite element method (FEM) and the discrete element method (DEM) for analysis of the motion of particles in non-Newtonian fluids. Particles are assumed to be spherical and immersed in the fluid mesh. A new method for computing the drag force on the particles in a non-Newtonian fluid is presented. A drag force correction for non-spherical particles is proposed. The FEM-DEM coupling procedure is explained for Eulerian and Lagrangian flows and the basic expressions of the discretized solution algorithm are given. The usefulness of the FEM-DEM technique is demonstrated in its application to the transport of drill cuttings in wellbores.
Abstract
We present a procedure for coupling the finite element method (FEM) and the discrete element method (DEM) for analysis of the motion of particles in non-Newtonian fluids. [...]
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Lagrangian analysis of multiscale particulate flows with the particle finite element method
E. Oñate, M. Celigueta, S. Latorre, G. Casas, R. Rossi, J. Rojek

Comp. Part. Mech (2014). Vol. 1 pp. 85-102 (prepint) Vol. 1 pp. 85-102

Abstract
We present a Lagrangian numerical technique for the analysis of flows incorporating physical particles of different sizes. The numerical approach is based on the Particle Finite Element Method (PFEM) which blends concepts from particle-based techniques and the FEM. The basis of the Lagrangian formulation for particulate flows and the procedure for modelling the motion of small and large particles that are submerged in the fluid are described in detail. The numerical technique for analysis of this type of multiscale particulate flows using a stabilized mixed velocity-pressure formulation and the PFEM is also presented. Examples of application of the PFEM to several particulate flows problems are given.
Abstract
We present a Lagrangian numerical technique for the analysis of flows incorporating physical particles of different sizes. The numerical approach is based on the Particle [...]
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Finite increment calculus (FIC). A framework for deriving enhanced computational methods in mechanics
E. Oñate

Adv. Model. and Simul. in Eng. Sci (2016). Vol. 3 pp. 14 Vol. 3 (14)

Abstract
In this paper we present an overview of the possibilities of the ﬁnite increment calculus (FIC) approach for deriving computational methods in mechanics with improved numerical properties for stability and accuracy. The basic concepts of the FIC procedure are presented in its application to problems of advection-diﬀusion-reaction, ﬂuid mechanics and ﬂuid-structure interaction solved with the ﬁnite element method (FEM). Examples of the good features of the FIC/FEM technique for solving some of these problems are given. A brief outline of the possibilities of the FIC/FEM approach for error estimation and mesh adaptivity is given.
Abstract
In this paper we present an overview of the possibilities of the ﬁnite increment calculus (FIC) approach for deriving computational methods in mechanics with improved numerical [...]
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A simple FEM-DEM technique for fracture prediction in materials and structures
F. Zárate, E. Oñate

Comp. Part. Mech (2015). Vol. 2(3) pp. 301-314 (prepint) Vol. 2 (3), pp. 301-314

Abstract
This paper presents a new computational technique for predicting the onset and evolution of fracture in a continuum in a simple manner combining the finite element method (FEM) and the discrete element method (DEM). Once a crack is detected at an element side in the FE mesh, discrete elements are generated at the nodes sharing the side and a simple DEM mechanism is considered to follow the evolution of the crack. The combination of the DEM with simple 3-noded linear triangular elements correctly captures the onset of fracture and its evolution, as shown in several examples of application in two and three dimensions.
Abstract
This paper presents a new computational technique for predicting the onset and evolution of fracture in a continuum in a simple manner combining the finite element method [...]
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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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Adjoint-based Adaptive Finite Element Method For The Compressible Euler Equations Using Finite Calculus
M. Kouhi, E. Oñate, D. Mavriplis

