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

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

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

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A fast and accurate method to solve the incompressible Navier‐Stokes equations
S. Idelsohn, N. Nigro, J. Gimenez, R. Rossi, J. Marti

Engineering Computations (2013). Vol. 30 (2), pp. 197-222; doi: 10.1108/02644401311304854

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

Advances in Engineering Software (2000). Vol. 31 (5), pp. 339-346; doi: 10.1016/S0965-9978(99)00059-9

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

Advances in Engineering Software (2000). Vol. 31 (5), pp. 347-353; doi: 10.1016/S0965-9978(99)00060-5

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

J. Appl. Mech (2003). Vol. 70 (1), pp. 18-26; doi:10.1115/1.1530631

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

Comput. Methods Appl. Mech. Engrg., (2017). Vol. 315, pp. 1080-1097; doi: 10.1016/j.cma.2016.12.003

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

Int. J. Numer. Meth. Engng. (2012). Vol. 89 (13), pp. 1635-1651; doi: 10.1002/nme.3302

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

Int. J. Numer. Meth. Engng. (1996). Vol. 39 (22), pp. 3839-3866; doi: 10.1002/(SICI)1097-0207(19961130)39:22<3839::AID-NME27>3.0.CO;2-R

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

Comput. Methods Appl. Mech. Engrg., (2017). Vol. 326, pp. 739-756; doi: 10.1016/j.cma.2017.08.036

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

Comput. Methods Appl. Mech. Engrg., (2016). Vol. 300, pp. 106-128; doi: 10.1016/j.cma.2015.11.001

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

Comput. Methods Appl. Mech. Engrg., (2015). Vol. 291; pp. 173-196; doi: 10.1016/j.cma.2015.03.020

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

Comput. Methods Appl. Mech. Engrg., (2014). Volume 274, pp. 237-263; doi: 10.1016/j.cma.2014.02.011

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

Comput. Methods Appl. Mech. Engrg., (2013). Vol. 267, pp. 23-42; doi: 10.1016/j.cma.2013.08.001

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

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

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

Underground Space (2018). (prepint)

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

Comp. Part. Mech (2018). (prepint) Vol. 5 (3), pp. 355-373 doi: 10.1007/s40571-017-0174-3

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

Comp. Part. Mech (2018). (prepint) Vol. 5 (3) , pp. 411-420; doi: 10.1007/s40571-017-0178-z

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

Int. J. Numer. Meth. Biomed. Engng (2010). Vol. 26 (10), pp. 1313-1330; doi: 10.1002/cnm.1216

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

Computational Materials Science (2005). Vol. 32 (2), pp. 175-195; doi: 10.1016/j.commatsci.2004.08.001

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

Int. J. Computational Fluid Dynamics (2002). Vol. 16 (4), pp. 263-275; doi: 10.1080/1061856021000025148

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

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

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

Computing and Visualization in Science (2000). Vol. 3 (1), pp. 67-75; doi: 10.1007/s007910050053

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

Computing Systems in Engineering (1994). Vol. 5 (1), pp. 91-102; doi: 10.1016/0956-0521(94)90040-X

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

Int. J. of Vehicle Design (2005). Vol. 39 (1-2), pp. 110–124; doi: 10.1504/IJVD.2005.007223

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

Int. J. Mechanical Sciences (1983). Vol. 25 (5), pp. 305-335; doi: 10.1016/0020-7403(83)90011-5

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

Rapid Prototyping Journal (1995). Vol. 1 (2), pp. 13-23; doi: 10.1108/13552549510086835

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

International Journal of Forming Processes (2002). Vol. 5 (2-3-4), pp. 493-503; doi: 10.3166/ijfp.5.493-503

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

Engineering Fracture Mechanics (1990). Vol. 35 (1-2-3), pp. 219-231; doi: 10.1016/0013-7944(90)90200-Z

