Eugenio Oñate's Journal Papers : Scipedia

A numerical framework for modelling tire mechanics accounting for composite materials, large strains and frictional contact
A. Cornejo Velázquez, V. Mataix, P. Wriggers, L. Barbu, E. Oñate

Computational Mechanics (2023). Open Access, Online June, pp. 1-25

Abstract
We present a general framework for the analysis and modelling of frictional contact involving composite materials. The study has focused on composite materials formed by a matrix of rubber and synthetic or metallic fibres, which is the case of standard tires. We detail the numerical treatment of incompressibility at large deformations that rubber can experience, as well as the stiffening effect that properly oriented fibres will induce within the rubber. To solve the frictional contact between solids, a Dual Augmented Lagrangian Multiplier Method is used together with the Mortar method. This ensures a variationally consistent estimation of the contact forces. A modified Serial-Parallel Rule of Mixtures is employed to model the behaviour of composite materials. This is a simple and novel methodology that allows the blending of constitutive behaviours as diverse as rubber (very low stiffness and incompressible behaviour) and steel (high stiffness and compressible behaviour) taking into account the orientation of the fibres within the material. The locking due to the incompressibility constraint in the rubber material has been overcome by using Total Lagrangian mixed displacement-pressure elements. A collection of numerical examples is provided to show the accuracy and consistency of the methodology presented when solving frictional contact, incompressibility and composite materials under finite strains.
Abstract
We present a general framework for the analysis and modelling of frictional contact involving composite materials. The study has focused on composite materials formed by a [...]
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Dataset of the temperature rise during granular flows in a rotating drum
R. Rangel, F. Kisuka, C. Hare, V. Vivacqua, A. Franci, E. Oñate, C. Wu

Data in Brief (2023). Vol. 48, Art. 109282

Abstract
This paper provides experimental data on the temperature rise during granular flows in a small-scale rotating drum due to heat generation. All heat is believed to be generated by conversion of some mechanical energy, through mechanisms such as friction and collisions between particles and between particles and walls. Particles of different material types were used, while multiple rotation speeds were considered, and the drum was filled with different amounts of particles. The temperature of the granular materials inside the rotating drum was monitored using a thermal camera. The temperature increases at specific times of each experiment are presented in form of tables, along with the average and standard deviation of the repetitions of each setup configuration. The data can be used as a reference to set the operating conditions of rotating drums, in addition to calibrating numerical models and validating computer simulations.
Abstract
This paper provides experimental data on the temperature rise during granular flows in a small-scale rotating drum due to heat generation. All heat is believed to be generated [...]
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Experimental investigation of heat generation during granular flow in a rotating drum using infrared thermography
R. Rangel, F. Kisuka, C. Hare, V. Vivacqua, A. Franci, E. Oñate, C. Wu

Powder Technology (2023). Vol. 426, Art. 118619

Abstract
Granular flow is common in many industrial applications, and involves heat generation from frictional contacts and inelastic collisions between particles. The self-heating process is still poorly understood despite being intrinsic to many processes. This work, for the first time, explores this problem experimentally by quantifying the temperature rise of granular flows in a rotating drum with a robust methodology based on infrared thermography. Particles of four different materials (lead, steel, plastic and glass) are used in the experiments, at various rotation speeds and drum fill ratios. To assess the mechanical behaviour, the flow regime of every experiment was determined. It was inferred that particles with higher density tend to generate more heat. It was also revealed that increasing the rotation speed favours the temperature rise. At the same time, the fill ratio had the least influence on the thermal response of the particulate systems considered.
Abstract
Granular flow is common in many industrial applications, and involves heat generation from frictional contacts and inelastic collisions between particles. The self-heating [...]
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Enhanced semi-explicit particle finite element method via a modified Strang splitting operator for incompressible flows
J. Marti, E. Oñate

Computational Particle Mechanics (2023). Published Online

Abstract
This work presents an enhanced version of the semi-explicit particle finite element method for incompressible flow problems. This goal is achieved by improving the methodology that results from applying the Strang splitting operator by adding an acceleration term. The advective step is evaluated on the mesh considering the new term leading to a more efficient algorithm. Two test cases are solved for validating the methodology and estimating its accuracy. The numerical results demonstrate that the proposed scheme improves the accuracy and the computational efficiency of the semi-explicit PFEM scheme.
Abstract
This work presents an enhanced version of the semi-explicit particle finite element method for incompressible flow problems. This goal is achieved by improving the methodology [...]
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A prototype of a micro-scale model for the distribution of NO2 in urban areas
I. Pouplana, S. Latorre, M. Maso, C. Alonso, E. Pérez, X. Guinart, I. Hernández, X. Baulies, E. Oñate

Atmospheric Pollution Research (2023). Vol. 14 (2), 101668

Abstract
We present a new 2.5D model for predicting the concentration of nitrogen dioxide (NO2) at street level in an urban area. This work develops the first prototype of a tool that should provide fast quantitative answers to help decision-making on the suitability of implementing traffic restrictions during air pollution episodes. The model first solves the wind flow over the city streets ignoring vorticity and turbulence. The obtained velocity field is used to transport the pollutant via a semi-Lagrangian model, combining the particle finite element method of second generation (PFEM2) with the finite element method. A variable absorption term is used to account for the part of the contaminant entering and leaving the calculation plane. The NO2 emissions are estimated from the historical traffic data. The model has been tested during four air pollution episodes in the city of Barcelona (Spain), two in summer and two in winter. A comparison against experimental measurements has been performed at seven different locations throughout the city with promising results.
Abstract
We present a new 2.5D model for predicting the concentration of nitrogen dioxide (NO2) at street level in an urban area. This work develops the first prototype of a tool that [...]
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Assessment of simplified momentum equations for free surface flows through rigid porous media
W. Düsterhöft-Wriggers, A. LARESE, E. Oñate, R. Thomas

Experimental and Computational Multiphase Flow (2023). Vol. 5, pp. 159–177

Abstract
In many applications, free surface flow through rigid porous media has to be modeled. Examples refer to coastal engineering applications as well as geotechnical or biomedical applications. Albeit the frequent applications, slight inconsistencies in the formulation of the governing equations can be found in the literature. The main goal of this paper is to identify these differences and provide a quantitative assessment of different approaches. Following a review of the different formulations, simulation results obtained from three alternative formulations are compared with experimental and numerical data. Results obtained by 2D and 3D test cases indicate that the predictive differences returned by the different formulations remain small for most applications, in particular for small porous Reynolds number ReP < 5000. Thus it seems justified to select a simplified formulation that supports an efficient algorithm and coding structure in a computational fluid dynamics environment. An estimated accuracy depending on the porous Reynolds number or the mean grain diameter is given for the simplified formulation.
Abstract
In many applications, free surface flow through rigid porous media has to be modeled. Examples refer to coastal engineering applications as well as geotechnical or biomedical [...]
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Development and coupling of numerical techniques for modeling micromechanical discrete and continuous media using real particle morphologies
R. Valera, J. Irazábal González, M. Junior, M. Muniz, M. Castro, R. Martínez, J. Pena, L. Moreno, C. Recarey, E. Oñate

Computational Particle Mechanics (2023). Vol.10 (1), pp. 121-141

Abstract
The main objective of this research is to formulate and couple technologies for modeling discrete and continuous media using real particle morphologies. To that end, two coupled formulations based on virtual modeling technologies of single real particles with another one called real particle packing technique are presented. The first formulation employs Fourier descriptors’ theory to virtually achieve the morphology and construct a repository of real particle geometries. The second formulation is a particle packing method, supported by advancing front techniques combined with dynamic methods. This method presents a stochastic formulation and allows the packing of particle systems following continuous, discrete and empirical statistical distributions. The coupling of both techniques is a very efficient tool to achieve discrete or continuous media geometries to solve engineering problems. Three different examples are developed to illustrate the usefulness of the formulations. The first one is a discrete angle-of-repose problem involving clusters of spheres (real particle morphologies are described with groups of spheres); in the second example the same angle-of-repose problem is resolved with real particles. In the third case, which involves continuous medium mechanics, a small-scale road engineering problem is modeled, specifically, the testing of an asphalt concrete.
Abstract
The main objective of this research is to formulate and couple technologies for modeling discrete and continuous media using real particle morphologies. To that end, two coupled [...]
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An enhanced semi-explicit particle finite element method for incompressible flows
J. Marti, E. Oñate

Computational Mechanics (2022). Vol. 70, pp. 607–620

Abstract
In this paper an enhanced version of the semi-explicit Particle Finite Element Method for incompressible flow problems is presented. This goal is achieved by improving the solution of the advective sub-problem that results of applying the Strang operator splitting to the Navier–Stokes equations. An acceleration term is taken into account in the solution of the advective step and the Stokes problem. The solution of the advetive step is perfomed using a SPH kernel. Two test cases are solved for validating the methodology and estimating its accuracy. The numerical results demonstrate that the proposed scheme improves the accuracy of the semi-explicit PFEM scheme.
Abstract
In this paper an enhanced version of the semi-explicit Particle Finite Element Method for incompressible flow problems is presented. This goal is achieved by improving the [...]
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A multiscale approach for the study of particle-laden flows using a continuous model
S. Idelsohn, J. Gimenez, R. Lohner, E. Oñate

Computer Methods in Applied Mechanics and Engineering (2022). Volume 401, Part A, 115174

Abstract
The methodology previously proposed by the authors to solve particle-laden turbulent flows through a multiscale approach is extended by introducing a continuous function for the dispersed phase concentration. The proposed continuous model is especially useful for studying the motion of particle streams in which gravitational and inertial effects cause the particles to deviate from a simple trajectory following the surrounding flow, as would be the case for the limit of very small, massless particles. The results show an excellent comparison between the solutions obtained using the continuous model and simulations evaluating the forces on each particle individually. Distinct advantages of the continuous approach are a much lower computational overhead, a better load balance and ease of parallelization. The multiscale methodology proposed may be used in the area of modeling and simulation of airborne infectious diseases.
Abstract
The methodology previously proposed by the authors to solve particle-laden turbulent flows through a multiscale approach is extended by introducing a continuous function for [...]
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A deterministic pathogen transmission model based on high-fidelity physics
R. Lohner, H. Antil, J. Gimenez, S. Idelsohn, E. Oñate

Computer Methods in Applied Mechanics and Engineering (2022). Volume 401, Part A, 114929

Abstract
A deterministic pathogen transmission model based on high-fidelity physics has been developed. The model combines computational fluid dynamics and computational crowd dynamics in order to be able to provide accurate tracing of viral matter that is exhaled, transmitted and inhaled via aerosols. The examples shown indicate that even with modest computing resources, the propagation and transmission of viral matter can be simulated for relatively large areas with thousands of square meters, hundreds of pedestrians and several minutes of physical time. The results obtained and insights gained from these simulations can be used to inform global pandemic propagation models, increasing substantially their accuracy.
Abstract
A deterministic pathogen transmission model based on high-fidelity physics has been developed. The model combines computational fluid dynamics and computational [...]
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A Lagrangian–Eulerian procedure for the coupled solution of the Navier–Stokes and shallow water equations for landslide-generated waves
M. Maso, A. Franci, I. de-Pouplana, A. Cornejo Velázquez, E. Oñate

Advanced Modeling and Simulation in Engineering Sciences (2022). Vol. 9(1), Article 15, 2022

Abstract
This work presents a partitioned method for landslide-generated wave events. The proposed strategy combines a Lagrangian Navier Stokes multi-fluid solver with an Eulerian method based on the Boussinesq shallow water equations. The Lagrangian solver uses the Particle Finite Element Method to model the landslide runout, its impact against the water body and the consequent wave generation. The results of this fully-resolved analysis are stored at selected interfaces and then used as input for the shallow water solver to model the far-field wave propagation. This one-way coupling scheme reduces drastically the computational cost of the analyses while maintaining high accuracy in reproducing the key phenomena of the cascading natural hazard. Several numerical examples are presented to show the accuracy and robustness of the proposed coupling strategy and its applicability to large-scale landslide-generated wave events. The validation of the partitioned method is performed versus available results of other numerical methods, analytical solutions and experimental measures.
Abstract
This work presents a partitioned method for landslide-generated wave events. The proposed strategy combines a Lagrangian Navier Stokes multi-fluid solver with an Eulerian [...]
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A unified non-linear energy dissipation-based plastic-damage model for cyclic loading
A. Cornejo Velázquez, S. Jiménez, L. Barbu, S. Oller, E. Oñate

Computer Methods in Applied Mechanics and Engineering (2022). Vol. 400,115543

Abstract
A new energy-dissipation-based rate-independent constitutive law within the framework of elastoplasticity coupled with damage is proposed. With this methodology, the inelastic strains and the stiffness degradation exhibited by quasi-brittle materials under monotonic or cyclic loading conditions are taken into account. The proposed constitutive model is able to capture micro-cracks closure-reopening effects due to load reversal. A wide variety of hardening/softening laws on the stress–strain relationship are described and considered for the novel normalized plastic-damage energy dissipation internal variable. This normalized internal variable allows the model to be independent on the sign of the load and dissipate different fracture energies (tensile, compressive and potentially shear) in a natural way. Several numerical examples are presented in order to ensure the efficiency and validity of the proposed model for simulating the non-linear behaviour of quasi-brittle materials under monotonic and cyclic loading. Some numerical aspects of the implemented algorithm and the return mapping procedure are also described in detail and discussed.
Abstract
A new energy-dissipation-based rate-independent constitutive law within the framework of elastoplasticity coupled with damage is proposed. With this methodology, the inelastic [...]
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Explicit time integration scheme with large time steps for first order transient problems using finite increment calculus (preprint)
E. Oñate, I. de-Pouplana, F. Zarate

Computer Methods in Applied Mechanics and Engineering (2022). Available online 14 July, 115332

Abstract
We present an explicit integration scheme for solving the transient heat conduction equation that allows larger time steps than the standard forward Euler scheme. The derivation starts from a higher order form of the governing differential equations of the problem obtained using a Finite Increment Calculus (FIC) procedure. The efficiency of the new explicit integration scheme in terms of substantial gains in the time step size versus the forward Euler scheme is verified in the solution of transient heat conduction problems in one and two dimensions. The method is readily extendible to other problems in mechanics governed by the first order transient differential equation.
Abstract
We present an explicit integration scheme for solving the transient heat conduction equation that allows larger time steps than the standard forward Euler scheme. The derivation [...]
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Structural analysis and design of a large inflatable hangar for aircrafts (preprint)
J. Gonzalez, J. Marcipar, C. Estruch, E. Oñate

Structural Engineering International (2022). pp. 1-5

Abstract
Buildair S.A. has recently designed, manufactured and built an inflatable hangar (termed H75 hangar) for the aeronautic industry in Jeddah Airport (Kingdom of Saudi Arabia). H75 hangar is the largest aircell inflated structure ever built in the world, finally erected in July 2019. The structural analysis and design of the main body of the hangar has involved complex structural concepts due to the specificity of the structural elements employed, like membranes and straps which lead to a highly non-linear mechanical problem, or the treatment of wind over the structure without a defined standard for inflatable structures. In this paper, the structural conception and specificities of the structure are presented, as well as the design procedure for the H75 hangar based in the numerical analysis, to fulfill the design requirements in terms of stresses, and deformations for the structural elements of the main body.
Abstract
Buildair S.A. has recently designed, manufactured and built an inflatable hangar (termed H75 hangar) for the aeronautic industry in Jeddah Airport (Kingdom of Saudi Arabia). [...]
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Efficient aeroelastic analysis of inflatable structures using enhanced potential flow aerodynamics
E. Ortega, R. Flores, E. Cuartero, E. Oñate

Journal of Fluids and Structures (2019). Vol. 90, pp. 230-245

Abstract
An efficient method for the aeroelastic analysis of wind effects on inflatable structures is presented. The solution scheme is staggered and uses an explicit finite-element structural solver and potential flow aerodynamics. In order to take into account the essential features of the flow around blunt-shaped structures, a physics-based correction of the inviscid solution is proposed. The procedure involves automatic prediction of the detached flow areas (using Stratford’s criterion) and an empirical modification of the calculated pressure field intended to match the real viscous behavior. Several validation benchmarks and a realistic application example are presented. The results show the capability of the model to predict the wind loads on the structure with sufficient accuracy and low computational cost, making it possible to use aeroelastic analysis for routine calculation of inflatable structures.
Abstract
An efficient method for the aeroelastic analysis of wind effects on inflatable structures is presented. The solution scheme is staggered and uses an explicit finite-element [...]
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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. for Num. Meths. in Fluids (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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Lagrangian formulation for finite element analysis of quasi-incompressible fluids with reduced mass losses
E. Oñate, A. Franci, J. Carbonell

Int. J. for Numerical Methods in Fluids (2014). Vol. 74 pp. 699-731 Vol. 74 pp. 699-731 (preprint)

Abstract
We present a Lagrangian formulation for finite element analysis of quasi-incompressible fluids that has excellent mass preservation features. The success of the formulation lays on a new residual-based stabilized expression of the mass balance equation obtained using the Finite Calculus (FIC) method. The governing equations are discretized with the FEM using simplicial elements with equal linear interpolation for the velocities and the pressure. The merits of the formulation in terms of reduced mass loss and overall accuracy are verified in the solution of 2D and 3D quasi-incompressible free-surface flow problems using the Particle Finite Element Method (PFEM, www.cimne.com/pfem). Examples include the sloshing of water in a tank, the collapse of one and two water columns in rectangular and prismatic tanks and the falling of a water sphere into a cylindrical tank containing water. Copyright c 0000 John Wiley & Sons, Ltd.
Abstract
We present a Lagrangian formulation for finite element analysis of quasi-incompressible fluids that has excellent mass preservation features. The success of the formulation [...]
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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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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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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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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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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 (preprint)

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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An accurate FIC-FEM formulation for the 1D advection-diffusion-reaction equation
E. Oñate, J. Miquel, P. Nadukandi

Computer Methods in Applied Mechanics and Engineering (2016). 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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Application of an enhanced discrete element method to oil and gas drilling processes
P. Ubach, F. Arrufat, L. Ring, R. Gandikota, F. Zárate, E. Oñate

Comp. Part. Mech (2016). Vol. 3(1) pp. 39-4 (preprint)

Abstract
The authors present results on the use of the discrete element method (DEM) for the simulation of drilling processes typical in the oil and gas exploration industry. The numerical method uses advanced DEM techniques using a local deﬁnition of the DEM parameters and combined FEM-DEM procedures. This paper presents a step by step procedure to build a DEM model for analysis of the soil region coupled to a FEM model for discretizing the drilling tool that reproduces the drilling mechanics of a particular drill bit. A parameter study has been performed to determine the model parameters in order to maintain accurate solutions with reduced computational cost.
Abstract
The authors present results on the use of the discrete element method (DEM) for the simulation of drilling processes typical in the oil and gas exploration industry. The 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 (preprint)

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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Adjoint-based adaptive finite element method for the compressible Euler equations using finite calculus
M. Kouhi, E. Oñate, D. Mavriplis

Aerospace Science and Technology (2014). 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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On the effect of the bulk tangent matrix in partitioned solution schemes for nearly incompressible fluids
A. Franci, E. Oñate, J. Carbonell

Int. J. Numer. Meth. Engng. (2015). Vol. 102(3-4) pp. 257-277

Abstract
The purpose of this paper is to study the effect of the bulk modulus in the iterative matrix for the analysis of quasi-incompressible free surface fluid flows using a mixed Lagrangian finite element formulation and a partitioned solution scheme. A practical rule to set up the value of a pseudo-bulk modulus a priori in the tangent bulk stiffness matrix for improving the conditioning of the linear system of algebraic equations is also given. The efficiency of the proposed strategy is tested in several problems analyzing the advantage of the modified bulk tangent matrix with regard to the stability of the pressure field, the convergence rate and the computational speed of the analyses. The technique has been tested on the FIC/PFEM Lagrangian formulation presented in [19] but it can be easily extended to other quasi-incompressible stabilized finite element formulations. Copyright c 2010 John Wiley & Sons, Ltd.
Abstract
The purpose of this paper is to study the effect of the bulk modulus in the iterative matrix for the analysis of quasi-incompressible free surface fluid flows using a mixed [...]
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An implicit stabilized finite element method for the compressible Navier–Stokes equations using finite calculus
M. Kouhi, E. Oñate

Computational Mechanics (2015). Vol. 56(1) pp. 113-129

Abstract
A new implicit stabilized formulation for the numerical solution of the compressible NavierStokes equations is presented. The method is based on the Finite Calculus (FIC) scheme using the Galerkin finite element method (FEM) on triangular grids. Via the FIC formulation, two stabilization terms, called streamline term and transverse term, are added to the original conservation equations in the space-time domain. The non-linear system of equations resulting from the spatial discretization is solved implicitly using a damped Newton method benefiting from the exact Jacobian matrix. The matrix system is solved at each iteration with a preconditioned GMRES method. The efficiency of the proposed stabilization technique is checked out in the solution of 2D inviscid and laminar viscous flow problems where appropriate solutions are obtained especially near the boundary layer and shock waves. The work presented here can be considered as a follow up of a previous work of the authors [24]. In that paper, the stabilized Galerkin FEM based on the FIC formulation was derived for the Euler equations together with an explicit scheme. In the present paper, the extension of this work to the Navier-Stokes equations using an implicit scheme is presented.
Abstract
A new implicit stabilized formulation for the numerical solution of the compressible NavierStokes equations is presented. The method is based on the Finite Calculus (FIC) [...]
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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

Computational Particle Mechanics (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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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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Particle Finite Element Method (PFEM) for analysis of industrial forming processes
E. Oñate, A. Franci, J. Carbonell

Computational Mechanics (2014). Vol. 54 pp. 85-107

Abstract
We present a generalized Lagrangian formulation for analysis of industrial forming processes involving thermally coupled interactions between deformable continua. The governing equations for the deformable bodies are written in a unified manner that holds both for fluids and solids. The success of the formulation lays on a residual-based expression of the mass conservation equation obtained using the Finite Calculus (FIC) method that provides the necessary stability for quasi/fully incompressible situations. The governing equations are discretized with the FEM via a mixed formulation using simplicial elements with equal linear interpolation for the velocities, the pressure and the temperature. The merits of the formulation are demonstrated in the solution of 2D and 3D thermally-coupled forming processes using the Particle Finite Element Method (PFEM).
Abstract
We present a generalized Lagrangian formulation for analysis of industrial forming processes involving thermally coupled interactions between deformable continua. The governing [...]
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Simple and efficient numerical tools for the analysis of parachutes
R. Flores, E. Ortega, E. Oñate

Engineering Computations (2014). Vol. 31(5) pp. 957-985

Abstract
This work describes a set of simple yet effective, numerical method for the design and evaluation of parachute-payload system. The developments include a coupled fluidstructural solver for unsteady simulations of ram-air type parachutes. For an efficient solution of the aerodynamic problem, an unsteady panel method has been chosen exploiting the fact that large areas of separated flow are not expected under nominal flight conditions of ram-air parachutes. A dynamic explicit finite element solver is used for the structure. This approach yields a robust solution even when highly non-linear effects due to large displacements and material response are present. The numerical results show considerable accuracy and robustness. An added benefit of the proposed aerodynamic and structural techniques is that they can be easily vectored and thus suitable for use in parallel architectures. The main features of the computational tools are described and several numerical examples are provided to illustrate the performance and capabilities of the technique.
Abstract
This work describes a set of simple yet effective, numerical method for the design and evaluation of parachute-payload system. The developments include a coupled fluidstructural [...]
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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

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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A plastic-damage model for concrete
J. Lubliner, J. Oliver, S. Oller, E. Oñate

Int. J. Solids and Structures (1989). Vol. 25 (3), pp. 299-326

Abstract
In this paper a constitutive model based on an internal variable-formulation of plasticity theory for the non-linear analysis of concrete is presented. The model uses a new yield criterion which matches experimental data quite well and it accounts for both elastic and plastic stiffness degradations effects. Onset and amount of cracking can be studied by a simple postprocessing of the finite-element plasticity solution. The accuracy of the model is checked with some examples of application.
Abstract
In this paper a constitutive model based on an internal variable-formulation of plasticity theory for the non-linear analysis of concrete is presented. The model uses a new [...]
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Ensayos experimentales y numéricos de rotura en piezas de hormigón. Hacia el Laboratorio Virtual
F. Zarate, A. Gomez, E. Oñate