Eugenio Oñate's Journal Papers (2015). Vol. 46 pp. 422-435

Abstract
In this paper, an adjoint-based error estimation and mesh adaptation framework is developed for the compressible inviscid flows. The algorithm employs the Finite Calculus (FIC) scheme for the numerical solution of the flow and discrete adjoint equations in the context of the Galerkin finite element method (FEM) on triangular grids. The FIC scheme treats the instabilities normally generated in the numerical solution of the fluid equations through adding two stabilization terms, called streamline term and transverse term, to the original central-based discretized formulation. The non-linear system of equations resulting from the flow problem is solved implicitly using a damped Newton’s method accompanied with the exact Jacobian matrix. A defect corrected scheme is implemented to iteratively solve the linear system of equations related to the adjoint problem benefiting from the transpose of the Jacobian matrix. At each iteration, the linear systems of equations resulting from the fluid and adjoint problems are solved using a preconditioned GMRES method. Having calculated the error of a specified output functional locally, an h-refinement methodology based on the element subdivision is performed to refine the candidate elements. The quality of the numerical results proves the capability of the presented approach for the adjoint-based error estimation and mesh adaptation problems in different flow regimes.
Abstract
In this paper, an adjoint-based error estimation and mesh adaptation framework is developed for the compressible inviscid flows. The algorithm employs the Finite Calculus [...]
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A local constitutive model for the discrete element method. Application to geomaterials and concrete
E. Oñate, F. Zárate, J. Miquel, M. Santasusana, M. Celigueta, F. Arrufat, R. Gandikota, K. Valiullin, L. Ring

Eugenio Oñate's Journal Papers (2015). Vol. 2(2) pp. 139-160

Abstract
This paper presents a local constitutive model for modelling the linear and non linear behavior of soft and hard cohesive materials with the discrete element method (DEM). We present the results obtained in the analysis with the DEM of cylindrical samples of cement, concrete and shale rock materials under a uniaxial compressive strength (UCS) test, different triaxial tests, a uniaxial strain compaction (USC) test and a brazilian tensile strength (BTS) test. DEM results compare well with the experimental values in all cases.
Abstract
This paper presents a local constitutive model for modelling the linear and non linear behavior of soft and hard cohesive materials with the discrete element method (DEM). [...]
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A Stabilized Finite Element Formulation For High-Speed Inviscid Compressible Flows Using Finite Calculus
M. Kouhi, E. Oñate

Int. J. Numer. Meth. Engng. (2014). Vol. 74(2) pp. 872-897 Vol. 74 (2), pp. 872-897

Abstract
This paper aims at the development of a new stabilization formulation based on the Finite Calculus (FIC) scheme for solving the Euler equations using the Galerkin finite element method (FEM) on unstructured triangular grids. The FIC method is based on expressing the balance of fluxes in a space-time domain of finite size. It is used to prevent the creation of instabilities typically present in numerical solutions due to the high convective terms and sharp gradients. Two stabilization terms, respectively called streamline term and transverse term, are added via the FIC formulation to the original conservative equations in the spacetime domain. An explicit fourth order Runge-Kutta scheme is implemented to advance the solution in time. The presented numerical test examples for inviscid flows prove the ability of the proposed stabilization technique for providing appropriate solutions especially near shock waves. Although the derived methodology delivers precise results with a nearly coarse mesh, a mesh refinement technique is coupled to the solution process for obtaining a suitable mesh particularly in the high gradient zones.
Abstract
This paper aims at the development of a new stabilization formulation based on the Finite Calculus (FIC) scheme for solving the Euler equations using the Galerkin finite element [...]
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Seakeeping with the semi-Lagrangian particle finite element method
P. Nadukandi, B. Servan Camas, P. Becker, J. García-Espinosa

Comp. Part. Mech. (2016). 4: 321-329 (preprint)

Abstract
The application of the semi-Lagrangian particle finite element method (SL–PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL–PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.
Abstract
The application of the semi-Lagrangian particle finite element method (SL–PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating [...]
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A real-time decision support system for the adjustment of sailboat rigging
I. Ortigosa, J. García-Espinosa

Brodogradnja (2015). 66 (4), 39-56

Abstract
The operational complexity and performance requirements of modern racing yachts demand the use of advanced applications, such as a decision support system (DSS) able to assist crew members during navigation. In this article, the authors describe a near-time computational solver as the main piece of a DSS which analyses and monitors the behaviour of sails and rigging. The solver is made up of two different interconnected tools: an iterative FluidStructure Interaction algorithm and an advanced Wireless Sensor Network to monitor rigging. The real-time DSS quantifies crew manoeuvres in physical terms, which are reproduced by a simulation program. It can be used in the design phase of sailing yachts and as an aid for realtime boat performance optimisation and accident prevention. This novel DSS is a useful tool for navigation, especially in races.
Abstract
The operational complexity and performance requirements of modern racing yachts demand the use of advanced applications, such as a decision support system (DSS) able to assist [...]
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Modeling incompressible flows at low and high Reynolds numbers via a finite calculus–finite element approach
E. Oñate, A. Valls, J. García-Espinosa