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

Engineering Fracture Mechanics (1990). Vol. 35 (1-3), pp. 573-585; doi: 10.1016/0013-7944(90)90232-6

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

Int. J. of Num. Meths. for Heat and Fluid Flow (2000). Vol. 10 (5-6), pp. 616-633; doi: 10.1108/09615530010347196

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

Int. J. of Num. Meths. for Heat and Fluid Flow (1994). Vol. 4 (1), pp. 291-310; doi: 10.1108/EUM0000000004108

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

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

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

Finite Elements in Analysis and Design (2011). Vol. 47 (9), pp. 982-990; doi: 10.1016/j.finel.2011.03.014

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

Finite Elements in Analysis and Design (2010). Vol. 46 (1-2), pp. 140-151; doi: 10.1016/j.finel.2009.06.032

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

Finite Elements in Analysis and Design (2009). Vol. 45 (6-7), pp. 395-405; doi: 10.1016/j.finel.2008.11.008

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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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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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; doi: 10.1016/S0924-0136(01)00894-9

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

Journal of Materials Processing Technology (1998). Vols. 80-81, pp. 620-627; doi: 10.1016/S0924-0136(98)00169-1

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

Journal of Materials Processing Technology (1996). Vol. 60 (1-4), pp. 243-247; doi: 10.1016/0924-0136(96)02337-0

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

Journal of Materials Processing Technology (1995). Vol. 50 (1-4), pp. 17-38; doi: 10.1016/0924-0136(94)01367-A

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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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; doi: 10.1016/0924-0136(92)90096-B

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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High‐density sphere packing for discrete element method simulations
C. Labra, E. Oñate

Commun. Numer. Meth. Engng (2009). Vol. 25 (7), pp. 837-849; doi: 10.1002/cnm.1193

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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Parallel Delaunay triangulation for particle finite element methods
Y. Fragakis, E. Oñate

Commun. Numer. Meth. Engng (2008). Vol. 24 (11), pp. 1009-1017; doi: 10.1002/cnm.1007

Abstract
Delaunay triangulation is a geometric problem that is relatively difficult to parallelize. Parallel algorithms are usually characterized by considerable interprocessor communication or important serialized parts. In this paper, we propose a method that achieves high speed‐ups, but needs information regarding locally maximum element circumspheres prior to the beginning of the algorithm. Such information is directly available in iterative methods, like the particle finite element methods. The developed parallel Delaunay triangulation method, has minimum communication requirements, is quite simple and achieves high parallel efficiency.
Abstract
Delaunay triangulation is a geometric problem that is relatively difficult to parallelize. Parallel algorithms are usually characterized by considerable interprocessor communication [...]
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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; doi: 10.1002/(SICI)1099-0887(200001)16:1<1::AID-CNM310>3.0.CO;2-A

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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An advancing front point generation technique
R. Löhner, E. Oñate

Commun. Numer. Meth. Engng (1998). Vol. 14 (12), pp. 1097-1108; doi: 10.1002/(SICI)1099-0887(199812)14:12<1097::AID-CNM183>3.0.CO;2-7

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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Mixing anisotropic formulation for analysis of composites
S. Oller, E. Oñate, J. Canet

Commun. Numer. Meth. Engng (1996). Vol. 12 (8), pp. 471-482; doi: 10.1002/(SICI)1099-0887(199608)12:8<471::AID-CNM995>3.0.CO;2-6

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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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; doi: 10.1002/cnm.1640110207

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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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; doi: 10.1016/j.ijsolstr.2012.02.032

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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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; doi: 10.1016/S0020-7683(01)00240-2

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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A coupled thermomechanical model for the solidification of cast metals
D. Celentano, S. Oller, E. Oñate

Int. J. Solids and Structures (1996). Vol. 33 (5), pp. 647-673; doi: 10.1016/0020-7683(95)00056-G