Rev. int. métodos numér. cálc. diseño ing. (2019). Vol. 35, (1), 14

Abstract
This paper describes a computation methodology to evaluate the ultimate strength and fracture of concrete samples and structures and its application to four typical tests of experimental laboratories of strength of materials. The tests results are compared and analysed from the experimental and numerical points of view in order to highlight the need for experimental trials to use the information derived from numerical results and, in turn, to validate that numerical models follow the behaviour and physics that occur in laboratory tests This comparison allows to explain the different mechanisms that occur throughout the experiments.
Abstract
This paper describes a computation methodology to evaluate the ultimate strength and fracture of concrete samples and structures and its application to four typical tests [...]
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A FEM fluid-structure interaction algorithm for analysis of the seal dynamics of a Surface-Effect Ship
J. García-Espinosa, B. Servan Camas, E. Oñate, D. Di Capua, P. Ubach de Fuentes

Comp. Meth. App. Mech. Eng. (2015). 295, 290-304 (preprint)

Abstract
This paper shows the recent work of the authors in the development of a time-domain FEM model for evaluation of the seal dynamics of a surface effect ship. The fluid solver developed for this purpose, uses a potential flow approach along with a stream-line integration of the free surface. The paper focuses on the free surface-structure algorithm that has been developed to allow the simulation of the complex and highly dynamic behavior of the seals in the interface between the air cushion, and the water. The developed fluid-structure interaction solver is based, on one side, on an implicit iteration algorithm, communicating pressure forces and displacements of the seals at memory level and, on the other side, on an innovative wetting and drying scheme able to predict the water action on the seals. The stability of the iterative scheme is improved by means of relaxation, and the convergence is accelerated using Aitken’s method. Several validations against experimental results have been carried out to demonstrate the developed algorithm.
Abstract
This paper shows the recent work of the authors in the development of a time-domain FEM model for evaluation of the seal dynamics of a surface effect ship. The fluid solver [...]
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Surface tension problems solved with the Particle Finite Element Method using large time-steps
J. Giménez, N. Nigro, S. Idelsohn, E. Oñate

Computers and Fluids (2016). (preprint) Vol. 141, pp. 90-104

Abstract
In previous works [1,2], the authors have presented a highly efficient extension of the Particle Finite Element Method, called PFEM-2, to solve two-phase flows. The methodology which uses X-IVS [3] to treat convection terms allowing large time-steps was validated for problems where the gravity forces and/or the inertial forces dominate the flow. Although that is the target range of problems to solve with PFEM-2, most of real problems that fall in these categories also includes other flow regimes in certain regions of the domain. Maybe the most common secondary regime is when the surface tension dominates, as an example when drops or bubbles are released from the main flow, and this feature must be taken into account in any complete numerical strategy. Attending to that, in this work the treatment of the surface tension to PFEM-2 is included. An implicit CSF methodology is employed together with a coupling between the marker function with a Level Set function to obtain a smooth representation of the normal of the interface which allows an accurate curvature calculation. Examples for curvature calculation and isolated bubbles and drops are presented where the accuracy and the computational efficiency are analyzed and contrasted with other numerical methodologies. Finally, a simulation of a jet atomization is analyzed. This case presents the above mentioned features: it is a inertia-dominant flow with a surface tension phenomena on drops and ligaments break up that can not be neglected.
Abstract
In previous works [1,2], the authors have presented a highly efficient extension of the Particle Finite Element Method, called PFEM-2, to solve two-phase flows. The methodology [...]
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Finite volume for stress analysis upon polygonal, unstructured and non conforming meshes
V. Cardoso Nungaray, S. Botello, F. Zarate, E. Oñate

Rev. int. métodos numér. cálc. diseño ing. (2019). Vol. 35, (4), 47

Abstract
Within this paper we discuss a numerical strategy to solve the elasticity problem upon unstructured and non conforming meshes, allowing all kinds of flat-faced elements (polygons in 2D and polyhedra in 3D). The core of the formulation relies on two numerical procedures 1) the Control Volume Function Approximation (CVFA), and 2) the polynomial interpolation in the neighborhood of the control volumes, which is used to solve the surface integrals resulting from applying the divergence theorem. By comparing the estimated stress against the analytical stress field of the well known test of an infinite plate with a hole, we show that this conservative approach is robust and accurate.
Abstract
Within this paper we discuss a numerical strategy to solve the elasticity problem upon unstructured and non conforming meshes, allowing all kinds of flat-faced elements (polygons [...]
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Advances in the particle finite element method for the analysis of fluid-multibody interaction and bed erosion in free surface flows
E. Oñate, S. Idelsohn, M. Celigueta, R. Rossi

Comput. Methods Appl. Mech. Engrg., (2008). Vol. 197 (19-20), pp. 1777–1800

Abstract
We present some advances in the formulation of the Particle Finite Element Method (PFEM) for solving complex fluid-structure interaction problems with free surface waves. In particular, we present extensions of the PFEM for the analysis of the interaction between a collection of bodies in water allowing for frictional contact conditions at the fluid-solid and solid-solid interfaces via mesh generation. An algorithm to treat bed erosion in free surface flows is also presented. Examples of application of the PFEM to solve a number of fluid-multibody interaction problems involving splashing of waves, large motions of floating and submerged bodies and bed erosion situations are given.
Abstract
We present some advances in the formulation of the Particle Finite Element Method (PFEM) for solving complex fluid-structure interaction problems with free surface waves. [...]
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Interpretation of dam deformation and leakage with boosted regression trees
F. Salazar, M. Toledo, E. Oñate, B. Suarez

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

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

Comput. Methods Appl. Mech. Engrg., (2004). Vol 193, 3087-3128

Abstract
The paper presents combination of Discrete Element Method (DEM) and Finite Element Method (FEM) for dynamic analysis of geomechanics problems. Combined models can employ spherical (or cylindrical in 2D) rigid elements and finite elements in the discretization of different parts of the system. The DEM is a suitable tool to model soil/rock materials while the FEM in many cases can be a better choice to model other parts of the system considered. A typical example can be an idealization of rock cutting with a tool discretized with finite elements and rock or soil samples modelled with discrete elements. The FEM presented in the paper allows large elasto-plastic deformations in the solid regions. Such problems require the use of stabilized FEM to deal with the incompressibility constraint in order to eliminate the volumetric locking defect, especially when using triangular and tetrahedra elements with equal order interpolation for the displacement and the pressure variables. In the paper a stabilization based on the Finite Calculus (FIC) approach is used. Both theoretical algorithms of DEM and stabilized FEM are implemented in an explicit dynamic code. The paper presents some details of both formulations. A combined numerical algorithm is described finally. Selected numerical results illustrate the possibilities and performance of discrete/finite element analysis in geomechanics problems.
Abstract
The paper presents combination of Discrete Element Method (DEM) and Finite Element Method (FEM) for dynamic analysis of geomechanics problems. Combined models can employ spherical [...]
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Lagrangian versus Eulerian integration errors
S. Idelsohn, E. Oñate, N. Nigro, P. Becker

Comput. Methods Appl. Mech. Engrg., (2015). Vol. 293, pp. 191–206; (preprint)

Abstract
The possibility to use a Lagrangian frame to solve problems with large time-steps was successfully explored previously by the authors for the solution of homogeneous incompressible fluids and also for solving multi-fluid problems [28-30]. The strategy used by the authors was named Particle Finite Element Method second generation (PFEM-2). The objective of this paper is to demonstrate in which circumstances the use of a Lagrangian frame with particles is more accurate than a classical Eulerian finite element method, and when large time-steps and/or coarse meshes may be used.
Abstract
The possibility to use a Lagrangian frame to solve problems with large time-steps was successfully explored previously by the authors for the solution of homogeneous incompressible [...]
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Simple and accurate two-noded beam element for composite laminated beams using a refined zigzag theory
E. Oñate, A. Eijo, S. Oller

Comput. Methods Appl. Mech. Engrg., (2012). Vol. 213–216, pp. 362–382

Abstract
In this work we present a new simple linear two-noded beam element adequate for the analysis of composite laminated and sandwich beams based on the combination of classical Timoshenko beam theory and the refined zigzag kinematics proposed by Tessler ''et al.'' [[#cite-22|[22]]]. The element has just four kinematic variables per node. Shear locking is eliminated by reduced integration. The accuracy of the new beam element is tested in a number of applications to the analysis of composite laminated beams with simple supported and clamped ends under point loads and uniformly distributed loads. An example showing the capability of the new element for accurately reproducing delamination effects is also presented.
Abstract
In this work we present a new simple linear two-noded beam element adequate for the analysis of composite laminated and sandwich beams based on the combination of classical [...]
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The particle finite element method. An overview
E. Oñate, S. Idelsohn, F. Del Pin, R. Aubry

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

Abstract
We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use of a Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are thus viewed as particles which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations, expressed in an integral from, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility condition in the fluid is introduced via the finite calculus (FIC) method. A fractional step scheme for the transient coupled fluid-structure solution is described. Examples of application of the PFEM method to solve a number of fluid-structure interaction problems involving large motions of the free surface and splashing of waves are presented.
Abstract
We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use [...]
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Improvements in the membrane behaviour of the three node rotation-free BST shell triangle using an assumed strain approach
F. Flores, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2005). Vol. 194, pp. 907-932

Abstract
In this paper an assumed strain approach is presented in order to improve the membrane behaviour of a thin shell triangular element. The so called Basic Shell Triangle (BST) has three nodes with only translational degrees of freedom and is based on a Total Lagrangian Formulation. As in the original BST element the curvatures are computed resorting to the surrounding elements (patch of four elements). Membrane strains are now also computed from the same patch of elements which leads to a non-conforming membrane behaviour. Despite this non-conformity the element passes the patch test. Large strain plasticity is considered using a logarithmic strain-stress pair. A plane stress behaviour with an additive decomposition of elastic and plastic strains is assumed. A hyperplastic law is considered for the elastic part while for the plastic part an anisotropic quadratic (Hill) yield function with non-linear isotropic hardening is adopted. The element, termed CBST, has been implemented in an explicit (hydro-)code adequate to simulate sheet-stamping processes and in an implicit static/dynamic code. Several examples are given showing the good performance of the enhnaced rotation-free shell triangle.
Abstract
In this paper an assumed strain approach is presented in order to improve the membrane behaviour of a thin shell triangular element. The so called Basic Shell Triangle (BST) [...]
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Modelación numérica de deslizamientos de ladera en embalses mediante el Método de Partículas y Elementos Finitos (PFEM)
F. Salazar, E. Oñate, R. Morán

Rev. int. métodos numér. cálc. diseño ing. (2012). Vol. 28, (2)

Abstract
The paper presents the results of the application of the Particle Finite Element Method (PFEM) to the analysis of landslides in reservoirs. This is a complex phenomenon, because of the interaction between the landslide, the still water in the reservoir and the dam. PFEM combines a Lagrangian approach with the solution of the governing equations of the problem using the FEM. A mesh connecting the initial set of particles (nodes) is re-generated in every time step. Some validation cases are presented, in which PFEM results are compared with experimental data. More complex calculations have been made over the actual geometry of reservoirs taken from the cartographic information of the sites. In these cases the wave generation, its propagation and dam overtopping are reproduced. Finally, Lituya bay rock slide in which 90 × 106 tons of rocks fell on the bay, generating a huge wave that caused a maximum run-up of 524 m on the opposite shore, has been simulated in 3D. The results show that PFEM is a useful tool in risk assessment related with landslides in reservoirs as it gives a good approximation to the potential affections, thus allowing the appropriate design of protection measures.
Abstract
The paper presents the results of the application of the Particle Finite Element Method (PFEM) to the analysis of landslides in reservoirs. This is a complex phenomenon, because [...]
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Extended rotation-free plate and beam elements with shear deformation effects
E. Oñate, F. Zárate

Int. J. Numer. Meth. Engng. (2010). Vol. 83 (2), pp.196-227

Abstract
The paper describes a methodology for extending rotation-free plate and beam elements in order to accounting for transverse shear deformation effects. The ingredients for the element formulation are: a Hu-Washizu type mixed functional, a linear interpolation for the deflection and the shear angles over standard finite elements and a finite volume approach for computing the bending moments and the curvatures over a patch of elements. As a first application of the general procedure we present an extension of the 3-noded rotation-free basic plate triangle (BPT) originally developed for thin plate analysis to accounting for shear deformation effects of relevance for thick plates and composite laminated plates. The nodal deflection degrees of freedom (DOFs) of the original BPT element are enhanced with the two shear deformation angles. This allows to computing the bending and shear deformation energies leading to a simple triangular plate element with 3 DOFs per node (termed BPT+ element). For the thin plate case the shear angles vanish and the element reproduces the good behaviour of the original thin BPT element. As a consequence the element is applicable to thick and thin plate situations without exhibiting shear locking effects. The numerical solution for the thick case can be found iteratively starting from the deflection values for the Kirchhoff theory using the original thin BPT element. A 2-noded rotation-free beam element termed CCB+ applicable to slender and thick beams is derived as a particular case of the plate formulation. The examples presented show the robustness and accuracy of the BPT+ and the CCB+ elements for thick and thin plate and beam problems.
Abstract
The paper describes a methodology for extending rotation-free plate and beam elements in order to accounting for transverse shear deformation effects. The ingredients for [...]
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Combination of an adaptive remeshing technique with a coupled FEM-DEM approach for analysis of crack propagation problems (preprint)
A. Cornejo, V. Mataix, F. Zarate, E. Oñate

Computational Particle Mechanics (2020). Vol. 7, pp. 735–752, doi: 10.1007/s40571-019-00306-4

Abstract
This paper presents an enhanced coupled approach between the Finite Element Method (FEM) and the Discrete Element Method (DEM) in which an adaptative remeshing technique has been implemented. The remeshing technique is based on the computation of the Hessian of a selected nodal variable, i.e. the mesh is refined where the curvature of the variable field is greater. Once the Hessian is known, a metric tensor is defined node-wise that serves as input data for the remesher (MmgTools) that creates a new mesh. After remeshing, the mapping of the internal variables and the nodal values is performed and a regeneration of the discrete elements on the crack faces of the new mesh is carried out. Several examples of fracturing problems using the enhanced FEM-DEM formulation are presented. Accurate results in comparison with analytical and experimental solutions are obtained.
Abstract
This paper presents an enhanced coupled approach between the Finite Element Method (FEM) and the Discrete Element Method (DEM) in which an adaptative remeshing technique has [...]
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Unified Lagrangian formulation for elastic solids and incompressible fluids. application to fluid-structure interaction problems via the PFEM
S. Idelsohn, J. Marti, A. Limache, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2008). Vol. 197, pp. 1762–1776

Abstract
We present a general Lagrangian formulation for treating elastic solids and quasi/fully incompressible fluids in a unified form. The formulation allows to treat solid and fluid subdomains in a unified manner in fluid-structure interaction (FSI) situations. In our work the FSI problem is solved via the Particle Finite Element Method (PFEM). The PFEM is an effective technique for modeling complex interactions between floating and submerged bodies and free surface flows, accounting for splashing of waves, large motions of the bodies and frictional contact conditions. Applications of the unified Lagrangian formulation to a number of FSI problems are given.
Abstract
We present a general Lagrangian formulation for treating elastic solids and quasi/fully incompressible fluids in a unified form. The formulation allows to treat solid and [...]
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A three dimensional FEM-DEM technique for predicting the evolution of fracture in geomaterials and concrete
F. Zarate, A. Cornejo Velázquez, E. Oñate

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

Abstract
This paper extends to three dimensions (3D) the computational technique developed by the authors in 2D for predicting the onset and evolution of fracture in a finite element mesh in a simple manner based on combining the finite element method (FEM) and the discrete element method (DEM) approach Zarate2D. Once a crack is detected at an element edge, discrete elements are generated at the adjacent element vertexes and a simple DEM mechanism is considered in order to follow the evolution of the crack. The combination of the DEM with simple 4-noded linear tetrahedron elements correctly captures the onset of fracture and its evolution, as shown in several 3D examples of application.
Abstract
This paper extends to three dimensions (3D) the computational technique developed by the authors in 2D for predicting the onset and evolution of fracture in a finite element [...]
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A finite point method in computational mechancis. Applications to convective transport and fluid flow.
E. Oñate, S. Idelsohn, O. Zienkiewicz, R. Taylor

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

Abstract
The paper presents a fully meshless procedure fo solving partial differential equations. The approach termed generically the ‘finite point method’ is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals. Some examples showing the accuracy of the method for solution of adjoint and non‐self adjoint equations typical of convective‐diffusive transport and also to the analysis of compressible fluid mechanics problem are presented.
Abstract
The paper presents a fully meshless procedure fo solving partial differential equations. The approach termed generically the ‘finite point method’ is based on [...]
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Formulación de elementos finitos para vigas de sección abierta formadas por laminados compuestos incluyendo las deformaciones tangenciales por cortante y torsión
P. Vargas, E. Oñate, S. Oller

Rev. int. métodos numér. cálc. diseño ing. (2014). Vol. 30, (4)

Abstract
In this paper we derive the field of displacements and strains for thin-walled open composite beams with composite laminated material including in their kinematics flexural and torsional shear deformations effects. The equilibrium equations are defined through the variational formulation and show that is possible to formulate Co finite elements taking into account the torsional shear deformation. Stress-strain relationships for the cross-section of thin-walled composite beams are obtained by extending first-order laminate (FSDT: first-order shear deformation) theory and using a «free stress resultant condition at the boundary». Three different one-dimensional finite elements with Co continuity are formulated for the study of thin-walled open composite beams and they are labelled as BSW (beam with shear and warping). The influence of the integration strategy in the BSW elements is evaluated via the shear-locking phenomenon and the rate of convergence for displacements and rotations. The stiffness matrix integration is compared using exact and reduced integration methods. Examples of pure torsion and flexo-torsion in a cantilever composite beam are performed. Numerical results are compared to those reported by other authors.
Abstract
In this paper we derive the field of displacements and strains for thin-walled open composite beams with composite laminated material including in their kinematics flexural [...]
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Finite volumes and finite elements: Two ‘good friends’
E. Oñate, S. Idelsohn

Int. J. Numer. Meth. Engng. (1994). Vol. 37 (19), pp. 3323-3341

Abstract
In this paper a comparison between the finite element and the finite volume methods is presented in the context of elliptic, convective–diffusion and fluid flow problems. The paper shows that both procedures share a number of features, like mesh discretization and approximation. Moreover, it is shown that in many cases both techniques are completely equivalent.
Abstract
In this paper a comparison between the finite element and the finite volume methods is presented in the context of elliptic, convective–diffusion and fluid flow problems. [...]
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An accurate nonlocal bonded discrete element method for non linear analysis of solids. Application to concrete fracture tests (preprint)
M. Celigueta, S. Latorre, F. Arrufat, E. Oñate

Computational Particle Mechanics (2020). Vol. 7, pp. 543–553, 10.1007/s40571-019-00278-5

Abstract
We present a numerical procedure for elastic and non linear analysis (including fracture situations) of solid materials and structures using the Discrete Element Method (DEM). It can be applied to strongly cohesive frictional materials such as concrete and rocks. The method consists on defining the non-local constitutive equations at the contact interfaces between discrete particles using the information provided by the stress tensor over the neighbour particles. The method can be used with different yield surfaces and in the paper it is applied to the analysis of fracture of concrete samples. Good comparison with experimental results is obtained.
Abstract
We present a numerical procedure for elastic and non linear analysis (including fracture situations) of solid materials and structures using the Discrete Element Method (DEM). [...]
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Pulse fracture simulation in shale rock reservoirs. DEM and FEM-DEM approaches
J. Gonzalez, F. Zarate, E. Oñate

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

Abstract
In this paper we analyze the capabilities of two numerical techniques based on DEM and FEM-DEM approaches for the simulation of fracture in shale rock caused by a pulse of pressure. We have studied the evolution of fracture in several fracture scenarios related to the initial stress state in the soil or the pressure pulse peak. Fracture length and type of failure have been taken as reference for validating the models. The results obtained show a good approximation to FEM results from the literature.
Abstract
In this paper we analyze the capabilities of two numerical techniques based on DEM and FEM-DEM approaches for the simulation of fracture in shale rock caused by a pulse of [...]
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Advances in the simulation of multi-fluid flows with the Particle Finite Element Method. Application to bubble dynamics
M. Mier-Torrecilla, S. Idelsohn, E. Oñate

Int. J. Numer. Meth. Fluids (2010). Vol. 67 (11), pp. 1516-1539

Abstract
In this work we extend the Particle Finite Element Method (PFEM) to multi-fluid flow problems with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking interfaces. We develop a numerical scheme able to deal with large jumps in the physical properties, included surface tension, and able to accurately represent all types of discontinuities in the flow variables. The scheme is based on decoupling the velocity and pressure variables through a pressure segregation method which takes into account the interface conditions. The interface is defined to be aligned with the moving mesh, so that it remains sharp along time, and pressure degrees of freedom are duplicated at the interface nodes to represent the discontinuity of this variable due to surface tension and variable viscosity. Furthermore, the mesh is refined in the vicinity of the interface to improve the accuracy and the efficiency of the computations. We apply the resulting scheme to the benchmark problem of a two-dimensional bubble rising in a liquid column presented in [[#cite-1|[1]]], and propose two breakup and coalescence problems to assess the ability of a multi-fluid code to model topology changes.
Abstract
In this work we extend the Particle Finite Element Method (PFEM) to multi-fluid flow problems with the aim of exploiting the fact that Lagrangian methods are specially well [...]
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Predicción de fracturas en estructuras de hormigón combinando los métodos de elementos finitos y de elementos discretos
F. Zarate, E. Oñate

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

Abstract
This paper presents the basic concepts and application of the strategy that combines finite element methods (FEM) and discrete elements (DEM)for the study of the propagation of fractures in concrete structures. The calculation of the structure, modeled as a continuum, begins with the FEMand the DEM is used to start and grow the cracks that may appear in the structure. This methodology has been proposed by the authors in two andthree dimensions. Recently, the use of one-dimensional steel elements embedded in the continuum has been added to model the reinforcement inconcrete structures. The work presents different examples of application to the study of the breakage of parts and structures of concrete in massand armed, as well as the multiple breakage of a historic structure of masonry due to an earthquake.
Abstract
This paper presents the basic concepts and application of the strategy that combines finite element methods (FEM) and discrete elements (DEM)for the study of the propagation [...]
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Finite element formulation for convective-diffusive problems with sharp gradients using finite calculus
E. Oñate, F. Zarate, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195 (13-16), pp. 1793–1825

Abstract
A finite element method (FEM) for steady-state convective-diffusive problems presenting sharp gradients of the solution both in the interior of the domain and in boundary layers is presented. The necessary stabilization of the numerical solution is provided by the Finite Calculus (FIC) approach. The FIC method is based in the solution by the Galerkin FEM of a modified set of governing equations which include characteristic length parameters. It is shown that the FIC balance equation for the multidimensional convection-diffusion problem written in the principal curvature axes of the solution, introduces an orthotropic diffusion which stabilizes the numerical solution both in smooth regions as well in the vicinity of sharp gradients. The dependence of the stabilization terms with the principal curvature directions of the solution makes the method non linear. Details of the iterative scheme to obtain stabilized results are presented together with examples of application which show the efficiency and accuracy of the approach.
Abstract
A finite element method (FEM) for steady-state convective-diffusive problems presenting sharp gradients of the solution both in the interior of the domain and in boundary [...]
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A unified monolithic approach for multi-fluid flows and Fluid-Structure Interaction using the Particle Finite Element Method with fixed mesh
P. Becker, S. Idelsohn, E. Oñate

Computational Mechanics (2015). (preprint) Vol. 55, pp. 1091–1104

Abstract
This paper describes a strategy to solve multi-fluid and Fluid-Structure Interaction (FSI) problems using Lagrangian particles combined with a fixed Finite Element (FE) mesh . Our approach is an extension of the fluid-only PFEM-2 [1,2] which uses explicit integration over the streamlines to improve accuracy. As a result, the convective term does not appear in the set of equations solved on the fixed mesh. Enrichments in the pressure field are used to improve the description of the interface between phases.
Abstract
This paper describes a strategy to solve multi-fluid and Fluid-Structure Interaction (FSI) problems using Lagrangian particles combined with a fixed Finite Element (FE) mesh [...]
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Advances in the formulation of the rotation-free basic shell triangle
E. Oñate, F. Flores

