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).

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CBS versus GLS stabilization of the incompressible Navier–Stokes equations and the role of the time step as stabilization parameter
R. Codina, O. Zienkiewicz

Commun. Numer. Meth. Engng (2001). Vol 18 (2), pp. 99-112

Abstract
In this work we compare two apparently different stabilization procedures for the finite element approximation of the incompressible Navier–Stokes equations. The first is the characteristic‐based split (CBS). It combines the characteristic Galerkin method to deal with convection dominated flows with a classical splitting technique, which in some cases allows us to use equal velocity–pressure interpolations. The second approach is the Galerkin‐least‐squares (GLS) method, in which a least‐squares form of the element residual is added to the basic Galerkin equations. It is shown that both formulations display similar stabilization mechanisms, provided the stabilization parameter of the GLS method is identified with the time step of the CBS approach. This identification can be understood from a formal Fourier analysis of the linearized problem.
Abstract
In this work we compare two apparently different stabilization procedures for the finite element approximation of the incompressible Navier–Stokes equations. The first [...]
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Implementation of a stabilized finite element formulation for the incompressible Navier-Stokes equations based on a pressure gradient projection
R. Codina, J. Blasco, G. Buscaglia, A. Huerta

Int. J. Numer. Meth. Fluids (2001). Vol. 37 (4), pp. 419-444

Abstract
We discuss in this paper some implementation aspects of a finite element formulation for the incompressible Navier-Stokes which allows the use of equal order velocity-pressure interpolations. The method consists in introducing the project of the pressure gradient and adding the difference between the pressure Laplacian and divergence of this new field to the incompressibility equations, both multiplied by suitable algorithmic parameters. The main purpose of this paper is to discuss how to deal with the new variable in the implementation of the algorithm. Obviously, it could be treated as one extra unknown, either explicitly or as a condensed variable. However, we take for granted that the only way or another. Here we discuss some iterative schemes to perform this uncoupling of the pressure gradient projection (PGP) from the calculation of the velocity and the pressure, both for stationary and the transient of the linearization loop and the iterative segregation of the PGP, whereas in the second the main dilemma concerns the explicit or implicit treatment of the PGP.
Abstract
We discuss in this paper some implementation aspects of a finite element formulation for the incompressible Navier-Stokes which allows the use of equal order velocity-pressure [...]
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Numerical modeling of magma withdrawal during explosive caldera-forming eruptions
A. Folch, J. Martí i Castell, R. Codina

Journal of Geophysical Research (2001). Vol. 106 (B8), pp. 16 163-16 175

Abstract
We propose a simple physical model to characterize the dynamics of magma withdrawal during the course of caldera-forming eruptions. Simplification involves considering such eruptions as a piston-like system in which the host rock is assumed to subside as a coherent rigid solid. Magma behaves as a Newtonian incompressible fluid below the exsolution level and as a compressible gas-liquid mixture above this level. We consider caldera-forming eruptions within the frame of fluid-structure interaction problems, in which the flow-governing equations are written using an arbitrary Lagrangian-Eulerian (ALE) formulation. We propose a numerical procedure to solve the ALE governing equations in the context of a finite element method. The numerical methodology is based on a staggered algorithm in which the flow and the structural equations are alternatively integrated in time by using separate solvers. The procedure also involves the use of the quasi-Laplacian method to compute the ALE mesh of the fluid and a new conservative remeshing strategy. Despite the fact that we focus the application of the procedure toward modeling caldera-forming eruptions, the numerical procedure is of general applicability. The numerical results have important geological implications in terms of magma chamber dynamics during explosive caldera-forming eruptions. Simulations predict a nearly constant velocity of caldera subsidence that strongly depends on magma viscosity. They also reproduce the characteristic eruption rates of the different phases of an explosive calderaforming eruption. Numerical results indicate that the formation of vortices beneath the ring fault, which may allow mingling and mixing of parcels of magma initially located at different depths in the chamber, is likely to occur for low-viscosity magmas. Numerical results confirm that exsolution of volatiles is an efficient mechanism to sustain explosive caldera-forming eruptions and to explain the formation of large volumes of ignimbrites.
Abstract
We propose a simple physical model to characterize the dynamics of magma withdrawal during the course of caldera-forming eruptions. Simplification involves considering such [...]
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Space and time error estimates for a first order, pressure stabilized finite element method for the incompressible Navier–Stokes equations
J. Blasco, R. Codina