Abstract
A coupled thermomechanical model to simulate solidification problems in casting is presented. The model is formulated from a phenomenological point of view using a general isotropic thermoelasto-plasticity theory. Generalized phase-change effects accounting for the different thermomechanical behaviour of the solidifying material during its evolution from liquid to solid have been considered. For this purpose, a phase-change function, plastic evolution equations and a temperature-dependent constitutive law have been defined. Full thermomechanical effects as well as variable thermal and mechanical boundary conditions are also taken into account. Particular details concerning the numerical implementation of the model are given, where special emphasis is devoted to the resulting highly non-linear fully coupled finite element equations. The behaviour of this formulation is studied first in a simple quenching problem. Finally, a cylindrical casting test problem including phase-change phenomena, temperature-dependent constitutive properties and contact effects is analysed. Numerical results are compared with laboratory measurements.
Abstract
A coupled thermomechanical model to simulate solidification problems in casting is presented. The model is formulated from a phenomenological point of view using a general [...]
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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; doi: 10.1016/0020-7683(95)00161-1

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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A hygro-thermo-mechanical constitutive model for multiphase composite materials
S. Oller, E. Oñate

Int. J. Solids and Structures (1996). Vol. 33 (20-22), pp. 3179-3186; doi: 10.1016/0020-7683(95)00248-0

Abstract
The paper describes a hygro-thermo-mechanical constitutive model appropriate for numerical simulation of multiphase composite material behaviour. The theory is based on the mixture of the basic substances of the composite and allows to evaluate the inter-dependent behaviour between the different compounding constitutive models. The initial anisotropy of each compounding can be taken into account by means of a mapped isotropic plastic formulation. This is a generalization of classic isotropic plasticity theory applied to orthotropic or anisotropic materials. The basic assumption is the existence of a stress and strain real anisotropic spaces and the respective fictitious isotropic spaces where a mapped fictitious problem is solved. Those spaces are related by means of two fourth order transformation tensor. The combination of mixing theory and the mapped isotropic plastic approach provides a powerful constitutive framework for the numerical treatment of bulk-fiber composite materials.
Abstract
The paper describes a hygro-thermo-mechanical constitutive model appropriate for numerical simulation of multiphase composite material behaviour. The theory is based [...]
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A plastic-damage model for concrete
J. Lubliner, X. oliver, S. Oller, E. Oñate

Int. J. Solids and Structures (1989). Vol. 25 (3), pp. 299-326; doi: 10.1016/0020-7683(89)90050-4

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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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; doi: 10.1016/0020-7683(78)90062-8

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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Real-time micro-modelling of city evacuations
E. Haug, R. Löhner, C. Zinggerling, E. Oñate

Comp. Part. Mech (2018). Vol. 5 (1), pp. 71-86; doi: 10.1007/s40571-016-0154-z

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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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; doi: 10.1007/s40571-017-0164-5

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 three-dimensional FEM–DEM technique for predicting the evolution of fracture in geomaterials and concrete
F. Zárate, A. Cornejo Velázquez, E. Oñate

Comp. Part. Mech (2018). Vol. 5 (3) , pp. 411-420; doi: 10.1007/s40571-017-0178-z

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 and the discrete element method (DEM) approach (Zárate and Oñate in Comput Part Mech 2(3):301–314, 2015). 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 four-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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Pulse fracture simulation in shale rock reservoirs: DEM and FEM–DEM approaches
F. Zárate, A. Cornejo Velázquez, E. Oñate

Comp. Part. Mech (2018). Vol. 5 (3), pp. 355-373; doi: 10.1007/s40571-017-0174-3

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 [...]
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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; 10.1007/s40571-017-0171-6

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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Air demand estimation in bottom outlets with the particle finite element method
F. Salazar, J. San-Mauro, M. Celigueta, E. Oñate

Comp. Part. Mech (2017). Vol. 4 (3), pp. 345-356; doi: 10.1007/s40571-016-0117-4

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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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; doi: 10.1007/s-40571-016-0144-1