Comput. Methods Appl. Mech. Engrg., (2005). Vol. 194 (21-24), pp. 2406-2443

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

Computational Mechanics (1995). Vol. 15 (6), pp. 572-593

Abstract
In this paper the general non symmetric parametric form of the incremental secant stiffness matrix for non linear analysis of solids using the finite element metod is derived. A convenient symmetric expression for a particular value of the parameters is obtained. The geometrically non linear formulation is based on a Generalized Lagrangian approach. Detailed expressions of all the relevant matrices involved in the analysis of 3D solids are obtained. The possibilities of application of the secant stiffness matrix for non linear structural problems including stability, bifurcation and limit load analysis are also discussed. Examples of application are given for the non linear analysis of pin joined frames.
Abstract
In this paper the general non symmetric parametric form of the incremental secant stiffness matrix for non linear analysis of solids using the finite element metod is derived. [...]
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Rotation-free finite element for the non-linear analysis of beams and axisymmetric shells
F. Flores, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 5297–5315

Abstract
In this paper a finite element for the non-linear analysis of two dimensional beams and axisymmetric shells is presented. The element uses classical thin shell assumptions (no transverse shear strains). The main feature of the element is that it has no rotational degrees of freedom. Curvatures are computed using geometrical information from the patch of three elements formed by the main element and the two neighbour (adjacent) elements. Special attention is devoted to non-smooth geometries and branching shells. An elastic-plastic material law is considered. Large strains are treated using a logarithmic strain measure and a through-the-thickness numerical integration of the constitutive equations. Several examples are presented including linear problems to study convergence properties, and non-linear problems for both elastic and elastic-plastic materials and large strains.
Abstract
In this paper a finite element for the non-linear analysis of two dimensional beams and axisymmetric shells is presented. The element uses classical thin shell assumptions [...]
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Optimización robusta en aplicaciones aeronáuticas con la combinación de cálculo estocástico y algoritmos evolutivos
J. Pons-Prats, G. Bugeda, F. Zárate, E. Oñate

Rev. int. métodos numér. cálc. diseño ing. (2012). Vol. 28, (1)

Abstract
Uncertainties are a daily issue to deal with in aerospace engineering and applications. Robust optimization methods commonly use a random generation of the inputs and take advantage of multi-point criteria to look for robust solutions accounting with uncertainty definition. From the computational point of view, the application to coupled problems, like fluid-dynamics (CFD) or fluid-structure interaction (FSI), can be extremely expensive. This work presents a coupling between stochastic analysis techniques and evolutionary optimization algorithms for the definition of a stochastic robust optimization procedure. At first, a stochastic procedure is proposed to be applied into optimization problems. The proposed method has been applied to both CFD and FSI problems for the reduction of drag and flutter, respectively.
Abstract
Uncertainties are a daily issue to deal with in aerospace engineering and applications. Robust optimization methods commonly use a random generation of the inputs and take [...]
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FIC-FEM formulation for the multidimensional transient advection-diffusion-absorption equation (preprint)
A. Puigferrat, I. de-Pouplana, E. Oñate

Computer Methods in Applied Mechanics and Engineering (2020). Vol 365, pp. 112984, DOI: 10.1016/j.cma.2020.112984

Abstract
In this paper we present a stabilized FIC-FEM formulation for the multidimensional transient advection-diffusion-absorption equation. The starting point is the non-local form of the governing equations for the multidimensional transient advection-diffusion-absorption problems obtained via the Finite Increment Calculus (FIC) procedure. The FIC governing equations have a residual form that introduces a characteristic length vector that depends on streamline, absorption and shock capturing stabilization parameters, as well as on a characteristic element size that ensures a stabilized numerical solution using a standard Galerkin FEM. The value of the stabilization parameters is obtained as an extension of the steady-state form. The accuracy of the FIC-FEM formulation is verified in the solution of several transient advection-diffusion-absorption problems using regular meshes of 3-noded triangles and 4-noded quadrilaterals.
Abstract
In this paper we present a stabilized FIC-FEM formulation for the multidimensional transient advection-diffusion-absorption equation. The starting point is the non-local form [...]
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Stabilized formulation for the advection-diffusion-absorption equation using finite calculus and linear finite elements
E. Oñate, J. Miquel, G. Hauke

Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 3926–3946

Abstract
A stabilized finite element method (FEM) for the steady state advection-diffusion-absorption equation is presented. The stabilized formulation is based on the modified governing differential equations derived via the Finite Calculus (FIC) method. The basis of the method is detailed for the 1D problem. It is shown that the stabilization terms act as a non linear additional diffusion governed by a single stabilization parameter. A critical constant value of this parameter ensuring a stabilized solution using two node linear elements is given. More accurate numerical results can be obtained by using a simple expression of the non linear stabilization parameter depending on the signs of the numerical solution and of its derivatives. A straightforward two steps algorithm yielding a stable and accurate solution for all the range of physical parameters and boundary conditions is described. The extension to the multi-dimensional case is briefly described. Numerical results for 1D and 2D problems are presented showing the efficiency and accuracy of the new stabilized formulation.
Abstract
A stabilized finite element method (FEM) for the steady state advection-diffusion-absorption equation is presented. The stabilized formulation is based on the modified governing [...]
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A simple and efficient element for axisymmetric shells
O. Zienkiewicz, J. Bauer, K. Morgan, E. Oñate

International Journal for Numerical Methods in Engineering (1977). Vol. 11 (10), pp. 1545-1558

Abstract
A two noded, straight element which includes shear deformation effects is presented and shown to be extremely efficient in the analysis of axisymmetric shells. A single point of numerical integration is essential for its success when applied to thin shells where the results compare favourably with those achieved with more complex curved elements.
Abstract
A two noded, straight element which includes shear deformation effects is presented and shown to be extremely efficient in the analysis of axisymmetric shells. A single point [...]
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Fluid-structure interaction using the Particle Finite Element Method
S. Idelsohn, E. Oñate, F. Pin, N. Calvo

Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195 (17-18), pp. 2100-2123

Abstract
In the present work a new approach to solve fluid-structure interaction problems is described. Both, the equations of motion for fluids and for solids have been approximated using a material (lagrangian) formulation. To approximate the partial differential equations representing the fluid motion, the shape functions introduced by the Meshless Finite Element Method (MFEM) have been used. Thus, the continuum is discretized into particles that move under body forces (gravity) and surface forces (due to the interaction with neighboring particles). All the physical properties such as density, viscosity, conductivity, etc., as well as the variables that define the temporal state such as velocity and position and also other variables like temperature are assigned to the particles and are transported with the particle motion. The so called Particle Finite Element Method (PFEM) provides a very advantageous and efficient way for solving contact and free-surface problems, highly simplifying the treatment of fluid-structure interactions. '''Key words: '''Fluid-Structure interaction, Particle methods, Lagrange formulations, Incompressible Fluid Flows, Meshless Methods, Finite Element Method.
Abstract
In the present work a new approach to solve fluid-structure interaction problems is described. Both, the equations of motion for fluids and for solids have been approximated [...]
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Melting and Spread of Polymers in Fire with the Particle Finite Element Method
E. Oñate, R. Rossi, K. Butler, S. Idelsohn

Int. J. Numer. Meth. Engng. (2010). Vol. 81 (8), pp. 1046-1072

Abstract
A new computational procedure for analysis of the melting and flame spread of polymers under fire conditions is presented. The method, termed Particle Finite Element Method (PFEM), combines concepts from particle-based techniques with those of the standard finite element method (FEM). The key feature of the PFEM is the use of an updated Lagrangian description to model the motion of nodes (particles) in the thermoplastic material. Nodes are viewed as material points which can freely move and even separate from the main analysis domain representing, for instance, the effect of melting and dripping of polymer particles. A mesh connects the nodes defining the discretized domain where the governing equations are solved as in the standard FEM. An incremental iterative scheme for the solution of the nonlinear transient coupled thermal-flow problem, including loss of mass by gasification, is used. Examples of the possibilities of the PFEM for the modelling and simulation of the melting and flame spread of polymers under different fire conditions are described. Numerical results are compared with experimental data provided by NIST.
Abstract
A new computational procedure for analysis of the melting and flame spread of polymers under fire conditions is presented. The method, termed Particle Finite Element Method [...]
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The particle finite element method: a powerful tool to solve incompressible flows with free‐surfaces and breaking waves
S. Idelsohn, E. Oñate, F. Del Pin

Int. J. Numer. Meth. Engng. (2004). Vol. 61 (7), pp. 964-989

Abstract
Particle Methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal forces applied to it. Particle Methods may be used for both, discrete and continuous problems. In this paper, a Particle Method is used to solve the continuous fluid mechanics equations. To evaluate the external applied forces on each particle, the incompressible Navier–Stokes equations using a Lagrangian formulation are solved at each time step. The interpolation functions are those used in the Meshless Finite Element Method and the time integration is introduced by an implicit fractional‐step method. In this manner classical stabilization terms used in the momentum equations are unnecessary due to lack of convective terms in the Lagrangian formulation. Once the forces are evaluated, the particles move independently of the mesh. All the information is transmitted by the particles. Fluid–structure interaction problems including free‐fluid‐surfaces, breaking waves and fluid particle separation may be easily solved with this methodology.
Abstract
Particle Methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal [...]
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Analysis of some partitioned algorithms for fluid-structure interaction
R. Rossi, E. Oñate

Engineering Computations (2010). Vol. 27 (1), pp. 20-56

Abstract
The field of fluid-structure interaction (FSI) has important applications ranging from the bio-medical to the civil and aeronautical engineering fields. Despite the different approaches developed over recent years the general solution of FSI problems remains however far from being closed. This paper addresses the theoretical analysis of a several partitioned solution schemes for FSI. This is achieved by choosing a simple but representative model problem which allows to obtain analytical results. A loose coupling partitioned procedure is presented first. An iterative version of the same algorithm is presented next together with an analysis of its convergence properties and a brief discussion of a possible acceleration strategy. Finally a new iterative strategy based on solving a modified equation is described. Some examples of application of the partitioned algorithms considered are presented including the aeroelastic analysis of a bridge.
Abstract
The field of fluid-structure interaction (FSI) has important applications ranging from the bio-medical to the civil and aeronautical engineering fields. Despite the different [...]
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Error estimation and mesh adaptivity in incompressible viscous flows using a residual power approach
E. Oñate, J. Arteaga, J. García-Espinosa, R. Flores

Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 339-362

Abstract
A methodology for error estimation and mesh adaptation for finite element (FE) analysis of incompressible viscous flow is presented. The error estimation method is based on the evaluation of the energy rate (the power) of the FE residuals of the momentum and incompressibility equations. The residuals are computed using recovered values of the derivatives of the velocity and pressure variable obtained via a nodal derivative recovery technique. Two mesh adaptation procedures based on: a) the equi-distribution of the residual power among the elements in the mesh and b) the equi-distribution of the density of the total residual power are presented. The stabilized form of the Navier-Stokes equations using a finite calculus (FIC) formulation is solved with a fractional step FE scheme. This allows the use of linear triangles and tetrahedra with an equal order interpolation for the velocity and pressure variables. A nodal-based approach is used for computing the residual power integrals. The examples show the ability of the error estimation and the mesh adaptation process to capture the high gradients of the solution in the vecinity of boundary layers and in zones of high vorticity of the fluid for both steady state and transient flow situations.
Abstract
A methodology for error estimation and mesh adaptation for finite element (FE) analysis of incompressible viscous flow is presented. The error estimation method is based on [...]
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ODDLS: A new unstructured mesh finite element method for the analysis of free surface flow problems
J. García-Espinosa, A. Valls, E. Oñate

Int. J. Numer. Meth. Engng. (2008). Vol 76 (9), pp. 1297-1327

Abstract
This paper introduces a new stabilized finite element method based on the finite calculus (Comput. Methods Appl. Mech. Eng. 1998; 151:233–267) and arbitrary Lagrangian–Eulerian techniques (Comput. Methods Appl. Mech. Eng. 1998; 155:235–249) for the solution to free surface problems. The main innovation of this method is the application of an overlapping domain decomposition concept in the statement of the problem. The aim is to increase the accuracy in the capture of the free surface as well as in the resolution of the governing equations in the interface between the two fluids. Free surface capturing is based on the solution to a level set equation. The Navier–Stokes equations are solved using an iterative monolithic predictor–corrector algorithm (Encyclopedia of Computational Mechanics. Wiley: New York, 2004), where the correction step is based on imposing the divergence‐free condition in the velocity field by means of the solution to a scalar equation for the pressure. Examples of application of the ODDLS formulation (for overlapping domain decomposition level set) to the analysis of different free surface flow problems are presented. Copyright © 2008 John Wiley & Sons, Ltd.
Abstract
This paper introduces a new stabilized finite element method based on the finite calculus (Comput. Methods Appl. Mech. Eng. 1998; 151:233–267) and arbitrary [...]
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An unstructured finite element solver for ship hydrodynamics problems
J. García-Espinosa, E. Oñate

Journal of Applied Mechanics (2003). 70(1): 18-26

Abstract
A stabilized semi-implicit fractional step algorithm based on the ﬁnite element method for solving ship wave problems using unstructured meshes is presented. The stabilized gov-erning equations for the viscous incompressible ﬂuid and the free surface are derived at a differential level via a ﬁnite calculus procedure. This allows us to obtain a stabilized numerical solution scheme. Some particular aspects of the problem solution, such as the mesh updating procedure and the transom stern treatment, are presented. Examples of the efﬁciency of the semi-implicit algorithm for the analysis of ship hydrodynamics problems are presented.
Abstract
A stabilized semi-implicit fractional step algorithm based on the ﬁnite element method for solving ship wave problems using unstructured meshes is presented. The stabilized [...]
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Methodological-technological framework for construction 4.0
F. Muñoz, J. Mora-Serrano, I. Valero, E. Oñate

Archives of Computational Methods in Engineering (2021). Vol. 28, pp. 689–711

Abstract
The construction industry has traditionally been characterised by the high diversity of its agents and processes, high resistance to change and low incorporation of technology compared to manufacturing industries. However, the construction sector is experiencing now a strong renovation process in methodology and tools due to the incorporation of the Building Information Modelling, Lean Construction and Integrated Project Delivery. Meanwhile, in production systems, “Industry 4.0” is a new paradigm that proposes automation, monitoring, sensorisation, robotisation, and digitalisation to improve production and distribution processes. In this context, some authors have proposed the concept of “Construction 4.0” as the counterpart of Industry 4.0 for the construction sector, although the methodological-technological implications are not clear. This research shows a methodological-technological framework adapted to the Architecture, Engineering, Construction, and Operations industry. This papers includes a detailed proposal for a reference frameworks and related technologies that could impact on this sector, responding to its complexities and specific challenges, such as the unique spaces for each work, which are difficult to standardise, arbitrary cost overruns and a productivity far below the average for other industries, increasing competitiveness and globalisation, as opposed to its traditionally local deployment, and an increasing demand to reduce the carbon footprint for all its activities.
Abstract
The construction industry has traditionally been characterised by the high diversity of its agents and processes, high resistance to change and low incorporation of technology [...]
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Modelling the vertical UL 94 test: competition and collaboration between melt dripping, gasification and combustion
F. Kempel, B. Schartel, J. Marti, K. Butler, R. Rossi, S. Idelsohn, E. Oñate

Fire and Materials (2015). Vol. 39 (6), pp. 570-584

Abstract
An experimental and numerical investigation of the effect of bisphenol A bis(diphenyl phosphate) (BDP) and polytetraﬂuoroethylene (PTFE) on the ﬁre behaviour of bisphenol A polycarbonate/acrylonitrile butadiene styrene (PC/ABS) in the vertical UL 94 scenario is presented. Four PC/ABS blends were discussed, which satisfy different UL 94 classiﬁ cations d ue to the competing ef fects of gasiﬁca ti on, charring, ﬂame inhibition and melt ﬂow/dripping. For numerical investigation, the particle ﬁnite element method (PFEM) is used. Its capability to model the complex ﬁre behaviour of polymers in the UL 94 is analysed. The materials’ properties are characterised, in particular the additives impact on the dripping behaviour during thermal exposure. BDP is an efﬁcie nt p lasticiser; adding PTFE p reve nts dripping by causing a ﬂo w limit. P FEM simulation s reproduce the dripping and burning behaviour, in particular the competition between gasiﬁcation and dripping. The thermal impact of both the burner and the ﬂame is approximated taking into account ﬂame inhibition, charring and effective heat of combustion. PFEM is a promising numerical tool for the investigation of the ﬁre behaviour of polymers, particularly when large deformations are involved. Not only the principal phenomena but also the different UL 94 classi ﬁ cations and t he exti nc tion times are well predicted.
Abstract
An experimental and numerical investigation of the effect of bisphenol A bis(diphenyl phosphate) (BDP) and polytetraﬂuoroethylene (PTFE) on the ﬁre behaviour of bisphenol [...]
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On a non‐linear formulation for curved Timoshenko beam elements considering large displacement/rotation increments
E. Dvorkin, E. Oñate, J. Oliver

Int. J. Numer. Meth. Engng. (1988). Vol. 26 (7), pp. 1597-1613

Abstract
An incremental Total Lagrangian Formulation for curved beam elements that includes the effect of large rotation increments is developed. A complete and symmetric tangent stiffness matrix is obtained and the numerical results show, in general, an improvement over the standard formulation where the assumption of infinitesimal rotation increments is made in the derivation of the tangent stiffness matrix.
Abstract
An incremental Total Lagrangian Formulation for curved beam elements that includes the effect of large rotation increments is developed. A complete and symmetric tangent stiffness [...]
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Las herramientas numéricas y la práctica profesional en Ingeniería Civil
B. Suarez, E. Oñate, R. Ribó

Revista de Obras Públicas (2002). Vol. 149 (3418), pp. 7-15

Abstract
This paper presents some thoughts about the evolution of numerical methods and the difficulties posed by their applications to solve real problems of everyday´s engineering. Some remarks on the mathematical and computational tools needed for the practical use of numerical methods are given, together with some best practice rules. Finally the limits and perspectives of numerical methods are discussed.
Abstract
This paper presents some thoughts about the evolution of numerical methods and the difficulties posed by their applications to solve real problems of everyday´s engineering. [...]
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Stabilized solution of the multidimensional advection-diffusion-absorption equation using linear finite elements
E. Oñate, J. Miquel, F. Zárate

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

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

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

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

Comput. Methods Appl. Mech. Engrg., (1998). Vol. 151 (1-2), pp. 233-265

Abstract
The concept of the so called “artificial or balancing diffusion” used to stabilize the numerical solution of advective–diffusive transport and fluid flow problems is revised in this paper. It is shown that the standard forms of the balancing diffusion terms, usually chosen in a heuristic manner, can be naturally found by introducing higher order approximations in the derivation of the governing differential equations via standard conservation (or equilibrium) principles. This allows us to reinterprete many stabilization algorithms and concepts used in every day practice by numerical analysts and also provides an expression for computing the stabilization parameter.
Abstract
The concept of the so called “artificial or balancing diffusion” used to stabilize the numerical solution of advective–diffusive transport and fluid flow [...]
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Finite element nonlinear analysis of concrete structures using a “plastic-damage model”
S. Oller, E. Oñate, J. Oliver, J. Lubliner

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

Abstract
In this paper a plastic damage model for nonlinear finite element analysis of concrete is presented. The model is based on standard plasticity theory for frictional materials. Details of the expressions of a new yield function proposed and of the evolution laws of the model parameters are given. The model allows to include elastic and plastic stiffness degradation effects. This is also discussed in the paper together with the problem of mesh objectivity, and the a posteriori determination of cracks. Finally, one example of application which shows the accuracy of the model is also given.
Abstract
In this paper a plastic damage model for nonlinear finite element analysis of concrete is presented. The model is based on standard plasticity theory for frictional [...]
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Mejora de la solución fuertemente acoplada de problemas FSI mediante una aproximación de la matriz tangente de presión
R. Rossi, S. Idelsohn, E. Oñate, J. Cotela, F. Pin

Rev. int. métodos numér. cálc. diseño ing. (2011). Vol. 27, (3)

Abstract
La interacción de los fluidos con las estructuras de su entorno es un desafío clásico para las técnicas numéricas. El objetivo de este trabajo es doble: en primer lugar se proporciona una explicación teórica simple de los principales problemas que se deben superar cuando se trata con un fluido incompresible. A continuación se introduce y justifica un nuevo procedimiento para la solución de problemas complejos de interacción fluido-estructura. Dicha estrategia se basa en la introducción de un «laplaciano de interfase» en el contorno común entre ambos medios. La idea es considerar la dependencia entre la presión del fluido y la velocidad de la estructura como un problema no lineal, que se va a resolver mediante un esquema cuasi-Newton. Se demuestra que el término de interfase resultante es una aproximación de la matriz tangente de dicho problema no lineal, usando exclusivamente álgebra lineal discreta. Finalmente, se verifica la validez de la técnica propuesta mediante su aplicación a algunos ejemplos.
Abstract
La interacción de los fluidos con las estructuras de su entorno es un desafío clásico para las técnicas numéricas. El objetivo de este trabajo es doble: en primer lugar [...]
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Dynamic modelling of retrogressive landslides with emphasis on the role of clay sensitivity
X. Zhang, S. Sloan, E. Oñate

Int. Journal for Numerical and Analytical Methods in Geomechanics (2018). Vol. 42, pp. 1806-1822 (preprint)

Abstract
This paper presents a detailed numerical study of the retrogressive failure of landslides in sensitive clays. The dynamic modelling of the landslides is carried out using a novel continuum approach, the particle finite element method, complemented with an elastoviscoplastic constitutive model. The multiwedge failure mode in the collapse is captured successfully, and the multiple retrogressive failures that have been widely observed in landslides in sensitive clays are reproduced with the failure mechanism, the kinematics, and the deposition being discussed in detail. Special attention has been paid to the role of the clay sensitivity on each retrogressive failure as well as on the final retrogression distance and the final run‐ out distance via parametric studies. Moreover, the effects of the viscosity of sensitive clays on the failure are also investigated for different clay sensitivities.
Abstract
This paper presents a detailed numerical study of the retrogressive failure of landslides in sensitive clays. The dynamic modelling of the landslides is carried out [...]
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Un elemento de sólido con una mejora en el comportamiento del corte transversal para el tratamiento de láminas
F. Flores, E. Oñate

Rev. int. métodos numér. cálc. diseño ing. (2011). Vol. 27, (4)

Abstract
In this work a solid finite element based on a Total Lagrangian Formulation using logarithmic strains is combined with a classical assumed strain approach of the transverse strains for thick shells. The target is to use the element for shell simulations without shear locking. The selective mass scaling technique used to avoid that the discretization across the thickness reduce the critical time in codes with explicit integration of the momentum equations is summarized. Several examples are presented showing that the element is shear-locking free, the consequences of the selective mass scaling and the possibilities of the element for the analysis of composites laminates in non-linear material regime.
Abstract
In this work a solid finite element based on a Total Lagrangian Formulation using logarithmic strains is combined with a classical assumed strain approach of the transverse [...]
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Combination of the critical displacement method with a damage model for structural instability analysis
E. Oñate, H. Tschöpe, P. Wriggers

Engineering Computations (2001). Vol. 18 (3-4), pp. 642-662

Abstract
The paper describes the extension of the critical displacement method (CDM), presented by Oñate and Matias in 1996, to the instability analysis of structures with non-linear material behaviour using a simple damage model. The extended CDM is useful to detect instability points using a prediction of the critical displacement field and a secant load-displacement relationship accounting for material non-linearities. Examples of application of CDM to the instability analysis of structures using bar and solid finite elements are presented.
Abstract
The paper describes the extension of the critical displacement method (CDM), presented by Oñate and Matias in 1996, to the instability analysis of structures with [...]
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A coupled fluid FEM-DEM technique for predicting blasting operations in tunnels
F. Zarate, J. Gonzalez, J. Miquel, R. Lohner, E. Oñate

Underground Space (2018). Vol. 3 (4), pp. 310-316, (prepint)