Applied Numerical Mathematics (2001). Vol. 38 (4), pp. 475-497

Abstract
In this paper we analyze a pressure stabilized, finite element method for the unsteady, incompressible Navier–Stokes equations in primitive variables; for the time discretization we focus on a fully implicit, monolithic scheme. We provide some error estimates for the fully discrete solution which show that the velocity is first order accurate in the time step and attains optimal order accuracy in the mesh size for the given spatial interpolation, both in the spaces L2(Ω) and H10(Ω); the pressure solution is shown to be order 12 accurate in the time step and also optimal in the mesh size. These estimates are proved assuming only a weak compatibility condition on the approximating spaces of velocity and pressure, which is satisfied by equal order interpolations.
Abstract
In this paper we analyze a pressure stabilized, finite element method for the unsteady, incompressible Navier–Stokes equations in primitive variables; for the [...]
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Pressure stability in fractional step finite element methods for incompressible flows
R. Codina

Journal of Computational Physics (2001). Vol. 170 (1), pp. 112-140

Abstract
The objective of this paper is to analyze the pressure stability of fractional step finite element methods for incompressible flows. For the classical first order projection method, it is shown that there is a pressure control which depends on the time step size, and therefore there is a lower bound for this time step for stability reasons. The situation is much worse for a second order scheme in which part of the extremely weak. To overcome these shortcomings, a stabilized fractional step finite element method is also considered, and its stability is analyzed. Some simple numerical examples are presented to support the theoretical results.
Abstract
The objective of this paper is to analyze the pressure stability of fractional step finite element methods for incompressible flows. For the classical first order projection [...]
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Transmission conditions with constraints in finite element domain decomposition methods for flow problems
G. Houzeaux, R. Codina

Comput. Methods Appl. Mech. Engrg., (2001). Vol 17 (3), pp. 179-190

Abstract
This work presents a conservative scheme for iteration‐by‐subdomain domain decomposition (DD) strategies applied to the finite element solution of flow problems. The DD algorithm is based on the iterative update of the boundary conditions on the interfaces between the subregions, the so‐called transmission conditions. The transmission conditions involve the essential and natural boundary conditions of the weak form of the problem, and should ensure strong continuity of the velocity and weak continuity of the traction. As a first approach, the transmission conditions are interpolated using the classical Lagrange interpolation functions. Conservation problems might arise when two adjacent subdomains have a sensibly different mesh spacing. In order to conserve any desired quantity of interest, an interface constraining is introduced: continuity of the transmission conditions are constrained under a scalar conservation equation. An example of mass conservation illustrates the algorithm.
Abstract
This work presents a conservative scheme for iteration‐by‐subdomain domain decomposition (DD) strategies applied to the finite element solution of flow problems. The DD [...]
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A stabilized finite element method for generalized stationary incompressible flows
R. Codina

Comput. Methods Appl. Mech. Engrg., (2001). Vol. 190 (20-21), pp. 2681-2706

Abstract
In this paper we describe a finite element formulation for the numerical solution of the stationary Navier-Stokes equations including Coriolis forces and the permeability of the medium. The stabilized method is based on the algebraic version of the sub-grid scale approach. We first describe this technique for general systems of convection-diffusion-reaction equations and then we apply it to linearized flow equations. The important point is the design of the matrix of stabilization parameters that the method has. This design is based on the identification of the stability problems of the Galerkin method and a scaling of variables argument to determine which coefficients must be included in the stabilization matrix. This, together with the convergence analysis of the linearized problem, leads to a simple expression for the stabilization parameters in the general situation considered in the paper. The numerical analysis of the linearized problem also shows that the method has optimal convergence properties.
Abstract
In this paper we describe a finite element formulation for the numerical solution of the stationary Navier-Stokes equations including Coriolis forces and the permeability [...]
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On the constitutive modeling of coupled thermomechanical phase-change problems
C. Agelet de Saracibar, M. Cervera, M. Chiumenti

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

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

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

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

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

Abstract
The paper describes the extension of the critical displacement method (CDM), presented by Oñate and Matias in 1996, to the instability analysis of structures with non-linear material behaviour using a simple damage model. The extended CDM is useful to detect instability points using a prediction of the critical displacement field and a secant load-displacement relationship accounting for material non-linearities. Examples of application of CDM to the instability analysis of structures using bar and solid finite elements are presented.
Abstract
The paper describes the extension of the critical displacement method (CDM), presented by Oñate and Matias in 1996, to the instability analysis of structures with [...]
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A scalar damage model with a shear retention factor for the analysis of reinforced concrete structures: theory and validation
R. Scotta, R. Vitaliani, A. Saetta, E. Oñate, A. Hanganu