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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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 González, E. Oñate, J. Carbonell

Comp. Part. Mech (2016). Vol. 3, pp. 407-428; doi: 10.1007/s40571-016-0109-4

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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A modular, partitioned, discrete element framework for industrial grain distribution systems with rotating machinery
G. Casas, D. Mukherjee, M. Celigueta, T. Zohdi, E. Oñate

Comp. Part. Mech (2017). Vol. 4 (2), pp. 181-198; doi: 10.1007/s40571-015-0089-9

Abstract
A modular discrete element framework is presented for large-scale simulations of industrial grain-handling systems. Our framework enables us to simulate a markedly larger number of particles than previous studies, thereby allowing for efficient and more realistic process simulations. This is achieved by partitioning the particle dynamics into distinct regimes based on their contact interactions, and integrating them using different time-steps, while exchanging phase-space data between them. The framework is illustrated using numerical experiments based on fertilizer spreader applications. The model predictions show very good qualitative and quantitative agreement with available experimental data. Valuable insights are developed regarding the role of lift vs drag forces on the particle trajectories in-flight, and on the role of geometric discretization errors for surface meshing in governing the emergent behavior of a system of particles.
Abstract
A modular discrete element framework is presented for large-scale simulations of industrial grain-handling systems. Our framework enables us to simulate a markedly larger [...]
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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; doi: 10.1016/j.compstruc.2007.04.009

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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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; doi: 10.1016/j.compstruc.2007.05.010

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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Particle finite element method in fluid-mechanics including thermal convection-diffusion
S. Idelsohn, R. Aubry, E. Oñate

Computers and Structures (2005). Vol. 83 (17-18), pp. 1459-1475; doi: 10.1016/j.compstruc.2004.10.021

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 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; doi: 10.1016/S0045-7949(02)00477-7

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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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; doi: 10.1108/02644400110387190

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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Analysis of some partitioned algorithms for fluid-structure interaction
R. Rossi, E. Oñate

Engineering Computations (2010). Vol. 27 (1), pp. 20-56; doi: 10.1108/02644401011008513

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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Stress, strain and energy splittings for anisotropic elastic solids under volumetric constraints
C. Felippa, E. Oñate

Computers and Structures (2003). Vol. 81 (13), pp. 1343-1357; doi: 10.1016/S0045-7949(03)00060-9

Abstract
We define stress and strain splittings appropriate to linearly elastic anisotropic materials with volumetric constraints. The treatment includes rigidtropic materials, which develop no strains under a stress pattern that is a null eigenvector of the compliance matrix. This model includes as special case incompressible materials, for which the eigenvector is hydrostatic stress. The main finding is that pressure and volumetric strain must be redefined as effective quantities. Using this idea, an energy decomposition that exactly separates deviatoric and volumetric energy follows.
Abstract
We define stress and strain splittings appropriate to linearly elastic anisotropic materials with volumetric constraints. The treatment includes rigidtropic materials, [...]
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A finite element methodology for local/global damage evaluation in civil engineering structures
A. Hanganu, E. Oñate, A. Barbat

Computers and Structures (2002). Vol. 80 (20-21), pp. 1667-1687; doi: 10.1016/S0045-7949(02)00012-3

Abstract
The paper introduces a new global damage evaluation method which leads to a meaningful global damage index. A numerical procedure for the prediction of local and global damage in civil engineering structures using the finite element method and a continuum damage model, is presented. The method is adequate for the computation of the limit load in reinforced concrete (RC) structures and for the prediction of the failure mechanisms. Details of the applied damage model are given together with a description of the finite element implementation and the procedure for computing the global damage parameters. Examples of applications of the methodology to the nonlinear analysis of a range of RC structures, are presented.
Abstract
The paper introduces a new global damage evaluation method which leads to a meaningful global damage index. A numerical procedure for the prediction of local and [...]
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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; doi: 10.1108/02644400310488781