Journal of Computational Physics (2007). 224 (1), 332-351

Abstract
We present a formulation for incompressible ﬂows analysis using the ﬁnite element method (FEM). The necessary stabilization for dealing with convective eﬀects and the incompressibility condition is modeled via the ﬁnite calculus (FIC) method. The stabilization terms introduced by the FIC formulation allow to solve a wide range of ﬂuid ﬂow problems for low and high Reynolds numbers ﬂows without the need for a turbulence model. Examples of application of the FIC/FEM formulation to the analysis of 2D and 3D incompressible ﬂows with moderate and large Reynolds numbers are presented.
Abstract
We present a formulation for incompressible ﬂows analysis using the ﬁnite element method (FEM). The necessary stabilization for dealing with convective eﬀects and the [...]
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Tool development based on FAST for performing design optimization of offshore wind turbines: FASTLognoter
J. Gutiérrez Romero, B. Zamora, J. García-Espinosa, M. Peyrau

Renewable Energy (2012). 55, 69-78, 2012

Abstract
The new engineering FASTLognoter software is presented. This code is essentially the result of the integration of two tools, along with some additional features. Theﬁrst basis tool is FAST (developed by NREL), a comprehensive aeroelastic simulator code for wind turbines. The second basis tool is Lognoter (developed by CompassIS), a general-purpose commercial software for managing and creating engineering forms. The integration of FAST and Lognoter gives a useful, comprehensive and versatile toolkit, which is veriﬁed in this work by means of bibliographic documented cases. An important advantage of the tool presented is the parametric design capability, allowing the user of FAST/AeroDyn/HydroDyn codes to analyze a massive group of cases; therefore, optimal design can be carried out.
Abstract
The new engineering FASTLognoter software is presented. This code is essentially the result of the integration of two tools, along with some additional features. Theﬁrst [...]
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Simulation of Water Circulation over a Model of a Submarine Canyon by Using FIC-FEM Numerical Model
A. German, J. García-Espinosa, M. Espino, M. Maidana Silanes

Journal of Waterway, Port, Coastal, and Ocean Engineering (2011). 138 (1), 21-29

Abstract
A set of numerical model experiments has been conducted to simulate the circulation driven by oscillatory forcing over a theoretical continental slope configuration used previously in laboratory experiments. The test case considered was the numerical simulation of the flow over a model of a submarine canyon, and the numerical model used in the analysis was a coastal ocean model version based on an adaptation of the finite-calculus–finite-element method (FIC-FEM) approach implemented in the commercial package Tdyn. Two cases were analyzed involving changes in fluid density. Structured and unstructured finite-element spatial discretizations were generated for the same study domain to compare the resulting velocity field with outputs from the laboratory experiments and to assess which mesh provided a better representation of the complex geometry of the channel model and the water circulation process. The comparison between the laboratory results from the reference article and the output of the numerical model showed good agreement in the structure and magnitude of the phaseaveraged and residual velocity fields.
Abstract
A set of numerical model experiments has been conducted to simulate the circulation driven by oscillatory forcing over a theoretical continental slope configuration used previously [...]
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On the interpolation of normal vectors for triangle meshes
P. Ubach de Fuentes, C. Estruch, J. García-Espinosa

International journal for numerical methods in engineering (2013). 96 (4), 247-268

Abstract
This paper analyzes the problem arising from the need to assign information about the normal vectors to the surface at the nodes of a mesh of triangles. Meshes of triangles do not have normals uniquely defined at the nodes. A widely used technique to compute the normal direction at any given node is to compute the weighted average of the normals of each surrounding triangle. The present study proposes new weighting factors to compute the normal directions at the nodes of the mesh of triangles of a general surface. Previous weights found in the literature used the geometric dimensions of the triangles themselves to design the weighting factors. The new factors are proposed using the triangles’ circumscribed circles dimensions. The new weights provide superior results than the ones obtained by previous best practices for a wide range of surfaces. An advanced framework based on the approachability of smooth surfaces by quadrics is presented and used. This framework helps to understand the improved performance of the presented factors with respect to other factors found in the literature. A comprehensive numerical comparison analysis is performed, and the most precise of all factors is clearly identified.
Abstract
This paper analyzes the problem arising from the need to assign information about the normal vectors to the surface at the nodes of a mesh of triangles. Meshes of triangles [...]
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Non-linear dynamic analysis of the response of moored floating structures
J. Gutiérrez Romero, J. García-Espinosa, B. Servan Camas, B. Zamora-Parra