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

Int. J. Numer. Meth. Engng. (2011). Vol. 86 (1), pp. 18-46

Abstract
We propose a fourth‐order compact scheme on structured meshes for the Helmholtz equation given by R(φ):=f(x)+Δφ+ξ2φ=0. The scheme consists of taking the alpha‐interpolation of the Galerkin finite element method and the classical central finite difference method. In 1D, this scheme is identical to the alpha‐interpolation method (J. Comput. Appl. Math. 1982; 8(1):15–19) and in 2D making the choice α=0.5 we recover the generalized fourth‐order compact Padé approximation (J. Comput. Phys. 1995; 119:252–270; Comput. Meth. Appl. Mech. Engrg 1998; 163:343–358) (therein using the parameter γ=2). We follow (SIAM Rev. 2000; 42(3):451–484; Comput. Meth. Appl. Mech. Engrg 1995; 128:325–359) for the analysis of this scheme and its performance on square meshes is compared with that of the quasi‐stabilized FEM (Comput. Meth. Appl. Mech. Engrg 1995; 128:325–359). In particular, we show that the relative phase error of the numerical solution and the local truncation error of this scheme for plane wave solutions diminish at the rate O((ξℓ)4), where ξ, ℓ represent the wavenumber and the mesh size, respectively. An expression for the parameter α is given that minimizes the maximum relative phase error in a sense that will be explained in Section 4.5. Convergence studies of the error in the L2 norm, the H1 semi‐norm and the l∞ Euclidean norm are done and the pollution effect is found to be small. Copyright © 2010 John Wiley & Sons, Ltd.
Abstract
We propose a fourth‐order compact scheme on structured meshes for the Helmholtz equation given by R(φ):=f(x)+Δφ+ξ2φ=0. The scheme consists of taking [...]
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Numerical simulation of fiber reinforced composite materials––two procedures
E. Car, F. Zalamea, S. Oller, J. Canet, E. Oñate

Int. J. Solids and Structures (2002). Vol. 39 (7), pp. 1967-1986

Abstract
In this work, two methodologies for the analysis of unidirectional fiber reinforced composite materials are presented. The first methodology used is a generalized anisotropic large strains elasto-plastic constitutive model for the analysis of multiphase materials. It is based on the mixing theory of basic substance. It is the manager of the several constitutive laws of the different compounds and it allows to consider the interaction between the compounds of the composite materials. In fiber reinforced composite materials, the constitutive behavior of the matrix is isotropic, whereas the fiber is considered orthotropic. So, one of the constitutive model used in the mixing theory needs to consider this characteristic. The non-linear anisotropic theory showed in this work is a generalization of the classic isotropic plasticity theory (A Continuum Constitutive Model to Simulate the Mechanical Behavior of Composite Materials, PhD Thesis, Universidad Politécnica de Cataluña, 2000). It is based in a one-to-one transformation of the stress and strain spaces by means of a four rank tensor. The second methodology used is based on the homogenization theory. This theory divided the composite material problem into two scales: macroscopic and microscopic scale. In macroscopic level the composite material is assuming as a homogeneous material, whereas in microscopic level a unit volume called cell represents the composite (Tratamiento Numérico de Materiales Compuestos Mediante la teorı́a de Homogeneización, PhD Thesis, Universidad Politécnica, de Cataluña 2001). This formulation presents a new viewpoint of the homogenization theory in which can be found the equations that relate both scales. The solution is obtained using a coupled parallel code based on the finite elements method for each scale problem.
Abstract
In this work, two methodologies for the analysis of unidirectional fiber reinforced composite materials are presented. The first methodology used is a generalized anisotropic [...]
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Detailed simulation of viral propagation in the built environment (preprint)
R. Lohner, H. Antil, S. Idelsohn, E. Oñate

Computational Mechanics (2020). 10.1007/s00466-020-01881-7

Abstract
A summary is given of the mechanical characteristics of virus contaminants and the transmission via droplets and aerosols. The ordinary and partial differential equations describing the physics of these processes with high fidelity are presented, as well as appropriate numerical schemes to solve them. Several examples taken from recent evaluations of the built environment are shown, as well as the optimal placement of sensors.
Abstract
A summary is given of the mechanical characteristics of virus contaminants and the transmission via droplets and aerosols. The ordinary and partial differential equations [...]
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Sobre la necesidad de controlar el error de discretización de elementos finitos en optimización de forma estructural con algoritmos evolutivos
J. Ródenas, G. Bugeda, J. Albelda, E. Oñate, E. Nadal

Rev. int. métodos numér. cálc. diseño ing. (2012). Vol. 28, (1)

Abstract
This work analyzes the influence of the discretization error contained in the Finite Element (FE) analyses of each design configuration proposed by the structural shape optimization algorithms over the behavior of the algorithm. The paper clearly shows that if FE analyses are not accurate enough, the final solution provided by the optimization algorithm will neither be optimal nor satisfy the constraints. The need for the use of adaptive FE analysis techniques in shape optimum design will be shown. The paper proposes the combination of two strategies to reduce the computational cost related to the use of mesh adaptivity in evolutionary optimization algorithms: (a) the use of the algorithm described by Bugeda et al. [1] which reduces the computational cost associated to the adaptive FE analysis of each geometrical configuration and, (b) the successive increase of the required accuracy of the FE analyses in order to obtain a considerable reduction of the computational cost in the early stages of the optimization process.
Abstract
This work analyzes the influence of the discretization error contained in the Finite Element (FE) analyses of each design configuration proposed by the structural shape optimization [...]
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Advances in stabilized finite element and particle methods for bulk forming processes
E. Oñate, J. Rojek, M. Chiumenti, S. Idelsohn, F. Pin, R. Aubry

Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 6750-6777

Abstract
The paper describes some recent developments in finite element and particle methods for analysis of a wide range of bulk forming processes. The developments include new stabilized linear triangles and tetrahedra using finite calculus and a new procedure combining particle methods and finite element methods. Applications of the new numerical methods to casting, forging and other bulk metal forming problems and mixing processes are shown.
Abstract
The paper describes some recent developments in finite element and particle methods for analysis of a wide range of bulk forming processes. The developments include new stabilized [...]
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Derivation of thin plate bending elements with one degree of freedom per node: a simple three node triangle
E. Oñate, M. Cervera

Engineering Computations (1993). Vol. 10 (6), pp. 543-561

Abstract
A general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented. The formulation is based on the combination of a standard C0 finite element interpolation for the deflection field with an independent approximation of the curvatures which are expressed in terms of the deflection gradient along the sides using a finite volume‐like approach. The formulation is particularized for the simplest element of the family, i.e. the three node triangle with three degrees of freedom. The potential of the new element is shown through different examples of application.
Abstract
A general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented. The formulation is based on the combination of a standard C0 [...]
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Flow of solids during forming and extrusion: Some aspects of numerical solutions
O. Zienkiewicz, P. Jain, E. Oñate

Int. J. Solids and Structures (1978). Vol. 14 (1), pp. 15-38

Abstract
In the extrusion and forming of solids the plastic (or viscoplastic) deformations are so large that the elastic strain is negligible. The problem thus becomes one of incompressible viscous, non-Newtonian flow with prescribed boundary velocities. Various formulations of such problems (analogous to those of incompressible solid mechanics) are possible, and the paper investigates two basic processes. Details of application to some examples of steady state flow in extrusion, drawing and rolling are given and transient free surface solutions are demonstrated for stretch forming and deep drawing. The formulation is shown to be capable of dealing with boundary friction and strain hardening. The coupling with thermal effects is demonstrated in the last section of the paper, and in addition, some practical problems of elastic spring-back which occur on the removal of load are discussed.
Abstract
In the extrusion and forming of solids the plastic (or viscoplastic) deformations are so large that the elastic strain is negligible. The problem thus becomes one of incompressible [...]
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Discrete element simulation of rock cutting
J. Rojek, E. Oñate, C. Labra, H. Kargl

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

Abstract
This paper presents numerical modelling of rock cutting processes. The model consists of a tool–rock system. The rock is modelled using the discrete element method, which is suitable to study problems of multiple material fracturing such as those involved in rock cutting. Both 2D and 3D models are considered in this work. The paper presents a brief overview of the theoretical formulation and calibration of the discrete element model by a methodology combining the dimensional analysis with simulation of the unconfined compressive strength (UCS) and indirect tension (Brazilian) tests. The rock cutting process with roadheader picks, which is typical for underground excavation, has been simulated. The results of the 2D and 3D analyses have been compared with one another, and numerical results have been compared with the available experimental data.
Abstract
This paper presents numerical modelling of rock cutting processes. The model consists of a tool–rock system. The rock is modelled using the discrete element method, [...]
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A total Lagrangian formulation for the geometrically nonlinear-analysis of structures using finite-elements. Part II: arches, frames and axisymmetric shells
J. Oliver, E. Oñate

Int. J. Numer. Meth. Engng. (1986). Vol. 23 (2), pp. 253-274

Abstract
A geometrically nonlinear finite element formulation based on a total Lagrangian approach for axisymmetric shells, arches and frames has been presented. The formulation allows for large displacement-large rotations of the structure. Shear deformation effects have also been taken into account. It has been shown how the formulation can be presented in a unified manner to treat simultaneously the three types of structures.
Abstract
A geometrically nonlinear finite element formulation based on a total Lagrangian approach for axisymmetric shells, arches and frames has been presented. The formulation allows [...]
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Optimización de embarcaciones de recreo mediante la utilización de un código CFD
M. López-Rodríguez, J. García-Espinosa, E. Oñate

Ingeniería Naval (2001). Vol. 784, pp. 122-130

Abstract
En la actualidad las más avanzadas técnicas para diseño naval ya no se restringen sólo a proyectos de alto coste; si no que también ahora son de aplicación en el campo de las embarcaciones de recreo y turísticas, dando con ello un valor añadido al proyecto final. La utilización de un código CFD para el mayor conocimiento del comportamiento hidrodinámico de las embarcaciones de recreo y turísticas es de una gran utilidad debido a las complejidades que en el diseño de estas se presentan. Estas herramientas nos van a proporcionar una serie de datos como sustentación lateral en las embarcaciones de vela o interacción entre cascos en catamaranes con deriva lateral, que de otra forma nunca pudieran conocerse. Los resultados hidrodinámicos obtenidos nos sirven para comparar las diferentes alternativas, y para además obtener unos valores que directamente son usados para la predicción de velocidad de la embarcación, que más tarde se verán refrendadas por las pruebas de mar. La utilización de técnicas CFD, basadas en el método de los elementos finitos, para la resolución de las ecuaciones de Reynolds (RANSE), incluyendo efectos de superficie libre, hace que todo esto sea posible. En este trabajo se presentan diversos resultados de aplicación del código CFD SHYNE a varias embarcaciones deportivas y de recreo. SHYNE está basado en la técnica del Cálculo Finitesimal para la integración de las ecuaciones de Reynolds.
Abstract
En la actualidad las más avanzadas técnicas para diseño naval ya no se restringen sólo a proyectos de alto coste; si no que también ahora [...]
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Polyhedrization of an arbitrary 3D point set
S. Idelsohn, N. Calvo, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2003). Vol. 192, pp. 2649–2667

Abstract
Given a 3D point set, the problem of defining the volume associated, dividing it into a set of regions (elements) and defining a boundary surface is tackled. Several physical problems need to define volume domains, boundary surfaces and approximating functions from a given point distribution. This is for instance the case of particle methods, in which all the information is the particle positions and there are not boundary surfaces definition. Until recently, all the FEM mesh generators were limited to the generation of simple elements as tetrahedral or hexahedral elements (or triangular and quadrangular in 2D problems). The reason of this limitation was the lack of any acceptable shape function to be used in other kind of geometrical elements. Nowadays, there are several acceptable shape functions for a very large class of polyhedra. These new shape functions, together with a generalization of the Delaunay tessellation presented in this paper, gives an optimal marriage and a powerful tool to solve a large variety of physical problems by numerical methods. The domain partition into polyhedra presented here is not a standard mesh generation. The problem here is: for a given node distribution to find a suitable boundary surface and a suitable mesh to be used in the solution of a physical problem by a numerical method. To include new nodes or change their positions is not allowed.
Abstract
Given a 3D point set, the problem of defining the volume associated, dividing it into a set of regions (elements) and defining a boundary surface is tackled. Several [...]
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A high-resolution Petrov-Galerkin method for the 1D convection-diffusion-reaction problem
P. Nadukandi, E. Oñate, J. García-Espinosa

Int. J. Numer. Meth. Engng. (2010). Vol. 199, pp. 525–546

Abstract
We present the design of a high-resolution Petrov–Galerkin (HRPG) method using linear finite elements for the problem defined by the residual R (phi):= partial phi /partial t + u partial phi /partial x - k partial^2 phi /partial x^2 +s phi -f where k; s > o = 0. The structure of the method in 1D is identical to the consistent approximate upwind Petrov– Galerkin (CAU/PG) method [A.C. Galeão, E.G. Dutra do Carmo, A consistent approximate upwind Petrov– Galerkin method for the convection-dominated problems, Comput. Methods Appl. Mech. Engrg. 68 (1988) 83–95] except for the definitions of the stabilization parameters. Such a structure may also be attained via the finite-calculus (FIC) procedure [E. Oñate, Derivation of stabilized equations for numerical solution of advective–diffusive transport and fluid flow problems, Comput. Methods Appl. Mech. Engrg. 151 (1998) 233–265; E. Oñate, J. Miquel, G. Hauke, Stabilized formulation for the advection–diffusion– absorption equation using finite-calculus and linear finite elements, Comput. Methods Appl. Mech. Engrg. 195 (2006) 3926–3946] by an appropriate definition of the characteristic length. The prefix ‘high-resolution’ is used here in the sense popularized by Harten, i.e. second order accuracy for smooth/regular regimes and good shock-capturing in nonregular regimes. The design procedure embarks on the problem of circumventing the Gibbs phenomenon observed in L2-projections. Next we study the conditions on the stabilization parameters to circumvent the global oscillations due to the convective term. A conjuncture of the two results is made to deal with the problem at hand that is usually plagued by Gibbs, global and dispersive oscillations in the numerical solution. It is shown that the method indeed reproduces stabilized high-resolution numerical solutions for a wide range of values of u; k; s and f . Finally, some remarks are made on the extension of the HRPG method to multidimensions.
Abstract
We present the design of a high-resolution Petrov–Galerkin (HRPG) method using linear finite elements for the problem defined by the residual R (phi):= partial phi [...]
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A total Lagrangian formulation for the geometrically nonlinear analysis of structures using finite elements. Part I. Two‐dimensional problems: Shell and plate structures
J. Oliver, E. Oñate

Int. J. Numer. Meth. Engng. (1984). Vol. 20 (12), pp. 2253-2281

Abstract
A total Lagrangian finite element formulation for the geometrically nonlinear analysis (large displacement/large rotations) of shells is presented. Explicit expressions of all relevant finite element matrices are obtained by means of the definition of a local co‐ordinate system, based on the shell principal curvature directions, for the evaluation of strains and stresses. A series of examples of nonlinear analysis of shell and plate structures is given.
Abstract
A total Lagrangian finite element formulation for the geometrically nonlinear analysis (large displacement/large rotations) of shells is presented. Explicit expressions of [...]
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Multiscale computational analysis in mechanics using finite calculus. An introduction
E. Oñate

Comput. Methods Appl. Mech. Engrg., (2003). Vol. 192 (28-30), pp. 3043-3059

Abstract
The paper introduces a general procedure for computational analysis of a wide class of multiscale problems in mechanics using a finite calculus (FIC) formulation. The FIC approach is based in expressing the governing equations in mechanics accepting that the domain where the standard balance laws are established has a finite size. This introduces naturally additional terms into the classical equations of infinitesimal theory in mechanics which are useful for the numerical solution of problems involving different scales in the physical parameters. The discrete nodal values obtained with the FIC formulation and the finite element method (FEM) can be effectively used as the starting point for obtaining a more refined solution in zones where high gradients of the relevant variables occur using hierarchical or enriched FEM. Typical multiscale problems in mechanics which can be solved with the FIC method include convection-diffusion-reaction problems with high localized gradients, incompressible problems in solid and fluid mechanics, localization problems such as prediction of shear bands in solids and shock waves in compressible fluids, turbulence, etc. The paper presents an introduction of the treatment of multiscale problems using the FIC approach in conjunction with the finite element method (FEM). Examples of application of the FIC/FEM formulation to the solution of simple multiscale convection-diffusion problems are given.
Abstract
The paper introduces a general procedure for computational analysis of a wide class of multiscale problems in mechanics using a finite calculus (FIC) formulation. The FIC [...]
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A stabilized mixed implicit Material Point Method for non-linear incompressible solid mechanics
I. Iaconeta, A. LARESE, R. Rossi, E. Oñate

Computational Mechanics (2019). Vol. 63 (6), pp. 1243–1260

Abstract
In this work a stabilized mixed formulation for the solution of non-linear solid mechanics problems in nearly-incompressible conditions is presented. In order to deal with high material deformation, an implicit Material Point Method is chosen. Such choice allows avoiding the classical limitations of the Finite Element Method, e.g., element tangling and extreme mesh distortion. The proposed mixed formulation, with displacement and pressure as primary variables, is tested through classical benchmarks in solid and geo-mechanics where a Neo-Hookean, a J2 and a Mohr-Coulomb plastic law are employed. Further, the stabilized mixed formulation is compared with a displacement-based formulation to demonstrate how the proposed approach gets better results in terms of accuracy, not only when incompressible materials are simulated, but also in the case of compressible ones.
Abstract
In this work a stabilized mixed formulation for the solution of non-linear solid mechanics problems in nearly-incompressible conditions is presented. In order to deal with [...]
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Fatigue analysis of materials and structures using a continuum damage model
O. Salomon, S. Oller, E. Oñate

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

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

Commun. Numer. Meth. Engng (2009). Vol. 25 (7), pp. 837-849

Abstract
The first step in a discrete element simulation is the discretization of the domain into a set of particles. The cost of generating a good cylindrical or spherical packing has resulted in a great number of approaches during the last years. A new algorithm is proposed for high‐density packing using a scheme that minimizes the distance between each particle. Using the support of a finite element mesh, less time is needed in order to achieve a low porosity configuration. In addition, a boundary constraint is introduced. The application of the same optimization scheme is used as a condition to force a good surface definition. The results obtained show a high efficiency for the generation of low porosity packing, achieving values smaller than 10% in 2D cases and 30% in 3D cases.
Abstract
The first step in a discrete element simulation is the discretization of the domain into a set of particles. The cost of generating a good cylindrical or spherical packing [...]
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Numerical analysis of stereolithography processes using the finite element method
G. Bugeda, M. Cervera, G. Lombera, E. Oñate

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

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

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

Abstract
In this paper, a thermo-mechanical constitutive model for the predictions of fatigue in structures using the finite element method is formulated. The model is based on the damage mechanics of the continuous medium and allows the treatment in a unified way of coupled phenomena such as fatigue with damage, plasticity, viscosity and temperature effects. Basically it is gotten sensitive models to cyclic loads starting from classical non-linear constitutive formulations incorporating the special variable influenced by the characteristics of the cyclic load. A formulation based on the theories of damage and plasticity is developed. The necessary modifications of these theories are outlined in order to include the fatigue phenomena. A brief description of the finite element implementation is given. Finally, results of the performance of the proposed model are shown through the simple fatigue test and the fatigue analysis of an aluminium engine alternator support.
Abstract
In this paper, a thermo-mechanical constitutive model for the predictions of fatigue in structures using the finite element method is formulated. The model is based on the [...]
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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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A stabilized finite point method for analysis of fluid mechanics problems
E. Oñate, S. Idelsohn, O. Zienkiewicz, R. Taylor, C. Sacco

Comput. Methods Appl. Mech. Engrg., (1996). Vol. 195, pp. 6750-6777

Abstract
flow type problems is presented. The method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation integrals. Some examples of application to convective trasport and compressible flow problems are presented.
Abstract
flow type problems is presented. The method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation [...]
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Neural networks for variational problems in engineering
R. Lopez, E. Balsa-Canto, E. Oñate

Int. J. Numer. Meth. Engng. (2008). Vol. 75 (11), pp. 1341-1360

Abstract
In this work a conceptual theory of neural networks (NNs) from the perspective of functional analysis and variational calculus is presented. Within this formulation, the learning problem for the multilayer perceptron lies in terms of finding a function, which is an extremal for some functional. Therefore, a variational formulation for NNs provides a direct method for the solution of variational problems. This proposed method is then applied to distinct types of engineering problems. In particular a shape design, an optimal control and an inverse problem are considered. The selected examples can be solved analytically, which enables a fair comparison with the NN results. Copyright © 2008 John Wiley & Sons, Ltd.
Abstract
In this work a conceptual theory of neural networks (NNs) from the perspective of functional analysis and variational calculus is presented. Within this formulation, the learning [...]
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A finite point method for elasticity problems
E. Oñate, F. Perazzo, J. Canet

Computers and Structures (2001). Vol. 79 (22-25), pp. 2151-2163

Abstract
The basis of the finite point method (FPM) for the fully meshless solution of elasticity problems in structural mechanics is described. A stabilization technique based on a finite calculus procedure is used to improve the quality of the numerical solution. The efficiency and accuracy of the stabilized FPM in the meshless analysis of simple linear elastic structural problems is shown in some examples of applications.
Abstract
The basis of the finite point method (FPM) for the fully meshless solution of elasticity problems in structural mechanics is described. A stabilization [...]
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Nonlinear finite element analysis of orthotropic and prestressed membrane structures
J. Valdes-Vazquez, J. Canet, E. Oñate

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

Abstract
A new methodology for the geometrically nonlinear analysis of orthotropic membrane structures using triangular finite elements is presented. The approach is based on writing the constitutive equations in the principal fiber orientation of the material. A direct consequence of the fiber orientation strategy is the possibility to analyze initially out-of-plane prestressed membrane structures. An algorithm to model wrinkling behavior is also described. Examples of application to a number of membrane structures are presented.
Abstract
A new methodology for the geometrically nonlinear analysis of orthotropic membrane structures using triangular finite elements is presented. The approach is based on writing [...]
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Solving structural optimization problems with genetic algorithms and simulated annealing
S. Botello, J. Marroquín, E. Oñate

Int. J. Numer. Meth. Engng. (1999). Vol. 45 (8), pp. 1069-1084

Abstract
In this paper we study the performance of two stochastic search methods: Genetic Algorithms and Simulated Annealing, applied to the optimization of pin‐jointed steel bar structures. We show that it is possible to embed these two schemes into a single parametric family of algorithms, and that optimal performance (in a parallel machine) is obtained by a hybrid scheme. Examples of applications to the optimization of several real steel bar structures are presented.
Abstract
In this paper we study the performance of two stochastic search methods: Genetic Algorithms and Simulated Annealing, applied to the optimization of pin‐jointed steel bar [...]
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A simple method for automatic update of finite element meshes
G. Chiandussi, G. Bugeda, E. Oñate

Commun. Numer. Meth. Engng (2000). Vol. 16 (1), pp. 1-19

Abstract
A simple method to automatically update the finite element mesh of the analysis domain is proposed. The method considers the mesh as a fictitious elastic body subjected to prescribed displacements at selected boundary points. The mechanical properties of each mesh element are appropriately selected in order to minimize the deformation and the distortion of the mesh elements. Different selection strategies have been used and compared in their application to simple examples. The method avoids the use of remeshing in the solution of shape optimization problems and reduces the number of remeshing steps in the solution of coupled fluid–structure interaction problems
Abstract
A simple method to automatically update the finite element mesh of the analysis domain is proposed. The method considers the mesh as a fictitious elastic body subjected to [...]
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P1/P0+ elements for incompressible flows with discontinuous material properties
E. Oñate, P. Nadukandi, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2015). Vol. 293, pp. 191-206

Abstract
We present a 3-noded triangle and a 4-noded tetrahedra with a continuous linear velocity and a discontinuous linear pressure field formed by the sum of an unknown ''constant pressure field'' and ''a prescribed linear field'' that satisfies the steady state momentum equations for a constant body force. The elements are termed P1/P0+ as the “effective” pressure field is linear, although the unknown pressure field is piecewise constant within each element. The elements have an excellent behaviour for incompressible viscous flow problems with discontinuous material properties formulated in either Eulerian or Lagrangian descriptions. The necessary numerical stabilization for dealing with the inf-sup condition imposed by the incompressibility constraint and high convective effects (in Eulerian flows) is introduced via the Finite Calculus (FIC) approach. For the sake of clarity, the element derivation is presented first for the simpler Stokes equations written in the standard Eulerian frame. The extension of the formulation to the Navier-Stokes equations written in the Eulerian and Lagrangian frameworks is straightforward and is presented in the second part of the paper. The efficiency and accuracy of the new P1/P0+ triangle is verified by solving a set of incompressible multifluid flow problems using a Lagrangian approach and a classical Eulerian description. The excellent performance of the new triangular element in terms of mass conservation and general accuracy for analysis of fluids with discontinuous material properties is highlighted.
Abstract
We present a 3-noded triangle and a 4-noded tetrahedra with a continuous linear velocity and a discontinuous linear pressure field formed by the sum of an unknown ''constant [...]
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The challenge of mass conservation in the solution of free‐surface flows with the fractional‐step method: Problems and solutions
S. Idelsohn, E. Oñate