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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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; doi: 10.1016/S0045-7949(02)00105-0

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 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; doi: 10.1016/S0045-7949(00)00178-4

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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A finite point method for elasticity problems
E. Oñate, F. Perazzo, J. Canet

Computers and Structures (2001). Vol. 79 (22-25), pp. 2151-2163; doi: 10.1016/S0045-7949(01)00067-0

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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A layer-wise triangle for analysis of laminated composite plates and shells
S. Botello, E. Oñate, J. Canet

Computers and Structures (1999). Vol. 70 (6), pp. 635-646; doi: 10.1016/S0045-7949(98)00165-5

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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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; doi: 10.1016/0045-7949(90)90072-A

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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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; doi: 10.1016/0045-7949(89)90281-2

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; doi: 10.1016/0045-7949(83)90134-7

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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A unified approach for the analysis of bridges, plates and axisymmetric shells using the linear mindlin strip element
E. Oñate, B. Suarez

Computers and Structures (1983). Vol. 17 (3), pp. 407-426; doi: 10.1016/0045-7949(83)90133-5

Abstract
In this paper a finite strip formulation which allows to treat bridges, axisymmetric shells or plate structures of constant transverse cross section in an easily and unified manner is presented. The formulation is based on Mindlin's shell plate theory. One dimensional finite elements are used to discretize the transverse section and Fourier expansions are used to define the longitudinal/circumferential behavior of the structure. The element used is the simple two noded strip element with just one single integrating point. This allows to obtain all the element matrices in an explicit and economical form. Numerical examples for a variety of straight and curve bridges, axisymmetric shells and plate structures which show the efficiency of the formulation and accuracy of the linear strip element are given.
Abstract
In this paper a finite strip formulation which allows to treat bridges, axisymmetric shells or plate structures of constant transverse cross section in an easily and unified [...]
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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; doi: 10.1108/EC-04-2014-0095

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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Validation of the particle finite element method (PFEM) for simulation of free surface flows
A. Larese, R. Rossi, E. Oñate, S. Idelsohn

Engineering Computations (2008). Vol. 25 (3-4), pp. 385-425; doi: 10.1108/02644400810874976

Abstract
Purpose – The purpose of this paper is to evaluate the possibilities of the particle finite element method for simulation of free surface flows. Design/methodology/approach – A numerical simulation of a number of examples for which experimental data are available is performed. The simulations are run using the same scale as the experiment in order to minimize errors due to scale effects. Some examples are chosen from the civil engineering field: a study of the flow over a flip bucket is analyzed for both 2D and 3D models, and the flow under a planar sluice gate is studied in 2D. Other examples, such as a 2D and 3D “dam break” with an obstacle are taken from the smooth particle hydrodynamics literature. Findings – Different scenarios are simulated by changing the boundary conditions for reproducing flows with the desired characteristics. Different mesh sizes are considered for evaluating their influence on the final solution. Originality/value – Details of the input data for all the examples studied are given. The aim is to identify benchmark problems for future comparisons between different numerical approaches for free surface flows.
Abstract
Purpose – The purpose of this paper is to evaluate the possibilities of the particle finite element method for simulation of free surface flows. Design/methodology/approach [...]
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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 (5-6), pp. 662-706; doi: 10.1108/02644400210439119

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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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; doi: 10.1108/02644400310488790

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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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; doi: 10.1108/02644400310488781

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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The extended Delaunay tessellation
N. Calvo, S. Idelsohn, E. Oñate

Engineering Computations (2003). Vol. 20 (5-6), pp. 583-600; doi: 10.1108/02644400310488763

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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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; doi: 10.1108/02644409510799820

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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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; doi: 10.1108/02644409510799587

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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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; doi: /10.1108/eb023924

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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A study of mesh optimality criteria in adaptive finite element analysis
E. Oñate, G. Bugeda