Marine Structures (2016). Vol. 49 pp. 116-137 49, 116-137 (preprint)

Abstract
The complexity of the dynamic behaviour of offshore marine structures requires advanced simulations tools for the accurate assessment of the seakeeping behaviour of these devices. The aim of this work is to present a time-domain model for solving the dynamics of floating marine devices, subjected to non-linear environmental loads and paying special attention on the mooring dynamics. First, the formulation of the hydrodynamic approach for solving the wave-floater interaction is introduced. Second, the solver of the mooring dynamics, based on a non-linear Finite Element Method approach, is presented. Third, a procedure for coupling the hydrodynamic along with other external loads, with the floating structure and mooring dynamics is described. Fourth, some validation examples and comparisons among different mooring approaches are presented. Fifth, an analysis of the OC3 floating wind turbine concept is performed to study the influence of different mooring models, the effects of non-linear waves on the platform, and the tension in the mooring system. The dynamic mooring model along with the second-order wave model produce realistic simulations of the floating wind turbine performance.
Abstract
The complexity of the dynamic behaviour of offshore marine structures requires advanced simulations tools for the accurate assessment of the seakeeping behaviour of these [...]
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Computation of turbulent flows using a finite calculus–finite element formulation
E. Oñate, A. Valls, J. García-Espinosa

International journal for numerical methods in fluids (2007). 54 (6‐8), 609-637, 2007

Abstract
We present a formulation for analysis of turbulent incompressible flows using a stabilized finite element method (FEM) based on the finite calculus (FIC) procedure. The stabilization terms introduced by the FIC approach allow to solve a wide range of fluid flow problems at different Reynolds numbers, including turbulent flows, without the need of a turbulence model. Examples of application of the FIC/FEM formulation to the analysis of 2D and 3D incompressible flows at large Reynolds numbers exhibiting turbulence features are presented.
Abstract
We present a formulation for analysis of turbulent incompressible flows using a stabilized finite element method (FEM) based on the finite calculus (FIC) procedure. The stabilization [...]
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Analysis of a consistency recovery method for the 1D convection–diffusion equation using linear finite elements
J. García-Espinosa, A. Valls, E. Oñate

International journal for numerical methods in fluids (2008). 57 (9), 1291-1320, 2008

Abstract
For residual-based stabilization methods such as streamline-upwind Petrov–Galerkin (SUPG) and ﬁnite calculus (FIC), the higher-order derivatives of the residual that appear in the stabilization term vanish when simplicial elements are used. The sub-grid scale method using orthogonal sub-scales (OSS) attempts to recover the lost consistency by using a ﬁne-scale projected residual in the stabilization term. The FIC method may also be cast into an OSS form with very little manipulation using an auxiliary convective projection equation. This paper discusses the gain/loss by recovering the consistency of the discrete residual in the stabilization terms via the form that includes the convective projection (as in the OSS method). We present the von Neumann analysis of the FIC method with recovered consistency (FIC RC) for the 1D convection–diffusion problem and we compare it with the standard Bubnov–Galerkin linear ﬁnite element method and FIC/SUPG methods. The transient analysis is done by examining the discrete dispersion relation of the stabilization methods. The spectral results for the semi-discrete and fully discrete problem are presented with time integration done by the trapezoidal and second-order backward differencing formula schemes. The effect of lumping the effective mass matrix T is considered relative to using a consistent form. The effect of reﬁnement in space and time is also discussed. Finally, an optimal expression for the stabilization parameter for the FIC RC method on a uniform grid and for the steady state is given and its performance in the transient mode is discussed.
Abstract
For residual-based stabilization methods such as streamline-upwind Petrov–Galerkin (SUPG) and ﬁnite calculus (FIC), the higher-order derivatives of the residual that [...]
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