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

Abstract
The purpose of this paper is to put in evidence that the fractional‐step method (FSM) used to solve the incompressible transient Euler and Navier–Stokes equations for free‐surface flows has a problem inherent to the method that may produce unacceptable variations of the domain volume. A simple modification of the free‐surface boundary term is introduced in order to reduce considerably the volume loss and preserve the computational advantages of the FSM.
Abstract
The purpose of this paper is to put in evidence that the fractional‐step method (FSM) used to solve the incompressible transient Euler and Navier–Stokes equations [...]
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Análisis CFD del movimiento de balance de un portacontenedores
J. García-Espinosa, E. Oñate, J. Helmers, M. Chakkor

Revista de Ingeniería Naval (2004). Vol. 814, pp. 104-108

Abstract
In the present work a novel approach has been developed for the resolution of this problem of analysis of the movement of roll of a ship. The methodology used for this is based on the modification of the differential equations of the fluid dynamics (RANSE equations), including the movement of the free surface, by applying the finite calculus method. The modified equations are solved using an implicit predictor-corrector scheme and the finite element method (FEM). This resolution scheme is considered optimal for these types of problems, both in accuracy and in calculation time. As an example, it should be noted that for typical problems (more than 1,000,000 finite elements) less than 4 hours of CPU are required to solve several cycles of ship movement (Pentium IV). This allows the analysis of an array of tests in a few days or even hours, having a computer network or sufficient computing power.
Abstract
In the present work a novel approach has been developed for the resolution of this problem of analysis of the movement of roll of a ship. The methodology used for this is [...]
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Rotation‐free triangular plate and shell elements
E. Oñate, F. Zárate

Int. J. Numer. Meth. Engng. (2000). Vol. 47 (1-3), pp. 557-603

Abstract
The paper describes how the finite element method and the finite volume method can be successfully combined to derive two new families of thin plate and shell triangles with translational degrees of freedom as the only nodal variables. The simplest elements of the two families based on combining a linear interpolation of displacements with cell centred and cell vertex finite volume schemes are presented in detail. Examples of the good performance of the new rotation‐free plate and shell triangles are given.
Abstract
The paper describes how the finite element method and the finite volume method can be successfully combined to derive two new families of thin plate and shell triangles with [...]
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A constitutive model for cracking of concrete based on the incremental theory of plasticity
E. Oñate, S. Oller, J. Oliver, J. Lubliner

Engineering Computations (1988). Vol. 5 (4), pp. 309-319

Abstract
A constitutive model based on classical plasticity theory for non‐linear analysis of concrete structures using finite elements is presented. The model uses the typical parameters of non‐associated plasticity theory for frictional materials and a modified Mohr‐Coulomb yield surface is suggested. Onset and amount of cracking at a point are controlled by the values of the effective plastic strain and thus it can be studied by a posteriori postprocessing of numerical results. The accuracy and objectivity of the model is checked out with some examples of application.
Abstract
A constitutive model based on classical plasticity theory for non‐linear analysis of concrete structures using finite elements is presented. The model uses the typical parameters [...]
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Shape variable definition with C0 , C1 and C2 continuity functions
G. Chiandussi, G. Bugeda, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2000). Vol. 188, pp. 727-742

Abstract
The present paper proposes a new technique for the definition of the shape design variables in 2D and 3D optimisation problems. It can be applied to the discrete model of the analysed structure or to the original geometry without any previous knowledge of the analytical expression of the CAD defining surfaces. The proposed technique allows the surface continuity to be preserved during the geometry modification process to be defined a priori. This capability allows for the definition of shape variables suitable for every kind of discipline involved in the optimisation process (structural analysis, fluid-dynamic analysis, crash analysis, aerodynamic analysis, etc.).
Abstract
The present paper proposes a new technique for the definition of the shape design variables in 2D and 3D optimisation problems. It can be applied to the discrete model of [...]
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An investigation on thermal performance of wollastonite and bentonite reinforced intumescent fire-retardant coating for steel structures
F. Ahmad, S. Ullah, N. Merican, E. Oñate, A. Al-Sehemi, G. Yeoh

Construction and Building Material (2019). Vol. 228, 116734

Abstract
This research emphases on the synthesis of new formulations of intumescent coating with improved thermal performance for steel structures. The coating formulations were based on the expandable graphite reinforced with wollastonite and bentonite. Ten samples of five formulations were synthesized by varying grinding time duration between 1 and 2 min. To analyse the substrate temperature of coated steel, fire test was performed according to ASTM-E119. The char morphology was observed by Field Emission Scanning Electron (FESEM) and Transmission Electron Microscopy (TEM). FTIR and X-ray Diffraction (XRD) test is conducted to analyse the composition of the residual char. The residual char mass was perceived by Thermogravimetric analysis (TGA) of the coating. X-ray Photo Electron Spectroscopy (XPS) was utilized for binding energy and elemental composition of the char. One-hour fire protection test showed 166 _C, the lowest substrate temperature of IFRC5-2 and 40.46% residual mass was obtained by TGA analysis. XRD analysis showed that residual char has aluminum borate and borophosphate and confirmed by functional group analysis using and FTIR. FESEM and TEM illustrated that char relates to hexagonal particles of wollastonite. XPS analysis of IFRC5-2 showed the carbon and oxygen contents were 41.40% and 51.20%. Pyrolysis-Gas Chromatography–Mass Spectrometry (Pyrolysis GC–MS) results showed IFRC-5 produced less concentration of the gaseous products compared to IFRC-C. The formulations developed by grinding solid ingredients for 2 min showed improved thermal performance compared with the formulation produced by grinding solid ingredients for 1 min. Longer grinding time and higher amount of filler improved the thermal properties of the intumescent coating.
Abstract
This research emphases on the synthesis of new formulations of intumescent coating with improved thermal performance for steel structures. The coating formulations were based [...]
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A family of residual‐based stabilized finite element methods for Stokes flows
E. Oñate, P. Nadukandi, S. Idelsohn, J. García-Espinosa, C. Felippa

Int. J. Numer. Meth. Fluids (2011). Vol. 65 (1-3), pp. 106-134

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

Comput. Methods Appl. Mech. Engrg., (1992). Vol. 94, pp. 239-262

Abstract
In this paper the functions of the Péclet number that appear in the intrinsic time of the streamline upwind/Petrov-Galerkin (SUPG) formulation are analyzed for quadratic elements. Some related issues such as the computation of the characteristic element length and the introduction of source terms in the one-dimensional model problem are also addressed.
Abstract
In this paper the functions of the Péclet number that appear in the intrinsic time of the streamline upwind/Petrov-Galerkin (SUPG) formulation are analyzed for quadratic [...]
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On the simulation of flows with violent free surface motion
R. Lohner, C. Yang, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 5597–5620

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 to obtain velocities and pressure in the gas region near the free surface have been implemented. The VOF technique is validated against the classic dam-break problem, as well as series of 2D sloshing experiments and results from smoothed particle hydrodynamics (SPH) calculations. These and a series of other examples demonstrate that the present CFD method is capable of simulating violent free surface flows with strong nonlinear behavior.
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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An advancing front point generation technique
R. Löhner, E. Oñate

Commun. Numer. Meth. Engng (1998). Vol. 14 (12), pp. 1097-1108

Abstract
An algorithm to construct boundary‐conforming, isotropic clouds of points with variable density in space is described. The input required consists of a specified mean point distance and an initial triangulation of the surface. Borrowing a key concept from advancing front grid generators, one point at a time is removed and, if possible, surrounded by admissible new points. This operation is repeated until no active points are left. Timings show that the scheme is about an order of magnitude faster than volume grid generators based on the advancing front technique, making it possible to generate large (>106) yet optimal clouds of points in a matter of minutes on a workstation. Several examples are included that demonstrate the capabilities of the technique.
Abstract
An algorithm to construct boundary‐conforming, isotropic clouds of points with variable density in space is described. The input required consists of a specified mean point [...]
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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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Discrete/finite element modelling of rock cutting with TBM disc cutter
C. Labra, J. Rojek, E. Oñate

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

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

Computational Mechanics (2012). Vol. 50 (6), pp. 805-819

Abstract
This paper aims to present a coupled solution strategy for the problem of seepage through a rockfill dam taking into account the free-surface flow within the solid as well as in its vicinity. A combination of a Lagrangian model for the structural behavior and an Eulerian approach for the fluid is used. The particle finite element method is adopted for the evaluation of the structural response, whereas an Eulerian fixed-mesh approach is employed for the fluid. The free surface is tracked by the use of a level set technique. The numerical results are validated with experiments on scale models rockfill dams.
Abstract
This paper aims to present a coupled solution strategy for the problem of seepage through a rockfill dam taking into account the free-surface flow within the solid as well [...]
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Plate bending elements with discrete constraints: New triangular elements
O. Zienkiewicz, R. Taylor, P. Papadopoulos, E. Oñate

Computers and Structures (1990). Vol. 35 (4), pp. 505-522

Abstract
In recent years a series of elements based on Reissner-Mindlin assumptions and using discrete (collocation type) constraints has been introduced. These elements have proved to be very effective, however their relation to straightforward mixed approximations has not been clear. In this paper this relationship is discussed and the reasons for their success explained. This allows new and effective triangular elements to be developed. The presentation shows the close relationships with the DKT (Discrete Kirchhoff Theory) element previously available only for thin plates and allows extension of their applications.
Abstract
In recent years a series of elements based on Reissner-Mindlin assumptions and using discrete (collocation type) constraints has been introduced. These elements have [...]
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Lagrangian formulations to solve free surface incompressible inviscid fluid flows
S. Idelsohn, M. Storti, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2001). Vol. 191 (6–7), pp. 583-593

Abstract
A particle method is presented for the solution of the incompressible inviscid fluid flow equation using a Lagrangian formulation. The interpolated function are those used in "meshless" approximations and the time integration is introduced in a semi-implicit way by a fractional step method. In this manner, both classical stabilization terms used in incompressible Euler equations are unnecessary: numerical diffusion for convective terms are unnecessary due to the Lagrangian formulation, and stabilization of pressure due to the incompressibility constraint for equal order interpolations is eliminated using the fractional step method.
Abstract
A particle method is presented for the solution of the incompressible inviscid fluid flow equation using a Lagrangian formulation. The interpolated function are those used [...]
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A simple triangular element for thick and thin plate and shell analysis
E. Oñate, F. Zárate, F. flores

Int. J. Numer. Meth. Engng. (1994). Vol. 37 (15), pp. 2569-2582

Abstract
A new plate triangle based on Reissner–Mindlin plate theory is proposed. The element has a standard linear deflection field and an incompatible linear rotation field expressed in terms of the mid‐side rotations. Locking is avoided by introducing an assumed linear shear strain field based on the tangential shear strains at the mid‐sides. The element is free of spurious modes, satisfies the patch test and behaves correctly for thick and thin plate and shell situations. The element degenerates in an explicit manner to a simple discrete Kirchhoff form.
Abstract
A new plate triangle based on Reissner–Mindlin plate theory is proposed. The element has a standard linear deflection field and an incompatible linear rotation field [...]
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A finite point method for adaptive three‐dimensional compressible flow calculations
E. Ortega, E. Oñate, S. Idelsohn

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

Abstract
The finite point method (FPM) is a meshless technique, which is based on both, a weighted least‐squares numerical approximation on local clouds of points and a collocation technique which allows obtaining the discrete system of equations. The research work we present is part of a broader investigation into the capabilities of the FPM to deal with 3D applications concerning real compressible fluid flow problems. In the first part of this work, the upwind‐biased scheme employed for solving the flow equations is described. Secondly, with the aim of exploiting the meshless capabilities, an h‐adaptive methodology for 2D and 3D compressible flow calculations is developed. This adaptive technique applies a solution‐based indicator in order to identify local clouds where new points should be inserted in or existing points could be safely removed from the computational domain. The flow solver and the adaptive procedure have been evaluated and the results are encouraging. Several numerical examples are provided in order to illustrate the good performance of the numerical methods presented.
Abstract
The finite point method (FPM) is a meshless technique, which is based on both, a weighted least‐squares numerical approximation on local clouds of points and a collocation [...]
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Analysis of a consistency recovery method for the 1D convection–diffusion equation using linear finite elements
P. Nadukandi, E. Oñate, J. García-Espinosa

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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To mesh or not to mesh. That is the question. . .
S. Idelsohn, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 4681–4696

Abstract
In the last decade a family of methods called meshless methods has been developed both for structural and fluid mechanics problems. After these ideas, a possible classification for numerical formulations may be to separate the methods that make use of a standard finite element mesh (such as those made of tetrahedra or hexahedra), from those that do not need a standard mesh, namely the meshless methods. For solving a partial different equation by a numerical method, a possible alternative may be either to use a mesh method or a meshless method. This paper discusses this issue to show that this choice is not, in the large majorities of the cases, the right question.
Abstract
In the last decade a family of methods called meshless methods has been developed both for structural and fluid mechanics problems. After these ideas, a possible classification [...]
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A Lagrangian meshless finite element method applied to fluid–structure interaction problems
S. Idelsohn, E. Oñate, F. Del Pin

Computers and Structures (2003). Vol. 81 (8-11), pp. 655-671

Abstract
A method is presented for the solution of the incompressible fluid flow equations using a Lagrangian formulation. The interpolation functions are those used in the meshless finite element method and the time integration is introduced in a semi-implicit way by a fractional step method. Classical stabilization terms used in the momentum equations are unnecessary due to the lack of convective terms in the Lagrangian formulation. Furthermore, the Lagrangian formulation simplifies the connections with fixed or moving solid structures, thus providing a very easy way to solve fluid–structure interaction problems.
Abstract
A method is presented for the solution of the incompressible fluid flow equations using a Lagrangian formulation. The interpolation functions are [...]
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A Petrov–Galerkin formulation for the alpha interpolation of FEM and FDM stencils: Applications to the Helmholtz equation
P. Nadukandi, E. Oñate, J. García-Espinosa

Int. J. Numer. Meth. Engng. (2012). Vol. 89 (11), pp. 1367-1391

Abstract
A new Petrov–Galerkin (PG) method involving two parameters, namely α1 and α2, is presented, which yields the following schemes on rectangular meshes: (i) a compact stencil obtained by the linear interpolation of the Galerkin FEM and the classical central finite difference method (FDM), should the parameters be equal, that is, α1 = α2 = α; and (ii) the nonstandard compact stencil presented in (Int. J. Numer. Meth. Engng 2011; 86:18–46) for the Helmholtz equation if the parameters are distinct, that is, α1 ≠ α2. The nonstandard compact stencil is obtained by taking the linear interpolation of the diffusive terms (specified by α1) and the mass terms (specified by α2) that appear in the stencils obtained by the standard Galerkin FEM and the classical central FDM, respectively. On square meshes, these two schemes were shown to provide solutions to the Helmholtz equation that have a dispersion accuracy of fourth and sixth order, respectively (Int. J. Numer. Meth. Engng 2011; 86:18–46). The objective of this paper is to study the performance of this PG method for the Helmholtz equation using nonuniform meshes and the treatment of natural boundary conditions.
Abstract
A new Petrov–Galerkin (PG) method involving two parameters, namely α1 and α2, is presented, which yields the following schemes on rectangular [...]
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Application of explicit FE codes to simulation of sheet and bulk metal forming processes
J. Rojek, E. Oñate, E. Postek

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

Abstract
This paper presents the application of an explicit dynamic finite element code for simulation of metal forming processes, of both sheet and bulk forming. The experiences reported here have been gained during the development and use of our own explicit program Stampack. An original formulation of a triangular shell element without rotational degrees of freedom is reviewed combining the explicit sheet forming simulation with the implicit springback analysis as well as the parallelization of the explicit program described. An extension of a finite element code for coupled thermomechanical analysis is discussed. A new thermomechanical constitutive model developed by the authors and implemented in the program is presented. Numerical examples illustrate some of the possibilities of the finite element code developed.
Abstract
This paper presents the application of an explicit dynamic finite element code for simulation of metal forming processes, of both sheet and bulk forming. The experiences [...]
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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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A Lagrangian nodal integration method for free-surface fluid flows
A. Franci, M. Cremonesi, U. Perego, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2020). Vol. 361, 112816

Abstract
We present a Lagrangian nodal integration method for the simulation of Newtonian and non-Newtonian free-surface fluid flows. The proposed nodal Lagrangian method uses a finite element mesh to discretize the computational domain and to define the (linear) shape functions for the unknown nodal variables, as in the standard Particle Finite Element Method (PFEM). In this approach, however, the integrals are performed over nodal patches and not over elements, and strains/stresses are defined at nodes and not at Gauss points. This allows to limit the drawbacks associated with the remeshing and leads to a more accurate stress computation than in the classical elemental PFEM. Several numerical tests, in 2D and in 3D, are presented to validate the proposed nodal PFEM. In all cases, the method has shown a very good agreement with analytical solutions and with experimental and numerical results from the literature. A thorough comparison between nodal and elemental PFEMs is also presented, focusing on crucial issues, such as solution accuracy, convergence, mass conservation and sensitivity to mesh distortion.
Abstract
We present a Lagrangian nodal integration method for the simulation of Newtonian and non-Newtonian free-surface fluid flows. The proposed nodal Lagrangian method uses a finite [...]
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A general methodology for deriving shear constrained Reissner-Mindlin plate elements
E. Oñate, O. Zienkiewicz, B. Suarez, R. Taylor

Int. J. Numer. Meth. Engng. (1992). Vol. 33 (2), pp. 345-367

Abstract
In this paper the necessary requirements for the good behaviour of shear constrained Reissner–Mindlin plate elements for thick and thin plate situations are re‐interpreted and a simple explicit form of the substitute shear strain matrix is obtained. This extends the previous work of the authors presented in References 18 and 31. The general methodology is applied to the re‐formulation of some well known quadrilateral plate elements and some new triangular and quadrilateral plate elements which show promising features. Some examples of the good behaviour of these elements are given.
Abstract
In this paper the necessary requirements for the good behaviour of shear constrained Reissner–Mindlin plate elements for thick and thin plate situations are re‐interpreted [...]
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Air demand estimation in bottom outlets with the particle finite element method. Susqueda Dam case study.
F. Salazar, J. San-Mauro, M. Celigueta, E. Oñate

Comp. Part. Mech (2017). Vol. 4 (3), pp. 345-356

Abstract
Dam bottom outlets play a vital role in dam operation and safety, as they allow controlling the water surface elevation below the spillway level. For partial openings, water flows under the gate lip at high velocity and drags the air downstream of the gate, which may cause damages due to cavitation and vibration. The convenience of installing air vents in dam bottom outlets is well known by practitioners. The design of this element depends basically on the maximum air flow through the air vent, which in turn is a function of the specific geometry and the boundary conditions. The intrinsic features of this phenomenon makes it hard to analyse either on site or in full scaled experimental facilities. As a consequence, empirical formulas are frequently employed, which offer a conservative estimate of the maximum air flow. In this work, the particle finite element method was used to model the air–water interaction in Susqueda Dam bottom outlet, with different gate openings. Specific enhancements of the formulation were developed to consider air–water interaction. The results were analysed as compared to the conventional design criteria and to information gathered on site during the gate operation tests. This analysis suggests that numerical modelling with the PFEM can be helpful for the design of this kind of hydraulic works.
Abstract
Dam bottom outlets play a vital role in dam operation and safety, as they allow controlling the water surface elevation below the spillway level. For partial openings, water [...]
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Comparative study of different discrete element models and evaluation of equivalent micromechanical parameters
J. Rojek, C. Labra, O. Su, E. Oñate

Int. J. Solids and Structures (2012). Vol 49 (13), pp. 1497-1517

Abstract
Comparative studies of different discrete element models of a rock-type material are presented. The discrete element formulation employs spherical particles with the cohesive interaction model combining linear elastic behaviour with brittle failure. Numerical studies consisted in simulation of the uniaxial compression test. Two cylindrical specimens with particle size distributions yielding different degree of heterogeneity have been used. Macroscopic response produced by different discrete element models has been compared. The main difference between the compared models consists in the evaluation of micromechanical constitutive parameters. Two approaches are compared. In the first approach, the contact stiffness and strength parameters depend on the local particle size, while in the second approach, global uniform contact parameters are assumed for all the contacting pairs in function of average geometric measures characterizing the particle assembly. The size dependent contact parameters are calculated as functions of geometric parameters characterizing each contacting particle pair. As geometric scaling parameters, the arithmetic and harmonic means, as well as the minimum of the radii of two contacting particles are considered. Two different models with size dependent contact parameters are formulated. The performance of these models is compared with that of the discrete element model with global uniform contact parameters. Equivalence between the models with size dependent and uniform contact parameters has been checked. In search of this equivalence, different methods of evaluation of global uniform parameters have been studied. The contact stiffness has been evaluated in terms of the average radius of the particle assembly or in terms of the averages of the arithmetic and harmonic means of the contact pair radii, the geometric parameters used in the evaluation of the contact stiffness in the size-dependent models. The uniform contact strengths have been determined as functions of the averages of radii squares, squares of arithmetic radii means or squares of minimum radii of the contacting pairs. For the more homogenous specimen, the models with local size dependent parameters and models with global uniform parameters give similar response. The models with uniform parameters evaluated according to the averages of the geometric parameters used in the evaluation of local parameters ensure better agreement with the respective models with size-dependent parameters than the models with uniform parameters evaluated according to the particle radii. Simulations using the more heterogenous specimen reveal differences between the considered models. There are significant differences in stress–strain curves as well as in the failure pattern. The models with local size-dependent parameters are more sensitive to the change of heterogeneity than the model with global uniform parameters.
Abstract
Comparative studies of different discrete element models of a rock-type material are presented. The discrete element formulation employs spherical particles with the cohesive [...]
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Wrinkling and folding analysis of elastic membranes using an enhanced rotation-free thin shell triangular element
F. Flores, E. Oñate

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

Abstract
This paper presents a formulation for analysis of thin elastic membranes using a rotation-free shell element within an explicit time integration strategy. The applications presented are isotropic/anisotropic rectangular membranes under shear forces and fabric drapes falling over a pedestal. Results are compared with other numerical results existing in the literature.
Abstract
This paper presents a formulation for analysis of thin elastic membranes using a rotation-free shell element within an explicit time integration strategy. The applications [...]
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A computational model for progressive cracking in large dams due to the swelling of concrete
M. Cervera, J. Oliver, E. Herrero, E. Oñate

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

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

Computational Mechanics (2006). Vol. 38 (4-5), pp. 440-455

Abstract
We present a general formulation for incompressible fluid flow analysis using the finite element method. The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the Finite Calculus method using a matrix form of the stabilization parameters. This allows to model a wide range of fluid flow problems for low and high Reynolds numbers flows without introducing a turbulence model. Examples of application to the analysis of incompressible flows with moderate and large Reynolds numbers are presented.
Abstract
We present a general formulation for incompressible fluid flow analysis using the finite element method. The necessary stabilization for dealing with convective effects and [...]
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Modelling and simulation of the sea-landing of aerial vehicles using the Particle Finite Element Method
P. Ryzhakov, R. Rossi, A. Viña, E. Oñate

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

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

Nuclear Engineering and Design (1998). 180, 251 – 270

Abstract
The evaluation of the failure pressure of the containment building of a large dry PWR-W three loops nuclear power plant, based on computer numerical simulation, is described in this paper. The proposed method considers fully three-dimensional finite element models in order to take into account the effect of the most significant structural characteristics (presence of three buttresses, penetrations, additional reinforcement around the penetrations, etc.), the lack of symmetry of the forces generated by the prestressing system, as well as the nonlinear behaviour of the materials and the sensitivity of the results to uncertainties associated with several parameters. The computational model is completely described, including the constitutive equations for the concrete, the reinforcing steel and prestressing tendons, the spatial discretization—isoparametric elements including the reinforcement are used. The structural models and the analyses performed for their calibration are also described. The influence on the failure pressure of incorporating the foundation slab in the structural model, and the influence of the thermal effects, are discussed. One of the conclusions of the numerical study is that the failure process can be appropriately simulated by means of a structural model which does not include either the foundation slab or the thermal effects. Finally, results of a probabilistic simulation of the failure pressure are given.
Abstract
The evaluation of the failure pressure of the containment building of a large dry PWR-W three loops nuclear power plant, based on computer numerical simulation, is described [...]
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Flow behaviour of negatively buoyant jets in immiscible ambient fluid
A. Geyer, J. Phillips, M. Mier-Torrecilla, S. Idelsohn, E. Oñate