Engineering Computations (1993). Vol. 10 (4), pp. 307-321; doi: 10.1108/eb023910

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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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; doi: 10.1108/eb023734

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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A constitutive model for cracking of concrete based on the incremental theory of plasticity
E. Oñate, S. Oller, X. oliver, J. Lubliner

Engineering Computations (1988). Vol. 5 (4), pp. 309-319; doi: http://dx.doi.org/10.1108/eb023750

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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A stabilized mixed implicit Material Point Method for non-linear incompressible solid mechanics
I. Iaconeta, A. Larese, R. Rossi, E. Oñate

Computational Mechanics (2018). Published online; doi: 10.1007/s00466-018-1647-9

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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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; doi: 10.1007/s00466-017-1394-3

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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A-posteriori error estimation for the finite point method with applications to compressible flow
E. Ortega, R. Flores, E. Oñate, S. Idelsohn

Computational Mechanics (2017). Vol. 60 (2), pp. 219-233; doi: 10.1007/s00466-017-1402-7

Abstract
An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained from an approximation to the truncation terms of the governing equations. This approximation is calculated from the discrete nodal differential residuals using a reconstructed solution field on a modified stencil of points. Both the error estimation methodology and the flow solution scheme are implemented using the Finite Point Method, a meshless technique enabling higher-order approximations and reconstruction procedures on general unstructured discretizations. The performance of the proposed error indicator is studied and applications to adaptive grid refinement are presented.
Abstract
An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained [...]
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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; doi: 10.1007/s00466-015-1161-2

Abstract
A new implicit stabilized formulation for the numerical solution of the compressible Navier–Stokes 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 Kouhi, Oñate (Int J Numer Methods Fluids 74:872–897, 2014). 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 Navier–Stokes equations is presented. The method is based on the finite calculus [...]
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Numerically stable formulas for a particle-based explicit exponential integrator
P. Nadukandi, E. Oñate

Computational Mechanics (2015). Vol. 55 (5), pp. 903-920; doi: 10.1007/s00466-015-1142-5

Abstract
Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.
Abstract
Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential [...]
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A particle finite element method for analysis of industrial forming processes
E. Oñate, A. Franci, J. Carbonell

Computational Mechanics (2014). Vol. 54 (1), pp. 85-107; doi: 10.1007/s00466-014-1016-2

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 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.
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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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; doi: 10.1007/s00466-014-1040-2

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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A contact algorithm for shell problems via Delaunay-based meshing of the contact domain
K. Kamran, R. Rossi, E. Oñate

Computational Mechanics (2003). Vol. 52 (1), pp. 1-16; doi: 10.1007/s00466-012-0791-x

Abstract
The simulation of the contact within shells, with all of its different facets, represents still an open challenge in Computational Mechanics. Despite the effort spent in the development of techniques for the simulation of general contact problems, an all-seasons algorithm applicable to complex shell contact problems is yet to be developed. This work focuses on the solution of the contact between thin shells by using a technique derived from the particle finite element method together with a rotation-free shell triangle. The key concept is to define a discretization of the contact domain (CD) by constructing a finite element mesh of four-noded tetrahedra that describes the potential contact volume. The problem is completed by using an assumed-strain approach to define an elastic contact strain over the CD.
Abstract
The simulation of the contact within shells, with all of its different facets, represents still an open challenge in Computational Mechanics. Despite the effort spent in the [...]
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Modelling of tunnelling processes and rock cutting tool wear with the particle finite element method
J. Carbonell, E. Oñate

Computational Mechanics (2013). Vol. 52 (3), pp. 607-629; doi: 10.1007/s00466-013-0835-x

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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Computer Programming of free GUIs for the Analysis of the Behaviour of Marine Structures
J. Gutiérrez Romero, Z. B, J. García-Espinosa, M. Peyrau Rubio