Experiments in Fluids (2012). Vol 52 (1), pp. 261-257

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

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

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

Comput. Methods Appl. Mech. Engrg., (2000). Vol. 182 (3-4), pp. 355-370

Abstract
A stabilized finite element formulation for incompressible viscous flows is derived. The starting point are the modified Navier-Stokes equations incorporating naturally the necessary stabilization terms via a finite increment calculus (FIC) procedure. Application of the standard finite element Galerkin method to the modified differential equations leads to a stabilized discrete system of equations overcoming the numerical instabilities emanating from the advective terms and those due to the lack of compatibility between approximate velocity and pressure fields. The FIC method also provides a natural explanation for the stabilization terms appearing in all equations for both the Navier-Stokes and the simpler Stokes equations. Transient solution schemes with enhanced stabilization properties are also proposed. Finally a procedure for computing the stabilization parameters is presented.
Abstract
A stabilized finite element formulation for incompressible viscous flows is derived. The starting point are the modified Navier-Stokes equations incorporating naturally the [...]
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Analisis de la inestabilidad de estructuras por el método de desplazamiento crítico
W. Matias Silva, E. Oñate

Rev. int. métodos numér. cálc. diseño ing. (1997). Vol. 13, (2)

Abstract
Se presenta una nueva técnica de predicción de puntos críticos en el análisis de inestabilidad estructural por el MEF. El procedimiento se basa en la determinación de un camioo de desplazamiento critico aproximado. Se calculan estos desplazamientos críticos imponiendo la condición de singularidad en una expresión aproximada de la matriz de rigidez tangen.te en el punto crítico. Este procedimiento implica un problema no lineal de autovalores. La carga crítica se obtiene a posteriori, de modo directo, utilizando la relación secante entre carga y desplazamiento. Se detalla este procedimiento y la forma explícita de la matriz secante Para elementos de sólido en dos y tres dimensiones. Los resultados obtenidos constatan la efectkidad del método propuesto para análisis de distintas tipologías estructurales con elementos finitos de barra articulada 3D y de sólidos 2D y 3D.
Abstract
Se presenta una nueva técnica de predicción de puntos críticos en el análisis de inestabilidad estructural por el MEF. El procedimiento se basa [...]
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An anisotropic elastoplastic constitutive model for large deformation analysis of fibre reinforced composites
E. Car, S. Oller, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2000). Vol. 185, pp. 245-277

Abstract
In this work a generalized anisotropic elastoplastic constitutive model in large deformation is presented. It is used for the analysis of fiber-reinforced composite materials in the frame of the finite element method. Mixing theory is applied to simulate the behavior of the composite material. The elastic anisotropic behavior is simulated with classical elasticity theory, while that of a non-proportional anisotropic solid is simulated by means of the proposed generalized anisotropic elastoplastic model. The approach assumes the existence of a real anisotropic space and of a fictitious isotropic space where a mapped fictitious problem is solved. Both spaces are related by means of a linear transformation using a fourth order tensor incorporating complete information on the real anisotropic material. Details of the numerical implementations of the model into a non-linear, large deformations finite element solution scheme are provided. Examples of application showing the performance of the model for the analysis of fiber-reinforced composite materials are given.
Abstract
In this work a generalized anisotropic elastoplastic constitutive model in large deformation is presented. It is used for the analysis of fiber-reinforced composite materials [...]
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An anisotropic elastoplastic model based on an isotropic formulation
S. Oller, S. Botello, J. Canet, E. Oñate

Engineering Computations (1995). Vol. 12 (3), pp. 245-262

Abstract
This paper shows a generalization of the classic isotropic plasticity theory to be applied to orthotropic or anisotropic materials. This approach assumes the existence of a real anisotropic space, and other fictitious isotropic space where a mapped fictitious problem is solved. Both spaces are related by means of a linear transformation using a fourth order transformation tensor that contains all the information concerning the real anisotropic material. The paper describes the basis of the spaces transformation proposed and the expressions of the resulting secant and tangent constitutive equations. Also details of the numerical integration of the constitutive equation are provided. Examples of application showing the good performance of the model for analysis of orthotropic materials and fibre‐reinforced composites are given.
Abstract
This paper shows a generalization of the classic isotropic plasticity theory to be applied to orthotropic or anisotropic materials. This approach assumes the existence of [...]
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The Double Hierarchy Method. A parallel 3D contact method for the interaction of spherical particles with rigid FE boundaries using the DEM
M. Santasusana, J. Irazábal, E. Oñate, J. Carbonell

Comp. Part. Mech (2016). Vol. 3, pp. 407-428

Abstract
In this work, we present a new methodology for the treatment of the contact interaction between rigid boundaries and spherical discrete elements (DE). Rigid body parts are present in most of large-scale simulations. The surfaces of the rigid parts are commonly meshed with a finite element-like (FE) discretization. The contact detection and calculation between those DE and the discretized boundaries is not straightforward and has been addressed by different approaches. The algorithm presented in this paper considers the contact of the DEs with the geometric primitives of a FE mesh, i.e. facet, edge or vertex. To do so, the original hierarchical method presented by Horner et al. (J Eng Mech 127(10):1027–1032, 2001) is extended with a new insight leading to a robust, fast and accurate 3D contact algorithm which is fully parallelizable. The implementation of the method has been developed in order to deal ideally with triangles and quadrilaterals. If the boundaries are discretized with another type of geometries, the method can be easily extended to higher order planar convex polyhedra. A detailed description of the procedure followed to treat a wide range of cases is presented. The description of the developed algorithm and its validation is verified with several practical examples. The parallelization capabilities and the obtained performance are presented with the study of an industrial application example.
Abstract
In this work, we present a new methodology for the treatment of the contact interaction between rigid boundaries and spherical discrete elements (DE). Rigid body parts are [...]
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Direct computation of instability points with inequality constraints using the FEM
H. Tschöpe, P. Wriggers, E. Oñate

Engineering Computations (2003). Vol. 20 (5-6), pp. 611-628

Abstract
The subject of this paper is the computation of instability points in mechanical problems with the finite element method. The objective is to extend the application of critical point detection methods to problems with inequality constraints originating from damage and contact. A simple bilinear model is considered for the damage problems. A bilateral, frictionless contact formulation is used for the contact problems. Among the critical point detection methods the focus is laid on the critical displacement method and the extended system. At first a possible combination of both methods is evaluated by applying them to damage problems. A prediction method based on the extended system is developed to facilitate the comparison of both methods. Secondly, the extended system is used as a computation method for critical points in two‐dimensional contact problems.
Abstract
The subject of this paper is the computation of instability points in mechanical problems with the finite element method. The objective is to extend the application of critical [...]
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General advancing front packing algorithm for the discrete element method
C. Recarey Morfa, I. Pérez, M. Farías, E. Oñate, R. Valera, H. Casañas

Comp. Part. Mech (2018). Vol. 5, pp 13–33

Abstract
A generic formulation of a new method for packing particles is presented. It is based on a constructive advancing front method, and uses Monte Carlo techniques for the generation of particle dimensions. The method can be used to obtain virtual dense packings of particles with several geometrical shapes. It employs continuous, discrete, and empirical statistical distributions in order to generate the dimensions of particles. The packing algorithm is very flexible and allows alternatives for: 1—the direction of the advancing front (inwards or outwards), 2—the selection of the local advancing front, 3—the method for placing a mobile particle in contact with others, and 4—the overlap checks. The algorithm also allows obtaining highly porous media when it is slightly modified. The use of the algorithm to generate real particle packings from grain size distribution curves, in order to carry out engineering applications, is illustrated. Finally, basic applications of the algorithm, which prove its effectiveness in the generation of a large number of particles, are carried out.
Abstract
A generic formulation of a new method for packing particles is presented. It is based on a constructive advancing front method, and uses Monte Carlo techniques for the generation [...]
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On the pseudomaterial approach for the analysis of transient forming processes
M. Cruchaga, E. Oñate, S. Idelsohn

Commun. Numer. Meth. Engng (1995). Vol. 11 (2), pp. 137-148

Abstract
A fixed‐mesh method for the analysis of transient forming processes is presented. The mesh covers material regions and zones through which the material may flow. These last zones are identified by a pseudomaterial with relatively small physical parameters. During time processing, the interface between both materials is followed by an arbitrary Lagrangian mesh. This technique appears to be suitable for the treatment of moving surfaces with sharp corners. A particular boundary condition for the Navier‐Stokes equations is also introduced in order to model a porous wall.
Abstract
A fixed‐mesh method for the analysis of transient forming processes is presented. The mesh covers material regions and zones through which the material may flow. These last [...]
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Mould filling simulation using finite elements
R. Codina, U. Schäfer, E. Oñate

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

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

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

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

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

Abstract
We propose here a displacement-based updated Lagrangian fluid model developed to facilitate a monolithic coupling with a wide range of structural elements described in terms of displacements. The novelty of the model consists in the use of the explicit streamline integration for predicting the end-of-step configuration of the fluid domain. It is shown that this prediction considerably alleviates the time step size restrictions faced by the former Lagrangian models due to the possibility of an element inversion within one time step. The method is validated and compared with conventional approaches using three numerical examples. Time step size and corresponding Courant numbers leading to optimal behavior in terms of computational efficiency are identified.
Abstract
We propose here a displacement-based updated Lagrangian fluid model developed to facilitate a monolithic coupling with a wide range of structural elements [...]
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A bonded discrete element method for modeling ship–ice interactions in broken and unbroken sea ice fields
O. Jou Devesa, M. Celigueta, S. Latorre, F. Arrufat, E. Oñate

Computational Particle Mechanics (2019). Vol. 6 (4), pp 739–765

Abstract
This work investigates the failure patterns of ice cakes and floe-icewhen loaded by amoving and sloping structure (ice-breaking ships and cones). In the paper, we introduce the most frequently encountered ice infested scenarios, the main characteristics of ice-breaking ships and the predicted failure modes of floe-ice depending on the loading conditions, the structure type and the ice feature dimensions and thickness. For the simulations, a local bonded discrete element method (DEM) is used to model sea ice and its fractures. The packing of bonded spherical particles which reproduce the ice continuum can break due to ship–ice interactions and the failure modes are studied. A set of validation simulations are first carried out. A level ice sheet breaking against an installed ice-breaking cone with different slope angles is studied, and the results are compared with other DEM simulations. Then, a group of bonded DEM simulations are performed to predict the different failure modes produced when an ice-breaking ship bow contacts with ice cakes and floe-ice of different dimensions and thickness, typical in broken ice fields. Finally, the study of breaking a continuous level ice sheet is carried out by modeling with the bonded DEM an “infinite” large domain of sea ice and loaded by a single-degree-of-freedom model of an ice-breaking ship.
Abstract
This work investigates the failure patterns of ice cakes and floe-icewhen loaded by amoving and sloping structure (ice-breaking ships and cones). In the paper, we introduce [...]
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Large time-step explicit integration method for solving problems with dominant convection
S. Idelsohn, N. Nigro, A. Limache, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2012). Vol. 217-220, pp. 168-185

Abstract
An explicit time integrator without the CFL < 1 restriction for the momentum equation is presented. This allows stable large time-steps in problems dominated by convection, independently of the spatial discretization. The idea is to use the information existing at time t=tn in the velocity streamlines as well as in the acceleration streamlines to update the particle position as well as the velocity in an updated Lagrangian frame. The method may be used with moving or fixed meshes.
Abstract
An explicit time integrator without the CFL < 1 restriction for the momentum equation is presented. This allows stable large time-steps in problems dominated [...]
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A temperature‐based formulation for finite element analysis of generalized phase‐change problems
D. Celentano, E. Oñate, S. Oller

Int. J. Numer. Meth. Engng. (1994). Vol. 37 (20), pp. 3441-3465

Abstract
A finite element formulation for solving multidimensional phase‐change problems is presented. The formulation considers the temperature as the unique state variable, it is conservative in the weak form sense and it preserves the moving interface condition. In this work, an approximate jacobian matrix that preserves numerical convergence and stability is also derived. Furthermore, a comparative analysis with other different phase‐change finite element techniques is performed. Finally, several numerical examples are analysed in order to show the performance of the proposed methodology.
Abstract
A finite element formulation for solving multidimensional phase‐change problems is presented. The formulation considers the temperature as the unique state variable, it [...]
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A high-resolution Petrov-Galerkin method for the convection-diffusion-reaction problem. Part II-A multidimensional extension
P. Nadukandi, E. Oñate, J. García-Espinosa

Comput. Methods Appl. Mech. Engrg., (2012). Vol. 213-216, pp. 327-352

Abstract
A multidimensional extension of the HRPG method using the lowest order block finite elements is presented. First, we design a nondimensional element number that quantifies the characteristic layers which are found only in higher dimensions. This is done by matching the width of the characteristic layers to the width of the parabolic layers found for a fictitious 1D reaction–diffusion problem. The nondimensional element number is then defined using this fictitious reaction coefficient, the diffusion coefficient and an appropriate element size. Next, we introduce anisotropic element length vectors li and the stabilization parameters αi, βi are calculated along these li. Except for the modification to include the new dimensionless number that quantifies the characteristic layers, the definitions of αi, βi are a direct extension of their counterparts in 1D. Using αi, βiand li, objective characteristic tensors associated with the HRPG method are defined. The numerical artifacts across the characteristic layers are manifested as the Gibbs phenomenon. Hence, we treat them just like the artifacts formed across the parabolic layers in the reaction-dominant case. Several 2D examples are presented that support the design objective—stabilization with high-resolution
Abstract
A multidimensional extension of the HRPG method using the lowest order block finite elements is presented. First, we design a nondimensional element number that quantifies [...]
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A penalty finite element method for non‐Newtonian creeping flows
R. Codina, M. Cervera, E. Oñate

Int. J. Numer. Meth. Engng. (1993). Vol. 36 (8), pp. 1395-1412

Abstract
In this paper we present an iterative penalty finite element method for viscous non‐Newtonian creeping flows. The basic idea is solving the equations for the difference between the exact solution and the solution obtained in the last iteration by the penalty method. For the case of Newtonian flows, one can show that for sufficiently small penalty parameters the iterates converge to the incompressible solution. The objective of the present work is to show that the iterative penalization can be coupled with the iterative scheme used to deal with the non‐linearity arising from the constitutive law of non‐Newtonian fluids. Some numerical experiments are conducted in order to assess the performance of the approach for fluids whose viscosity obeys the power law.
Abstract
In this paper we present an iterative penalty finite element method for viscous non‐Newtonian creeping flows. The basic idea is solving the equations for the difference [...]
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Numerical modelling and simulation of frictional contact using a generalised coulomb law
A. Heege, P. Alart, E. Oñate

Engineering Computations (1995). Vol. 12 (7), pp. 641-656

Abstract
A consistent formulation for unilateral contact problems including frictional work hardening or softening is proposed. The approach is based on an augmented Lagrangian approach coupled to an implicit quasi‐static Finite Element Method. Analogous to classical work hardening theory in elasto‐plasticity, the frictional work is chosen as the internal variable for formulating the evolution of the friction convex. In order to facilitate the implementation of a wide range of phenomenological models, the friction coefficient is defined in a parametrised form in terms of Bernstein polynomials. Numerical simulation of a 3D deep‐drawing operation demonstrates the performance of the methods for predicting frictional contact phenomena in the case of large sliding paths including high curvatures.
Abstract
A consistent formulation for unilateral contact problems including frictional work hardening or softening is proposed. The approach is based on an augmented Lagrangian approach [...]
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Free vibration analysis of plates, bridges and axisymmetric shells using a thick finite strip method
B. Suarez, J. Canet, E. Oñate

Engineering Computations (1988). Vol. 5 (2), pp. 158-164

Abstract
A unified approach for the vibration analysis of curved or straight prismatic plates and bridges and axisymmetric shells using a finite strip method based in Reissner—Mindlin shell theory is presented. Details of obtaining all relevant strip matrices and vectors are given. It is also shown how the use of the simple linear two node strip with reduced integration leads to direct explicit forms of all relevant matrices. Examples of application which show the accuracy of the linear strip for free vibration analysis of structures are presented.
Abstract
A unified approach for the vibration analysis of curved or straight prismatic plates and bridges and axisymmetric shells using a finite strip method based in Reissner—Mindlin [...]
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Advances in FE explicit formulation for simulation of metalforming processes
J. Rojek, O. Zienkiewicz, E. Oñate, E. Postek

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

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

Computers and Structures (2001). Vol. 79 (7), pp. 737-755

Abstract
A local isotropic single parameter scalar model that can simulate the mechanical behaviour of quasi-brittle materials, such as concrete, is described. The constitutive law needs the mechanical characteristics and the fracture energy of concrete to be completely defined. The damage parameter is obtained directly from the value of an equivalent effective stress in order to reduce the computing effort. Due to the unique damage parameter, this model is suitable for the study of quasi-static problems involving monotonically increasing loads. The problem of localisation and mesh dependency have been partially overcome by using an enhanced local method in which a characteristic internal length related to the mesh dimension is employed instead of the characteristic fracture length. In this work, the model was enriched further with the introduction of a shear retention factor that accounts for the friction between the two surfaces of a crack. These new features assure a real improvement of the damage model, maintaining nevertheless its simplicity and low computing cost and making it suitable for the practical solution of large scale problems. Several numerical simulations of experimental tests, concerning fracture tests on concrete specimens and beams failing in shear, have been performed for the validation of the model. The main results from the numerical analyses are described and compared with the experimental ones.
Abstract
A local isotropic single parameter scalar model that can simulate the mechanical behaviour of quasi-brittle materials, such as concrete, is described. [...]
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The violation of objectivity in Laplace formulations of the Navier–Stokes equations
A. Limache, S. Idelsohn, R. Rossi, E. Oñate

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

Abstract
The Navier–Stokes equations written in Laplace form are often the starting point of many numerical methods for the simulation of viscous flows. Imposing the natural boundary conditions of the Laplace form or neglecting the viscous contributions on free surfaces are traditionally considered reasonable and harmless assumptions. With these boundary conditions any formulation derived from integral methods (like finite elements or finite volumes) recovers the pure Laplacian aspect of the strong form of the equations. This approach has also the advantage of being convenient in terms of computational effort and, as a consequence, it is used extensively. However, we have recently discovered that these resulting Laplacian formulations violate a basic axiom of continuum mechanics: the principle of objectivity. In the present article we give an accurate account about these topics. We also show that unexpected differences may sometimes arise between Laplace discretizations and divergence discretizations.
Abstract
The Navier–Stokes equations written in Laplace form are often the starting point of many numerical methods for the simulation of viscous flows. Imposing the natural [...]
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Modelación del ensayo brasileño empleando modelación discreta
C. Recarey Morfa, E. Oñate, J. Rojek, J. Canet, F. Zárate, G. Cadoce, C. Labra

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

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

Engineering Computations (2002). Vol. 19 (6), pp. 662-706

Abstract
The paper describes the application of the simple rotation‐free basic shell triangle (BST) to the non‐linear analysis of shell structures using an explicit dynamic formulation. The derivation of the BST element involving translational degrees of freedom only using a combined finite element–finite volume formulation is briefly presented. Details of the treatment of geometrical and material non linearities for the dynamic solution using an updated Lagrangian description and an hypoelastic constitutive law are given. The efficiency of the BST element for the non linear transient analysis of shells using an explicit dynamic integration scheme is shown in a number of examples of application including problems with frictional contact situations.
Abstract
The paper describes the application of the simple rotation‐free basic shell triangle (BST) to the non‐linear analysis of shell structures using an explicit dynamic formulation. [...]
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Variational Framework for FIC Formulations in Continuum Mechanics: High Order Tensor-Derivative Transformations and Invariants
C. Felippa, E. Oñate, S. Idelsohn

Archives of Comp. Meths. Engng. (2018). Vol. 25 (4), pp. 919–963

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

Int. J. Numer. Meth. Engng. (1999). Vol. 46 (10), pp. 1651-1671

Abstract
Masonry has been a broadly used material since the beginning of human life. Despite its popularity, the analysis of masonry structures is a complex task due to the heterogeneity and the non‐linear material behaviour. The need for reliable analysis procedures capable of predicting damage evolution and failure in historical structures in order to design efficient repair and maintenance has motivated the work of many structural analysts in this field. Here the finite element method has emerged as one of the most powerful procedures for linear and non‐linear analysis of masonry structures. The main problem pending is the development of accurate and efficient constitutive models capable of predicting the behaviour of masonry in the non‐linear range and this has been the motivation of this work. The constitutive model presented is based on the homogenized anisotropic elastoplasticity previously developed by the authors. The effect of anisotropy is introduced by means of fictitious isotropic stress and strain spaces. The material properties in the fictitious isotropic spaces are mapped into the actual anisotropic space by means of a consistent fourth‐order tensor. The advantage of the model is that the classical theory of plasticity can be used to model the non‐linear behaviour in the isotropic spaces. Details of the model for masonry structures and its implementation in a general non‐linear finite element code are given. Examples of application to the analysis of some masonry structures are presented, showing the efficiency of the model.
Abstract
Masonry has been a broadly used material since the beginning of human life. Despite its popularity, the analysis of masonry structures is a complex task due to the heterogeneity [...]
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Comparative study on sheet metal forming processes by numerical modelling and experiment
W. Sosnowski, E. Oñate, C. Agelet de Saracibar

Journal of Materials Processing Technology (1992). Vol. 34 (1-4), pp. 109-116

Abstract
In this paper some results of a wide experimental program are presented and compared with some finite element solution of sheet metal forming problems using a viscous shell formulation.
Abstract
In this paper some results of a wide experimental program are presented and compared with some finite element solution of sheet metal forming problems using a viscous shell [...]
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Particle finite element method in fluid-mechanics including thermal convection-diffusion
R. Aubry, S. Idelsohn, E. Oñate

Computers and Structures (2005). Vol. 83 (17-18), pp. 1459-1475

Abstract
A method is presented for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of the motion. Due to the severe element distortion, a frequent remeshing is performed in an efficient manner. An implicit time integration through a classical fractional step is presented. The non-linearities of the formulation are taken into account and solved with the fixed-point iteration method. The displacement and temperature solutions are coupled through the Boussinesq approximation. The Lagrangian formulation provides an elegant way of solving free-surface problems with thermal convection as the particles are followed during their motion. To illustrate the method, the Rayleigh–Bénard instability with and without free surface in two dimensions has been computed.
Abstract
A method is presented for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of the motion. Due [...]
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A basic thin shell triangle with only translational DOFs for large strain plasticity
F. Flores, E. Oñate

Int. J. Numer. Meth. Engng. (2001). Vol. 51 (1), pp. 57-83

Abstract
A simple finite element triangle for thin shell analysis is presented. It has only nine translational degrees of freedom and is based on a total Lagrangian formulation. Large strain plasticity is considered using a logarithmic strain–stress pair. A plane stress isotropic behaviour with an additive decomposition of elastic and plastic strains is assumed. A hyperelastic law is considered for the elastic part while for the plastic part a von Mises yield function with non‐linear isotropic hardening is adopted. The element is an extension of a previous similar rotation‐free triangle element based upon an updated Lagrangian formulation with hypoelastic constitutive law. The element termed BST (for basic shell triangle) has been implemented in an explicit (hydro‐) code adequate to simulate sheet‐stamping processes and in an implicit static/dynamic code. Several examples are shown to assess the performance of the present formulation.
Abstract
A simple finite element triangle for thin shell analysis is presented. It has only nine translational degrees of freedom and is based on a total Lagrangian formulation. Large [...]
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A finite point method for compressible flow
R. Löhner, C. Sacco, E. Oñate, S. Idelsohn

Int. J. Numer. Meth. Engng. (2002). Vol. 53 (8), pp. 1765-1779

Abstract
A weighted least squares finite point method for compressible flow is formulated. Starting from a global cloud of points, local clouds are constructed using a Delaunay technique with a series of tests for the quality of the resulting approximations. The approximation factors for the gradient and the Laplacian of the resulting local clouds are used to derive an edge‐based solver that works with approximate Riemann solvers. The results obtained show accuracy comparable to equivalent mesh‐based finite volume or finite element techniques, making the present finite point method competitive.
Abstract
A weighted least squares finite point method for compressible flow is formulated. Starting from a global cloud of points, local clouds are constructed using a Delaunay technique [...]
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Finite element analysis of sheet metal forming problems using a selective viscous bending/membrane formulation
E. Oñate, C. Agelet de Saracibar