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

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

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

Abstract
In this paper, the conception and design of a new monitoring system for a racing yachts rig is presented. The sensors developed are able to process the measured strain data, by applying artificial neural networks (ANN) algorithms, and then evaluate the load acting on an element and identify the direction of the action of that force. This way, it is possible to identify the actual operating conditions of the yacht rig. The required data for ANN training is generated from the results obtained from different finite element method (FEM) computational models of the device. Furthermore, during the design phase of the system, different experimental campaigns were carried out. The experimental tests were designed to serve as proof of concept, as well as to validate the different procedures used in the system development and application. The developed monitoring system is wireless, low-intrusive and easily adaptable to any yacht configuration. This work also presents the integration of the monitoring system into a coupled fluid-structure computation model for the sails and rig of a boat. The resulting system is an efficient tool for evaluating performance and decision support in the adjustment of a sailboat rig.
Abstract
In this paper, the conception and design of a new monitoring system for a racing yachts rig is presented. The sensors developed are able to process the measured strain data, [...]
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An accurate FIC-FEM formulation for the 1D convection-diffusion-reaction equation
E. Oñate, J. Miquel, P. Nadukandi

Comput. Methods Appl. Mech. Engrg., (2016). Vol. 298() pp. 373-406 Vol. 298, pp. 373-406; doi: 10.1016/j.cma.2015.09.022

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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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

Computational Particle Mechanics (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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Combination of a non-local damage model for quasi-brittle materials with a mesh-adaptive finite element technique
I. de-Pouplana, E. Oñate

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

Abstract
Progressive fracture in quasi-brittle materials is often treated via strain softening models in continuum damage mechanics. Such constitutive relations favour spurious strain localization and ill-posedness of boundary value problems. The introduction of non-local damage models together with a characteristic length parameter controlling the size of the fracture process zone is known to regularize the problem. In order to account for the non-locality of these models, it is crucial to work with fine spatial discretizations at the damage progress zone. In this paper we present a non-local damage model in combination with a mesh-adaptive finite element technique that can help automatize the analysis of progressive fracture problems in an efficient manner. Classical two-dimensional examples are given to illustrate the presented approach.
Abstract
Progressive fracture in quasi-brittle materials is often treated via strain softening models in continuum damage mechanics. Such constitutive relations favour spurious strain [...]
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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; doi: 10.1007/s40571-014-0012-9

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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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. Khardar, L. Ring

Computational Particle Mechanics (2015). Vol. 2(2) pp. 139-160 (preprint)

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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Adjoint-based Adaptive Finite Element Method For The Compressible Euler Equations Using Finite Calculus
M. Kouhi, E. Oñate, D. Mavriplis

Aerospace Science and Technology (2015). Vol. 46 pp. 422-435 (preprint)

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

Comp. Part. Mech (2015). Vol. 2(3) pp. 301-314 (prepint) Vol. 2 (3), pp. 301-314; doi: 10.1007/s40571-015-0067-2

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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A Stabilized Finite Element Formulation For High-Speed Inviscid Compressible Flows Using Finite Calculus
M. Kouhi, E. Oñate

Int. J. Numer. Meth. Engng. (2014). Vol. 74(2) pp. 872-897 Vol. 74 (2), pp. 872-897; doi: 10.1002/fld.3877

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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Computation of the stabilization parameter for the finite element solution of advective–diffusive problems
E. Oñate, J. García-Espinosa, S. Idelsohn

Int. J. of Num. Meths. in Fluid (1997). Vol. 25, pp. 1387-1407; doi: 10.1002/(SICI)1097-0363(19971230)25:12<1385::AID-FLD678>3.0.CO;2-7

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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Non-linear dynamic analysis of the response of moored floating structures
J. Gutiérrez Romero, J. García-Espinosa, B. Servan Camas, B. Zamora-Parra

Marine Structures (2017). Vol. 49 pp. 116-137 49, 116-137 (preprint)

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