Int. J. Numer. Meth. Engng. (1990). Vol. 30 (8), pp. 1577-1593

Abstract
In this paper the possibilities of the viscous voided shell approach for deriving bending/membrane finite elements for sheet metal forming problems are presented. These elements can be selectively used for membrane or full bending analysis of some parts of the sheet according to the nature of the deformation. Numerical aspects of this approach are discussed and some examples of application are also given.
Abstract
In this paper the possibilities of the viscous voided shell approach for deriving bending/membrane finite elements for sheet metal forming problems are presented. These elements [...]
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A general procedure for deriving symmetric expressions for the secant and tangent stiffness matrices in finite element analysis
A. Morán, E. Oñate, J. Miquel

Int. J. Numer. Meth. Engng. (1998). Vol. 42 (2), pp. 219-236

Abstract
The paper presents a general and straightforward procedure based on the use of the strain energy density for deriving symmetric expressions of the secant and tangent stiffness matrices for finite element analysis of geometrically non‐linear structural problems. The analogy with previously proposed methods for deriving secant and tangent matrices is detailed. The simplicity of the approach is shown in an example of application
Abstract
The paper presents a general and straightforward procedure based on the use of the strain energy density for deriving symmetric expressions of the secant and tangent stiffness [...]
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Composite materials non-linear modelling for long fibre-reinforced laminates: Continuum basis, computational aspects and validations
F. Rastellini, S. Oller, O. Salomon, E. Oñate

Computers and Structures (2008). Vol. 86 (9), pp. 879-896

Abstract
An innovative computational methodology is proposed for modelling the material non-linearmechanical behaviour of FRP structures. To model a single unidirectional composite lamina, a serial–parallel (SP) continuum approach has been developed assuming that components behave as parallel materials in the fibres alignment direction and as serial materials in orthogonal directions. The model is based on the appropriate management of the constitutive models of the component materials, by making use of suitable ‘closure equations’ that characterize the composite micro-mechanics [Rastellini F. Modelización numérica de la no-linealidad constitutiva de laminados compuestos. PhD thesis. ETSECCPB, Politechnical University of Catalonia, Barcelona, March, 2006. [in Spanish]]. Classical lamination theory is combined with the SP model to describe multidirectional laminates. The methodology is validated through several numerical analyses, which are contrasted against benchmark tests and experimental data taken from the world-wide failure exercise [Hinton MJ, Soden PD. Predicting failure in composite laminates: The background to the exercise. Comp Sci Technol 1998; 58:1001–10].
Abstract
An innovative computational methodology is proposed for modelling the material non-linearmechanical behaviour of FRP structures. To model a single unidirectional composite [...]
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A finite point method for incompressible flow problems
E. Oñate, C. Sacco, S. Idelsohn

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

Abstract
A stabilized finite point method (FPM) for the meshless analysis of incompressible fluid flow problems is presented. The stabilization approach is based in the finite increment calculus (FIC) procedure developed by Oñate [14]. An enhanced fractional step procedure allowing the semi-implicit numerical solution of incompressible fluids using the FPM is described. Examples of application of the stabilized FPM to the solution of two incompressible flow problems are presented.
Abstract
A stabilized finite point method (FPM) for the meshless analysis of incompressible fluid flow problems is presented. The stabilization approach is based in the finite increment [...]
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A residual correction method based on finite calculus
E. Oñate, R. Taylor, O. Zienkiewicz, J. Rojek

Engineering Computations (2003). Vol. 20 (5-6), pp. 629-658

Abstract
In this paper, a residual correction method based upon an extension of the finite calculus concept is presented. The method is described and applied to the solution of a scalar convection‐diffusion problem and the problem of elasticity at the incompressible or quasi‐incompressible limit. The formulation permits the use of equal interpolation for displacements and pressure on linear triangles and tetrahedra as well as any low order element type. To add additional stability in the solution, pressure gradient corrections are introduced as suggested from developments of sub‐scale methods. Numerical examples are included to demonstrate the performance of the method when applied to typical test problems.
Abstract
In this paper, a residual correction method based upon an extension of the finite calculus concept is presented. The method is described and applied to the solution of a scalar [...]
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Systemic characterization and evaluation of particle packings as initial sets for discrete element simulations
C. Recarey Morfa, L. Cortés, M. Farias, I. Pérez, R. Valera, E. Oñate

Comp. Part. Mech (2018). Vol. 5 (3), pp. 319-334

Abstract
A methodology that comprises several characterization properties for particle packings is proposed in this paper. The methodology takes into account factors such as dimension and shape of particles, space occupation, homogeneity, connectivity and isotropy, among others. This classification and integration of several properties allows to carry out a characterization process to systemically evaluate the particle packings in order to guarantee the quality of the initial meshes in discrete element simulations, in both the micro- and the macroscales. Several new properties were created, and improvements in existing ones are presented. Properties from other disciplines were adapted to be used in the evaluation of particle systems. The methodology allows to easily characterize media at the level of the microscale (continuous geometries—steels, rocks microstructures, etc., and discrete geometries) and the macroscale. A global, systemic and integral system for characterizing and evaluating particle sets, based on fuzzy logic, is presented. Such system allows researchers to have a unique evaluation criterion based on the aim of their research. Examples of applications are shown.
Abstract
A methodology that comprises several characterization properties for particle packings is proposed in this paper. The methodology takes into account factors such as dimension [...]
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A four‐noded quadrilateral element for composite laminated plates/shells using the refined zigzag theory
A. Eijo, E. Oñate, S. Oller

Int. J. Numer. Meth. Engng. (2013). Vol. 95 (8), pp. 631-660

Abstract
A new bilinear four‐noded quadrilateral element (called quadrilateral linear refined zigzag) for the analysis of composite laminated and sandwich plates/shells based on the refined zigzag theory is presented. The element has seven kinematic variables per node. Shear locking is avoided by introducing an assumed linear shear strain field. The performance of the element is studied in several examples where the reference solution is the 3D finite element analysis using 20‐noded hexahedral elements.
Abstract
A new bilinear four‐noded quadrilateral element (called quadrilateral linear refined zigzag) for the analysis of composite laminated and sandwich plates/shells based on [...]
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A methodology for adaptive mesh refinement in optimum shape design problems
G. Bugeda, E. Oñate

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

Abstract
This work presents a methodology based on the use of adaptive mesh refinement (AMR) techniques in the context of shape optimization problems analyzed by the Finite Element Method (FEM). A suitable and very general technique for the parametrization of the optimization problem using B-splines to define the boundary is first presented. Then, mesh generation using the advancing front method, the error estimation and the mesh refinement criteria are dealt with in the context of a shape optimization problems. In particular, the sensitivities of the different ingredients ruling the problem (B-splines, finite element mesh, design behaviour, and error estimator) are studied in detail. The sensitivities of the finite element mesh coordinates and the error estimator allow their projection from one design to the next, giving an “a priori knowledge” of the error distribution on the new design. This allows to build up a finite element mesh for the new design with a specified and controlled level of error. The robustness and reliability of the proposed methodology is checked out with some 2D examples.
Abstract
This work presents a methodology based on the use of adaptive mesh refinement (AMR) techniques in the context of shape optimization problems analyzed by the Finite Element [...]
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A meshless finite point method for three‐dimensional analysis of compressible flow problems involving moving boundaries and adaptivity
R. Ortega, E. Oñate, S. Idelsohn, R. Flores

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

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

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

Abstract
We present a mixed velocity-pressure finite element formulation for solving the updated Lagrangian equations for quasi and fully incompressible fluids. Details of the governing equations for the conservation of momentum and mass are given in both differential and variational form. The finite element interpolation uses an equal order approximation for the velocity and pressure unknowns. The procedure for obtaining stabilized FEM solutions is outlined. The solution in time of the discretized governing conservation equations using an incremental iterative segregated scheme is described. The linearization of these equations and the derivation of the corresponding tangent stiffness matrices is detailed. Other iterative schemes for the direct computation of the nodal velocities and pressures at the updated configuration are presented. The advantages and disadvantages of choosing the current or the updated configuration as the reference configuration in the Lagrangian formulation are discussed.
Abstract
We present a mixed velocity-pressure finite element formulation for solving the updated Lagrangian equations for quasi and fully incompressible fluids. Details of the governing [...]
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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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Modelo higro-termo-mecánico para el hormigón expuesto al fuego
D. Capua, E. Oñate

Rev. int. métodos numér. cálc. diseño ing. (2009). Vol. 25, (4)

Abstract
In this paper, a hygro-thermo-mechanical model for concrete exposed to fire, based in the mechanics of unsatured porous media of Coussy, is introduced. The model state variables are derived from a energetic potential which leads to thermodynamics consistency. The government equations of the problem are developed, including the balances equations of fluids phases mass of energy and linear momentum. Details of the FEM numerical solution of the proposed model are presented. A validation example for the developed model is presented. In this example an acceptable agreement between the numerical and experimental results is shown. Finally, as an application example the analysis of a concrete column exposed to fire is presented.
Abstract
In this paper, a hygro-thermo-mechanical model for concrete exposed to fire, based in the mechanics of unsatured porous media of Coussy, is introduced. The model state variables [...]
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VISCOUS DAMAGE MODEL FOR TIMOSHENKO BEAM STRUCTURES
A. Barbat, S. Oller, E. Oñate, A. Hanganu

International Journal of Solids Structures (1997). 34(30), 3953-3976

Abstract
A local damage constitutive model based on Kachanov’s theory is used within a finite element frame and applied to the case of 2D and 3D Timoshenko beam elements. The model takes into account viscous effects, thus allowing damping to be considered in a rigorous way. A damage index based on potential energy criteria, useful in evaluating the behaviour of structures or of parts of structures, is proposed. The procedure is applied to estimate the damage produced by seismic actions in reinforced concrete building structures, whose response is computed by using a non-linear Newmark-type incremental time integration scheme. Three numerical examples are included; one of them compares results obtained by using the proposed model with results of a laboratory test.
Abstract
A local damage constitutive model based on Kachanov’s theory is used within a finite element frame and applied to the case of 2D and 3D Timoshenko beam elements. The [...]
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A generalized streamline finite element approach for the analysis of incompressible flow problems including moving surfaces
M. Cruchaga, E. Oñate

Comput. Methods Appl. Mech. Engrg., (1999). Vol. 173, pp. 241-255

Abstract
In the present work a generalized streamline finite element formulation able to deal with incompressible flow problems is presented. In the finite element framework, this technique allows the use of equal order interpolation for the unknowns of the problem: velocity and pressure. In this context, stable and convergent solutions can be obtained without requiring tuning parameters defined outside this model. The tracking of moving surfaces is also included in the numerical model. This formulation has been checked in 21) and 3D tests.
Abstract
In the present work a generalized streamline finite element formulation able to deal with incompressible flow problems is presented. In the finite element framework, this [...]
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Possibilities of the particle finite element method for fluid–soil–structure interaction problems
E. Oñate, M. Celigueta, S. Idelsohn, F. Salazar, B. Suarez

Computational Mechanics (2011). Vol. 48 (3), pp. 307-318

Abstract
We present some developments in the particle finite element method (PFEM) for analysis of complex coupled problems in mechanics involving fluid–soil–structure interaction (FSSI). The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the solid domains (the later including soil/rock and structures). A mesh connects the particles (nodes) defining the discretized domain where the governing equations for each of the constituent materials are solved as in the standard FEM. The stabilization for dealing with an incompressibility continuum is introduced via the finite calculus method. An incremental iterative scheme for the solution of the non linear transient coupled FSSI problem is described. The procedure to model frictional contact conditions and material erosion at fluid–solid and solid–solid interfaces is described. We present several examples of application of the PFEM to solve FSSI problems such as the motion of rocks by water streams, the erosion of a river bed adjacent to a bridge foundation, the stability of breakwaters and constructions sea waves and the study of landslides.
Abstract
We present some developments in the particle finite element method (PFEM) for analysis of complex coupled problems in mechanics involving fluid–soil–structure [...]
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A new formulation for air-blast fluid–structure interaction using an immersed approach. Part I: basic methodology and FEM-based simulations
Y. Bazilevs, K. Kamran, G. Moutsanidis, D. Benson, E. Oñate

Computational Mechanics (2017). Vol. 60 (1), pp. 83-100

Abstract
In this two-part paper we begin the development of a new class of methods for modeling fluid–structure interaction (FSI) phenomena for air blast. We aim to develop accurate, robust, and practical computational methodology, which is capable of modeling the dynamics of air blast coupled with the structure response, where the latter involves large, inelastic deformations and disintegration into fragments. An immersed approach is adopted, which leads to an a-priori monolithic FSI formulation with intrinsic contact detection between solid objects, and without formal restrictions on the solid motions. In Part I of this paper, the core air-blast FSI methodology suitable for a variety of discretizations is presented and tested using standard finite elements. Part II of this paper focuses on a particular instantiation of the proposed framework, which couples isogeometric analysis (IGA) based on non-uniform rational B-splines and a reproducing-kernel particle method (RKPM), which is a Meshfree technique. The combination of IGA and RKPM is felt to be particularly attractive for the problem class of interest due to the higher-order accuracy and smoothness of both discretizations, and relative simplicity of RKPM in handling fragmentation scenarios. A collection of mostly 2D numerical examples is presented in each of the parts to illustrate the good performance of the proposed air-blast FSI framework.
Abstract
In this two-part paper we begin the development of a new class of methods for modeling fluid–structure interaction (FSI) phenomena for air blast. We aim to develop accurate, [...]
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Numerical aerodynamic analysis of large buildings using a finite element model with application to a telescope building
R. Codina, C. Morton, E. Oñate, O. Soto

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

Abstract
Presents a numerical strategy for the aerodynamic analysis of large buildings, with an application to the simulation of the air flow within a telescope building. The finite element formulation is presented first, and then the methodology followed to obtain significant data from the calculations is described. The quality of the ventilation of the building is defined by the average residence times, and the feasibility of this ventilation by the actions created on the instruments and the general flow pattern.
Abstract
Presents a numerical strategy for the aerodynamic analysis of large buildings, with an application to the simulation of the air flow within a telescope building. The finite [...]
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Modelling of tunnelling processes and rock cutting tool wear with the particle finite element method
J. Carbonell, E. Oñate, B. Suarez

Computational Mechanics (2013). Vol. 52 (3), pp. 607-629

Abstract
Underground construction involves all sort of challenges in analysis, design, project and execution phases. The dimension of tunnels and their structural requirements are growing, and so safety and security demands do. New engineering tools are needed to perform a safer planning and design. This work presents the advances in the particle finite element method (PFEM) for the modelling and the analysis of tunneling processes including the wear of the cutting tools. The PFEM has its foundation on the Lagrangian description of the motion of a continuum built from a set of particles with known physical properties. The method uses a remeshing process combined with the alpha-shape technique to detect the contacting surfaces and a finite element method for the mechanical computations. A contact procedure has been developed for the PFEM which is combined with a constitutive model for predicting the excavation front and the wear of cutting tools. The material parameters govern the coupling of frictional contact and wear between the interacting domains at the excavation front. The PFEM allows predicting several parameters which are relevant for estimating the performance of a tunnelling boring machine such as wear in the cutting tools, the pressure distribution on the face of the boring machine and the vibrations produced in the machinery and the adjacent soil/rock. The final aim is to help in the design of the excavating tools and in the planning of the tunnelling operations. The applications presented show that the PFEM is a promising technique for the analysis of tunnelling problems.
Abstract
Underground construction involves all sort of challenges in analysis, design, project and execution phases. The dimension of tunnels and their structural requirements are [...]
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Reliability estimation of the sheet stamping process using support vector machines
J. Hurtado, F. Zarate, E. Oñate

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

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

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

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

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

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

Int. J. Numer. Meth. Engng. (1988). Vol. 26 (11), pp. 2559-2568

Abstract
This letter represents an initiative started by a number of researchers signed below who are working in the field of numerical modelling of soil mechanics problems. We belive that the type of approach outlined is important in a serious numerical study of all problems in geomechanics and indeed is valid in other areas.
Abstract
This letter represents an initiative started by a number of researchers signed below who are working in the field of numerical modelling of soil mechanics problems. We belive [...]
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Simple modifications for stabilization of the finite point method
B. Boroomand, A. Tabatabaei, E. Oñate

Int. J. Numer. Meth. Engng. (2005). Vol. 63 (3), pp. 351-379

Abstract
A stabilized version of the finite point method (FPM) is presented. A source of instability due to the evaluation of the base function using a least square procedure is discussed. A suitable mapping is proposed and employed to eliminate the ill‐conditioning effect due to directional arrangement of the points. A step by step algorithm is given for finding the local rotated axes and the dimensions of the cloud using local average spacing and inertia moments of the points distribution. It is shown that the conventional version of FPM may lead to wrong results when the proposed mapping algorithm is not used. It is shown that another source for instability and non‐monotonic convergence rate in collocation methods lies in the treatment of Neumann boundary conditions. Unlike the conventional FPM, in this work the Neumann boundary conditions and the equilibrium equations appear simultaneously in a weight equation similar to that of weighted residual methods. The stabilization procedure may be considered as an interpretation of the finite calculus (FIC) method. The main difference between the two stabilization procedures lies in choosing the characteristic length in FIC and the weight of the boundary residual in the proposed method. The new approach also provides a unique definition for the sign of the stabilization terms. The reasons for using stabilization terms only at the boundaries is discussed and the two methods are compared. Several numerical examples are presented to demonstrate the performance and convergence of the proposed methods. Copyright © 2005 John Wiley & Sons, Ltd.
Abstract
A stabilized version of the finite point method (FPM) is presented. A source of instability due to the evaluation of the base function using a least square procedure is discussed. [...]
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A reduced-order model based on the coupled 1D-3D finite element simulations for an efficient analysis of hemodynamics problems
E. Soudah, R. Rossi, S. Idelsohn, E. Oñate

Computational Mechanics (2014). Vol. 54 (4), pp. 1013-1022

Abstract
A reduced-order model for an efficient analysis of cardiovascular hemodynamics problems using multiscale approach is presented in this work. Starting from a patient-specific computational mesh obtained by medical imaging techniques, an analysis methodology based on a two-step automatic procedure is proposed. First a coupled 1D-3D Finite Element Simulation is performed and the results are used to adjust a reduced-order model of the 3D patient-specific area of interest. Then, this reduced-order model is coupled with the 1D model. In this way, three-dimensional effects are accounted for in the 1D model in a cost effective manner, allowing fast computation under different scenarios. The methodology proposed is validated using a patient-specific aortic coarctation model under rest and non-rest conditions.
Abstract
A reduced-order model for an efficient analysis of cardiovascular hemodynamics problems using multiscale approach is presented in this work. Starting from a patient-specific [...]
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Boundary conditions for finite element simulations of convective flows with artificial boundaries
J. Heinrich, S. Idelsohn, E. Oñate, C. Vionnet

Int. J. Numer. Meth. Engng. (1996). Vol. 39 (6), pp. 1053-1071

Abstract
We examine the use of natural boundary conditions and conditions of the Sommerfeld type for finite element simulations of convective transport in viscous incompressible flows. We show that natural boundary conditions are superior in the sense that they always provide a correct boundary condition, as opposed to the Sommerfeld‐type conditions, which can lead to a singular formulation and a great loss of accuracy. For the Navier–Stokes equations, the natural boundary conditions must be combined with a simple method to eliminate perturbations on the pressure at the open boundary, which is the source of most errors.
Abstract
We examine the use of natural boundary conditions and conditions of the Sommerfeld type for finite element simulations of convective transport in viscous incompressible flows. [...]
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The meshless finite element method
S. Idelsohn, E. Oñate, N. Calvo, F. Del Pin

Int. J. Numer. Meth. Engng. (2003). Vol. 58 (6), pp. 893-912

Abstract
A meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n, and the condition that the shape functions depend only on the node positions. Furthermore, the method proposed also shares several of the advantages of the finite element method such as: (a) the simplicity of the shape functions in a large part of the domain; (b) C0 continuity between elements, which allows the treatment of material discontinuities, and (c) ease of introduction of the boundary conditions.
Abstract
A meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n, [...]
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Real-time micro-modelling of city evacuations
R. Löhner, E. Haug, C. Zinggerling, E. Oñate

Comp. Part. Mech (2018). Vol. 5 (1), pp. 71-86

Abstract
A methodology to integrate geographical information system (GIS) data with large-scale pedestrian simulations has been developed. Advances in automatic data acquisition and archiving from GIS databases, automatic input for pedestrian simulations, as well as scalable pedestrian simulation tools have made it possible to simulate pedestrians at the individual level for complete cities in real time. An example that simulates the evacuation of the city of Barcelona demonstrates that this is now possible. This is the first step towards a fully integrated crowd prediction and management tool that takes into account not only data gathered in real time from cameras, cell phones or other sensors, but also merges these with advanced simulation tools to predict the future state of the crowd.
Abstract
A methodology to integrate geographical information system (GIS) data with large-scale pedestrian simulations has been developed. Advances in automatic data acquisition and [...]
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A plastic damage constitutive model for composite materials
S. Oller, E. Oñate, J. Canet, S. Botello

Int. J. Solids and Structures (1996). Vol. 33 (17), pp. 2501-2518

Abstract
In this paper a generalized elasto-plastic damage model for the analysis of multiphase frictional composite materials is presented. Details of the derivation of the secant and tangent constitutive equations are given. Mixing theory is used to insert the basic constitutive expressions for each substance on the multiphase composite solid. Details of the numerical implementation of the model into a general non-linear finite element solution scheme are presented. Some examples of linear and non-linear behaviour of composites are given.
Abstract
In this paper a generalized elasto-plastic damage model for the analysis of multiphase frictional composite materials is presented. Details of the derivation of the secant [...]
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PFEM–DEM for particle-laden flows with free surface
A. Franci, I. de-Pouplana, G. Casas, M. Celigueta, J. González-Usúa, E. Oñate

Computational Particle Mechanics (2020). Vol. 7, pp. 101-120

Abstract
This work proposes a fully Lagrangian formulation for the numerical modeling of free-surface particle-laden flows. The fluid phase is solved using the particle finite element method (PFEM), while the solid particles embedded in the fluid are modeled with the discrete element method (DEM). The coupling between the implicit PFEM and the explicit DEM is performed through a sub-stepping staggered scheme. This work only considers suspended spherical particles that are assumed not to affect the fluid motion. Several tests are presented to validate the formulation. The PFEM–DEM results show very good agreement with analytical solutions, laboratory tests and numerical results from alternative numerical methods.
Abstract
This work proposes a fully Lagrangian formulation for the numerical modeling of free-surface particle-laden flows. The fluid phase is solved using the particle finite element [...]
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Simulation of light‐weight membrane structures by wrinkling model
R. Rossi, M. Lazzari, R. Vitaliani, E. Oñate

Int. J. Numer. Meth. Engng. (2005). Vol. 62 (15), pp. 2127-2153

Abstract
The computational challenge in dealing with membrane systems is closely connected to the lack of bending stiffness that constitutes the main feature of this category of structures. This manifests numerically in badly conditioned or singular systems requiring the use of stabilized solution procedures, in our case of a ‘pseudo‐dynamic’ approach. The absence of the flexural stiffness makes the membrane very prone to local instabilities which manifest physically in the formation of little ‘waves’ in ‘compressed’ areas. Current work presents an efficient, sub‐iteration free ‘explicit’, penalty material based, wrinkling simulation procedure suitable for the solution of ‘static’ problems. The procedure is stabilized by taking full advantage of the pseudo‐dynamic solution strategy, which allows to retain the elemental quadratic convergence properties inside the single solution step. Results are validated by comparison with published results and by setting up ‘numerical experiments’ based on the solution of test cases using dense meshes. Copyright © 2005 John Wiley & Sons, Ltd.
Abstract
The computational challenge in dealing with membrane systems is closely connected to the lack of bending stiffness that constitutes the main feature of this category of structures. [...]
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Dynamic analysis of structures using a Reissner-Mindlin finite strip formulation
J. Canet, B. Suarez, E. Oñate

Computers and Structures (1989). Vol. 31 (6), pp. 967-975

Abstract
In this paper a finite strip formulation based on Reissner-Mindlin plate theory for dynamic analysis of prismatic shell type structure is presented. Detailed expressions of the relevant strip matrices for a variety of structures using the simple two node linear strip element are given. Examples of the good performance of the linear strip element for free and forced vibration analysis of plates, bridges and axisymmetric shells are presented.
Abstract
In this paper a finite strip formulation based on Reissner-Mindlin plate theory for dynamic analysis of prismatic shell type structure is presented. Detailed expressions of [...]
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A comparison of the linear, quadratic and cubic mindlin strip elements for the analysis of thick and thin plates
E. Oñate, B. Suarez

Computers and Structures (1983). Vol. 17 (3), pp. 427-439

Abstract
The behaviour of the linear, quadratic and cubic elements of the Mindlin plate strip family for thick and very thin plate analysis is investigated in this paper. Selective integration techniques are used to ensure the good behaviour of the elements when dealing with thin plates. Numerical results showing the convergence and accuracy of the elements for the analysis of plates of a wide range of thicknesses are given. The general performance of the three elements is discussed in detail. In particular, the linear element with a single integration point seems to be the best value strip element for practical purposes.
Abstract
The behaviour of the linear, quadratic and cubic elements of the Mindlin plate strip family for thick and very thin plate analysis is investigated in this paper. Selective [...]
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Virtual modeling of polycrystalline structures of materials using particle packing algorithms and Laguerre cells
C. Recarey Morfa, M. Farias, I. Pérez, E. Oñate

Comp. Part. Mech (2018). Vol. 5 (2), pp. 213-226

Abstract
The influence of the microstructural heterogeneities is an important topic in the study of materials. In the context of computational mechanics, it is therefore necessary to generate virtual materials that are statistically equivalent to the microstructure under study, and to connect that geometrical description to the different numerical methods. Herein, the authors present a procedure to model continuous solid polycrystalline materials, such as rocks and metals, preserving their representative statistical grain size distribution. The first phase of the procedure consists of segmenting an image of the material into adjacent polyhedral grains representing the individual crystals. This segmentation allows estimating the grain size distribution, which is used as the input for an advancing front sphere packing algorithm. Finally, Laguerre diagrams are calculated from the obtained sphere packings. The centers of the spheres give the centers of the Laguerre cells, and their radii determine the cells’ weights. The cell sizes in the obtained Laguerre diagrams have a distribution similar to that of the grains obtained from the image segmentation. That is why those diagrams are a convenient model of the original crystalline structure. The above-outlined procedure has been used to model real polycrystalline metallic materials. The main difference with previously existing methods lies in the use of a better particle packing algorithm.
Abstract
The influence of the microstructural heterogeneities is an important topic in the study of materials. In the context of computational mechanics, it is therefore necessary [...]
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A finite element formulation for incompressible flow problems using a generalized streamline operator
M. Cruchaga, E. Oñate

Comput. Methods Appl. Mech. Engrg., (1997). Vol. 143, pp. 49-67

Abstract
A finite element formulation for solving incompressible flow problems is presented. In this paper, the generalized streamline operator presented by Hughes et al. (Comput. Methods Appl. Mech. Engrg. (1986) 58 305-328) for compressible flows is adapted to the incompressible Navier-Stokes equations. This new methodology allows the use of equal order interpolation for the unknowns of the problem: velocity and pressure. In this context, the definition of the ‘upwinding tensor’ does not require parameters defined outside this model. This formulation has been checked in classical tests with satisfactory results. Finally, a moving surface problem (Cruchaga et al., Comput. Numer. Methods Engrg. (1986) 59: 85-99) is also presented.
Abstract
A finite element formulation for solving incompressible flow problems is presented. In this paper, the generalized streamline operator presented by Hughes et al. (Comput. [...]
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2D particle contact-based meshfree method in CDEM and its application in geotechnical problems
C. Feng, S. Li, E. Oñate

Engineering Computations (2015). Vol. 32 (4), pp. 1080-1103

Abstract
Purpose – Continuum-based discrete element method is an explicit numerical method, which is a combination of block discrete element method (DEM) and FEM. When simulating large deformation problems, such as cutting, blasting, water-like material flowing, the distortion of elements will lead to no convergence of the numerical system. To solve the convergence problem, a particle contact-based meshfree method (PCMM) is introduced in. The paper aims to discuss this issue. Design/methodology/approach – PCMM is based on traditional particle DEM, and use particle contacts to generate triangular elements. If three particles are contact with each other, the element will be created. Once elements are created, the macroscopic constitutive law could be introduced in. When large deformation of element occurs, the contact relationship between particles will be changed. Those elements that do not meet the contact condition will be deleted, and new elements that coincide with the relationship will be generated. By the deletion and creation of elements, the convergence problem induced by element distortion will be eliminated. To solve FEM and PCMM coupled problems, a point-edge contact model is introduced in, and normal and tangential springs are adopted to transfer the contact force between particles and blocks. Findings – According to the deletion and recreation of elements based on particle contacts, PCMM could simulate large deformation problems. Some numerical cases (i.e. elastic field testing, uniaxial compression analysis and wave propagation simulation) show the accuracy of PCMM, and others (i.e. soil cutting, contact burst and water-like material flowing) show the rationality of PCMM. Originality/value – In traditional particle DEM, contact relationships are used to calculate contact forces. But in PCMM, contact relationships are adopted to generate elements. Compared to other meshfree methods, in PCMM, the element automatic deletion and recreation technique is used to solve large deformation problems.
Abstract
Purpose – Continuum-based discrete element method is an explicit numerical method, which is a combination of block discrete element method (DEM) [...]
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A layer-wise triangle for analysis of laminated composite plates and shells
S. Botello, E. Oñate, J. Miquel

Computers and Structures (1999). Vol. 70 (6), pp. 635-646

Abstract
The paper presents a new triangle for analysis of laminate plates and shells. The in-plane degrees of freedom are interpolated quadratically whereas a linear layer-wise approximation is chosen for the normal displacement. A substructuring technique is used to eliminate the in-plane degrees of freedom during the assembly process thus reducing substantially the computationed costs. The element performance is evaluated in the static and dynamic analysis of dierent laminate plate and shell structures
Abstract
The paper presents a new triangle for analysis of laminate plates and shells. The in-plane degrees of freedom are interpolated quadratically whereas a linear layer-wise approximation [...]
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NUMISTAMP: a research project for assessment of finite-element models for stamping processes
E. Oñate, J. Rojek, C. Garino

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

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

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

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

Commun. Numer. Meth. Engng (1996). Vol. 12 (8), pp. 471-482

Abstract
A general constitutive model adequate for analysis of the thermomechanical response of composite materials is presented. The model is based on the mixture of the basic substances of the composite and allows the evaluation of the interdependence between the constitutive behaviour of different compounding materials. The behaviour of the each compound is modelled by a general anisotropic thermo‐elasto‐plastic model, termed the ‘base model’. The different base models for each compound are combined using mixing theory to simulate the behaviour of the multiphase material.
Abstract
A general constitutive model adequate for analysis of the thermomechanical response of composite materials is presented. The model is based on the mixture of the basic substances [...]
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A compressible Lagrangian framework for modeling the fluid-structure interaction in the underwater implosion of an aluminum cylinder
K. Kamran, R. Rossi, E. Oñate, S. Idelsohn

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

Abstract
We propose a fully Lagrangian monolithic system for the simulation of the underwater implosion of cylindrical aluminum containers. A variationally stabilized form of the Lagrangian shock hydrodynamics is exploited to deal with the ultrahigh compression shock waves that travel in both air and water domains. The aluminum cylinder, which separates the internal atmospheric-pressure air from the external high-pressure water, is modeled by a three-node rotation-free shell element. The cylinder undergoes fast transient deformations, large enough to produce self-contact along it. A novel elastic frictionless contact model is used to detect contact and compute the non-penetrating forces in the discretized domain between the mid-planes of the shell. Mesh quality in the vicinity of the cylinder is guaranteed by regenerating the mesh in the air and water domains when large displacements occur. A monolithic fluid–structure interaction (FSI) system is then solved. Two schemes are tested, implicit using the predictor/multi-corrector Bossak scheme, and explicit, using the forward Euler scheme. The results of the two simulations are compared with experimental data.
Abstract
We propose a fully Lagrangian monolithic system for the simulation of the underwater implosion of cylindrical aluminum containers. A variationally stabilized form of the Lagrangian [...]
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Robust design optimisation of advance hybrid (fiber-metal) composite structures
D. Lee, C. Morillo, S. Oller, G. Bugeda, E. Oñate

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

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

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

Abstract
The present work is part of a broader investigation aimed at improving the understanding of the aerodynamics of the rear aircraft section. Complex flow phenomena (e.g., the thick fuselage boundary layer at the rear end) present a challenge to the accurate predictions of aerodynamic performance. Significant efficiency gains are expected from improved-fidelity computations and experimental techniques. As part of a joint effort between several research institutions and industrial partners, a series of wind-tunnel test campaigns focusing on accurate rear-end measurements was planned. To obtain accurate tail-force data, a nonstandard live-rear-end test model was adopted. This technique uses a mechanically separate rear-end section attached to the main body through internal balances, allowing direct measurement of the force acting on the tail. This mechanical setup precludes the use of a conventional tail-coneattached sting. Moreover, to minimize aerodynamic interference on the empennage caused by the support system, a wing-attached twinsting mounting was chosen
Abstract
The present work is part of a broader investigation aimed at improving the understanding of the aerodynamics of the rear aircraft section. Complex flow phenomena (e.g., [...]
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An Implicit Material Point Method Applied to Granular Flows
I. Iaconeta, A. LARESE, R. Rossi, E. Oñate

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

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

Computational Particle Mechanics (2019). Vol. 6 (4), pp 545–559

Abstract
The discrete element method (DEM) is an emerging tool for the calculation of the behaviour of bulk materials. One of the key features of this method is the explicit integration of the motion equations. Explicit methods are rapid, at the cost of a limited time step to achieve numerical stability. First- or second-order integration schemes based on a Taylor series are frequently used in this framework and shown to be accurate for the translational and rotational motion of spherical particles. However, they may lead to relevant inaccuracies when non-spherical particles are used since the orientation implies a modification in the second-order inertia tensor in the inertial reference frame. Specific integration schemes for non-spherical particles have been proposed in the literature, such as the fourth-order Runge–Kutta scheme presented by Munjiza et al. and the predictor–corrector scheme developed by Zhao and van Wachem which applies the direct multiplication algorithm for integrating the orientation. In this work, both methods are adapted to be used together with a velocity Verlet scheme for the translational integration. The performance of the resulting schemes, as well as that of the direct integration method, is assessed, both in benchmark tests with analytical solution and in real-scale problems. The results suggest that the fourth-order Runge–Kutta and the Zhao and van Wachem schemes are clearly more accurate than the direct integration method without increasing the computational time.
Abstract
The discrete element method (DEM) is an emerging tool for the calculation of the behaviour of bulk materials. One of the key features of this method is the explicit integration [...]
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Lagrangian finite element model for the 3D simulation of glass forming processes
P. Ryzhakov, J. García-Espinosa, E. Oñate

Computers and Structures (2016). 117, 126-140 (preprint)

Abstract
We propose here a numerical model for a three-dimensional simulation of glass forming processes. Using the basic philosophy of the Particle Finite Element method (PFEM), we introduce several new features adapting the strategy to suit the problem of interest. A modified fractional step method for the solution of the flow equations is applied. This approach, on the one hand, inherits the computational efficiency of the original fractional step approach, and on the other hand shows better mass conservation features. These features are particularly attractive taking into account the importance of the correct prediction of the glass product's wall thickness. A smart mesh update strategy and a simple mechanical contact scheme are introduced. In order to account for temperature-dependent viscosity, the heat equation is coupled to the mechanical model. Viscosity is obtained from the temperature field via an empirical law. The model is validated and an example modeling the processes in the final blow mold of the bottle manufacturing process is proposed.
Abstract
We propose here a numerical model for a three-dimensional simulation of glass forming processes. Using the basic philosophy of the Particle Finite Element method (PFEM), we [...]
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Validation of numerical flow simulations against in vitro phantom measurements in different type B aortic dissection scenarios
E. Soudah, P. Rudenick, M. Bordone, D. García-Dorado, A. Evangelista, E. Oñate

Computer Methods in Biomechanics and Biomedical Engineering (2015). Vol. 18 (8), pp. 805-815

Abstract
An aortic dissection (AD) is a serious condition defined by the splitting of the arterial wall, thus generating a secondary lumen [the false lumen (FL)]. Its management, treatment and follow-up are clinical challenges due to the progressive aortic dilatation and potentially severe complications during follow-up. It is well known that the direction and rate of dilatation of the artery wall depend on haemodynamic parameters such as the local velocity profiles, intra-luminal pressures and resultant wall stresses. These factors act on the FL and true lumen, triggering remodelling and clinical worsening. In this study, we aimed to validate a computational fluid dynamic (CFD) tool for the haemodynamic characterisation of chronic (type B) ADs. We validated the numerical results, for several dissection geometries, with experimental data obtained from a previous in vitro study performed on idealised dissected physical models. We found a good correlation between CFD simulations and experimental measurements as long as the tear size was large enough so that the effect of the wall compliance was negligible.
Abstract
An aortic dissection (AD) is a serious condition defined by the splitting of the arterial wall, thus generating a secondary lumen [the false lumen (FL)]. Its management, treatment [...]
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A mesh-free finite point method for advective-diffusive transport and fluid flow problems
E. Oñate, S. Idelsohn

Computational Mechanics (1998). Vol. 21 (4-5), pp. 283-292

Abstract
The finite point method (FPM) is a gridless numerical procedure based on the combination of weighted least square interpolations on a cloud of points with point collocation for evaluating the approximation integrals. In the paper, details of a procedure for stabilizing the numerical solution for advective-diffusive transport and fluid flow problems using the FPM are given. The method is based on a consistent introduction of the stabilizing terms in the governing differential equations. One example showing the applicability of the FPM is given.
Abstract
The finite point method (FPM) is a gridless numerical procedure based on the combination of weighted least square interpolations on a cloud of points with point collocation [...]
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A general formulation for coupled thermal flow of metals using finite elements
O. Zienkiewicz, E. Oñate, J. Heinrich

Int. J. Numer. Meth. Engng. (1981). Vol. 17 (10), pp. 1497-1514

Abstract
A finite element formulation to deal with the flow of metals coupled with thermal effects in presented. The deformation process of the metal is treated using the visco‐plastic flow approach and the solution technique for the coupled problem implies a simultaneous solution for velocities and temperatures. Some aspects of the numerical solution of the problem are given and in the last part of the paper some examples of steady‐state extrusion and rolling problems showing the applicability of the method are shown.
Abstract
A finite element formulation to deal with the flow of metals coupled with thermal effects in presented. The deformation process of the metal is treated using the visco‐plastic [...]
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Direct computation of instability points for contact problems
H. Tschöpe, E. Oñate, P. Wriggers

Computational Mechanics (2003). Vol. 31 (1-2), pp. 173–178

Abstract
The extended system is known as a reliable algorithm for the direct computation of instability points on the equilibrium path of mechanical structures. This article describes the application of the extended system as critical point computation method to mechanical contact problems. In this type of problems inequality constraints have to be considered. Moreover a prediction method based on the extended system algorithm is presented which allows the detection of favorable starting values for a critical point computation on the equilibrium path.
Abstract
The extended system is known as a reliable algorithm for the direct computation of instability points on the equilibrium path of mechanical structures. This article describes [...]
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Finite calculus formulation for incompressible solids using linear triangles and tetrahedra
E. Oñate, J. Rojek, R. Taylor, O. Zienkiewicz

Int. J. Numer. Meth. Engng. (2004). Vol. 59 (11), pp. 1473-1500

Abstract
Many finite elements exhibit the so‐called ‘volumetric locking’ in the analysis of incompressible or quasi‐incompressible problems.In this paper, a new approach is taken to overcome this undesirable effect. The starting point is a new setting of the governing differential equations using a finite calculus (FIC) formulation. The basis of the FIC method is the satisfaction of the standard equations for balance of momentum (equilibrium of forces) and mass conservation in a domain of finite size and retaining higher order terms in the Taylor expansions used to express the different terms of the differential equations over the balance domain. The modified differential equations contain additional terms which introduce the necessary stability in the equations to overcome the volumetric locking problem. The FIC approach has been successfully used for deriving stabilized finite element and meshless methods for a wide range of advective–diffusive and fluid flow problems. The same ideas are applied in this paper to derive a stabilized formulation for static and dynamic finite element analysis of incompressible solids using linear triangles and tetrahedra. Examples of application of the new stabilized formulation to linear static problems as well as to the semi‐implicit and explicit 2D and 3D non‐linear transient dynamic analysis of an impact problem and a bulk forming process are presented.
Abstract
Many finite elements exhibit the so‐called ‘volumetric locking’ in the analysis of incompressible or quasi‐incompressible problems.In this paper, a new approach [...]
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Possibilities of finite calculus in computational mechanics
E. Oñate

Int. J. Numer. Meth. Engng. (2004). Vol. 60 (1), pp. 255-281

Abstract
The expression ‘finite calculus’ refers to the derivation of the governing differential equations in mechanics by invoking balance of fluxes, forces, etc. in a space–time domain of finite size. The governing equations resulting from this approach are different from those of infinitesimal calculus theory and they incorporate new terms which depend on the dimensions of the balance domain. The new governing equations allow the derivation of naturally stabilized numerical schemes using any discretization procedure. The paper discusses the possibilities of the finite calculus method for the finite element solution of convection–diffusion problems with sharp gradients, incompressible fluid flow and incompressible solid mechanics problems and strain localization situations.
Abstract
The expression ‘finite calculus’ refers to the derivation of the governing differential equations in mechanics by invoking balance of fluxes, forces, etc. in a [...]
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The extended Delaunay tessellation
N. Calvo, S. Idelsohn, E. Oñate

Engineering Computations (2003). Vol. 20 (5-6), pp. 583-600

Abstract
The extended Delaunay tessellation (EDT) is presented in this paper as the unique partition of a node set into polyhedral regions defined by nodes lying on the nearby Voronoï spheres. Until recently, all the FEM mesh generators were limited to the generation of tetrahedral or hexahedral elements (or triangular and quadrangular in 2D problems). The reason for this limitation was the lack of any acceptable shape function to be used in other kind of geometrical elements. Nowadays, there are several acceptable shape functions for a very large class of polyhedra. These new shape functions, together with the EDT, gives an optimal combination and a powerful tool to solve a large variety of physical problems by numerical methods. The domain partition into polyhedra presented here does not introduce any new node nor change any node position. This makes this process suitable for Lagrangian problems and meshless methods in which only the connectivity information is used and there is no need for any expensive smoothing process.
Abstract
The extended Delaunay tessellation (EDT) is presented in this paper as the unique partition of a node set into polyhedral regions defined by nodes lying on the nearby Voronoï [...]
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Some algorithms to correct a geometry in order to create a finite element mesh
R. Ribó, G. Bugeda, E. Oñate

Computers and Structures (2002). Vol. 80 (16-17), pp. 1399-1408

Abstract
One of the major difficulties in meshing 3D complex geometries is to deal with non-proper geometrical definitions coming from CAD systems. Typically, CAD systems do not take care of the proper definition of the geometries for the analysis purposes. In addition, the use of standard CAD files (IGES, VDA, …) for the transfer of geometries between different systems introduce some additional difficulties. In this work, a collection of algorithms to repair and/or to improve the geometry definitions are provided. The aim of these algorithms is to make as easy as possible the generation of a mesh over complex geometries given some minimum requirements of quality and correctness. The geometrical model will be considered as composed of a set of NURBS lines and trimmed surfaces. Some examples of application of the algorithms and of the meshes generated from the corrected geometry are also presented in this work.
Abstract
One of the major difficulties in meshing 3D complex geometries is to deal with non-proper geometrical definitions coming from CAD systems. Typically, [...]
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A study of mesh optimality criteria in adaptive finite element analysis
E. Oñate, G. Bugeda

Engineering Computations (1993). Vol. 10 (4), pp. 307-321

Abstract
The concepts of solution error and optimal mesh in adaptive finite element analysis are revisited. It is shown that the correct evaluation of the convergence rate of the error norms involved in the error measure and the optimal mesh criteria chosen are essential to avoid oscillations in the refinement process. Two mesh optimality criteria based on: (a) the equal distribution of global error, and (b) the specific error over the elements are studied and compared in detail through some examples of application.
Abstract
The concepts of solution error and optimal mesh in adaptive finite element analysis are revisited. It is shown that the correct evaluation of the convergence rate of the error [...]
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Interaction between an elastic structure and free-surface flows: experimental versus numerical comparisons using the PFEM
S. Idelsohn, J. Marti, A. Souto-Iglesias, E. Oñate

Computational Mechanics (2008). Vol. 43 (1), pp. 125-132

Abstract
The paper aims to introduce new fluid–structure interaction (FSI) tests to compare experimental results with numerical ones. The examples have been chosen for a particular case for which experimental results are not much reported. This is the case of FSI including free surface flows. The possibilities of the Particle Finite Element Method (PFEM) for the simulation of free surface flows is also tested. The simulations are run using the same scale as the experiment in order to minimize errors due to scale effects. Different scenarios are simulated by changing the boundary conditions for reproducing flows with the desired characteristics. Details of the input data for all the examples studied are given. The aim is to identifying benchmark problems for FSI including free surface flows for future comparisons between different numerical approaches.
Abstract
The paper aims to introduce new fluid–structure interaction (FSI) tests to compare experimental results with numerical ones. The examples have been chosen for a particular [...]
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An integration of a low cost adaptive remeshing strategy in the solution of structural shape optimization problems using evolutionary methods
G. Bugeda, J. Ródenas, E. Oñate

Computers and Structures (2008). Vol. 86 (13-14), pp. 1563-1578

Abstract
Evolutionary methods are a powerful and robust tool for the solution of structural shape optimization problems. Nevertheless, the use of these methods requires the structural analysis of an important number of different designs, this making the computational cost of the analysis of each design a critical issue. For this reason, each design must be analyzed at a minimum computational cost but ensuring a minimum quality of the results. It is well known that the cheapest mesh for producing a solution with a fixed quality at minimum cost is an adapted one. Nevertheless, traditional adapted meshes are obtained from adaptive remeshing strategies, where each design has to be analyzed more than once, thereby also causing a high computational cost. This work presents a new strategy that allows generating an adapted mesh for each design without the necessity of performing a full adaptive remeshing procedure for each of them. It is based on the use of sensitivity analysis of all magnitudes related with adaptive remeshing (location of nodes, error estimation, etc.) with respect to the design variables. This sensitivity analysis is performed only once using a geometry of reference and it is used to project the results of the corresponding analysis to all other designs to be analyzed. The projected information allows generating an appropriate adapted mesh for each new design in one shot, greatly reducing the computational cost compared with standard strategies.
Abstract
Evolutionary methods are a powerful and robust tool for the solution of structural shape optimization problems. Nevertheless, the use of these methods requires the structural [...]
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A semi-analytical model for droplet dynamics on the GDL surface of a PEFC electrode
A. Jarauta, M. Secanell, J. Pons Prats, P. Ryzhakov, S. Idelsohn, E. Oñate

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

Abstract
Water management is one of the key factors in Proton Exchange Fuel Cell (PEFC) performance. The water produced within the fuel cell is evacuated through the gas channels, but at high current densities water can block the channel, thus limiting the current density generated in the fuel cell. A semi-analytical model of a water droplet emerging from a gas diffusion layer pore in a PEFC channel is developed. The transient model contains a detailed adhesion and drag force estimation model. Results show that the predicted values for both drag and surface tension force are higher than the results found in literature. The results for the detachment force are consistent with the experimental data available. Higher air velocity values lead to more deformation of the droplet and oscillation with lower frequency but higher amplitude. Similar effects have been identified when the liquid mass flow is increased, leading to faster detachment of the droplet.
Abstract
Water management is one of the key factors in Proton Exchange Fuel Cell (PEFC) performance. The water produced within the fuel cell is evacuated through the gas channels, [...]
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Analysis of multifluid flows with large time steps using the particle finite element method
S. Idelsohn, J. Marti, P. Becker, E. Oñate

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

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

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

Abstract
The paper presents advances in the discrete element modelling of underground excavation processes extending modelling possibilities as well as increasing computational efficiency. Efficient numerical models have been obtained using techniques of parallel computing and coupling the discrete element method with finite element method. The discrete element algorithm has been applied to simulation of different excavation processes, using different tools, TBMs and roadheaders. Numerical examples of tunnelling process are included in the paper, showing results in the form of rock failure, damage in the material, cutting forces and tool wear. Efficiency of the code for solving large scale geomechanical problems is also shown
Abstract
The paper presents advances in the discrete element modelling of underground excavation processes extending modelling possibilities as well as increasing computational efficiency. [...]
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Data-Based Models for the Prediction of Dam Behaviour: A Review and Some Methodological Considerations
F. Salazar, R. Morán Moya, M. Toledo, E. Oñate

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

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

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

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

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

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

F. Salazar, J. San-Mauro, M. Celigueta,

Development and coupling of numerical techniques for modeling micromechanical discrete and continuous media using real particle morphologies