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

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

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

Abstract
The basis of the finite point method (FPM) for the fully meshless solution of elasticity problems in structural mechanics is described. A stabilization technique based on a finite calculus procedure is used to improve the quality of the numerical solution. The efficiency and accuracy of the stabilized FPM in the meshless analysis of simple linear elastic structural problems is shown in some examples of applications.
Abstract
The basis of the finite point method (FPM) for the fully meshless solution of elasticity problems in structural mechanics is described. A stabilization [...]
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Rotation‐free triangular plate and shell elements
E. Oñate, F. Zárate

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

Abstract
The paper describes how the finite element method and the finite volume method can be successfully combined to derive two new families of thin plate and shell triangles with translational degrees of freedom as the only nodal variables. The simplest elements of the two families based on combining a linear interpolation of displacements with cell centred and cell vertex finite volume schemes are presented in detail. Examples of the good performance of the new rotation‐free plate and shell triangles are given.
Abstract
The paper describes how the finite element method and the finite volume method can be successfully combined to derive two new families of thin plate and shell triangles with [...]
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Shape variable definition with C0 , C1 and C2 continuity functions
G. Chiandussi, G. Bugeda, E. Oñate

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

Abstract
The present paper proposes a new technique for the definition of the shape design variables in 2D and 3D optimisation problems. It can be applied to the discrete model of the analysed structure or to the original geometry without any previous knowledge of the analytical expression of the CAD defining surfaces. The proposed technique allows the surface continuity to be preserved during the geometry modification process to be defined a priori. This capability allows for the definition of shape variables suitable for every kind of discipline involved in the optimisation process (structural analysis, fluid-dynamic analysis, crash analysis, aerodynamic analysis, etc.).
Abstract
The present paper proposes a new technique for the definition of the shape design variables in 2D and 3D optimisation problems. It can be applied to the discrete model of [...]
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An anisotropic elastoplastic constitutive model for large deformation analysis of fibre reinforced composites
E. Car, S. Oller, E. Oñate

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

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

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

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

Anales de Mecánica de Fractura (2000). Vol. 17, pp. 127-154

Abstract
El artículo es una panorámica de los aspectos teóricos y algunas aplicaciones prácticas de los modelos de fractura desarrollados por diversos grupos en la Escuela de Ingenieros de Caminos de Barcelona (EICB) durante los últimos quince años para el análisis no lineal de estructuras. La motivación fundamental para el desarrollo de estos modelos se centra en el análisis de la seguridad de estructuras de hormigón en masa y armado. La mayor parte de los modelos se basan en la teoría de daño continuo y utilizan el método de los elementos finitos para la solución numérica. Los modelos de daño se han extendido y aplicado también con éxito al análisis de diversas estructuras de edificios históricos. Los desarrollos más recientes de estos modelos en la EICB incluyen la predicción de fenómenos de localización en estructuras de hormigón y el análisis del comportamiento no lineal de estructuras con materiales compuestos. De todos estos modelos se presentan en el artículo unas breves pinceladas, las aplicaciones más relevantes y las referencias donde pueden encontrarse los detalles sobre cada caso.
Abstract
El artículo es una panorámica de los aspectos teóricos y algunas aplicaciones prácticas de los modelos de fractura desarrollados por diversos grupos [...]
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Adaptivity based on error estimation for viscoplastic softening materials
P. Diez, M. Arroyo, A. Huerta

Mechanics of Cohesive-Frictional Materials (2000). Vol. 5 (2), pp. 87-112

Abstract
This paper focuses on the numerical simulation of strain softening mechanical problems. Two problems arise: (1) the constitutive model has to be regular and (2) the numerical technique must be able to capture the two scales of the problem (the macroscopic geometrical representation and the microscopic behavior in the localization bands). The Perzyna viscoplastic model is used in order to obtain a regularized softening model allowing to simulate strain localization phenomena. This model is applied to quasistatic examples. The viscous regularization of quasistatic processes is also discussed: in quasistatics, the internal length associated with the obtained band width is no longer only a function of the material parameters but also depends on the boundary value problem (geometry and loads, specially loading velocity). An adaptive computation is applied to softening viscoplastic materials showing strain localization. As the key ingredient of the adaptive strategy, a residual type error estimator is generalized to deal with such highly nonlinear material model. In several numerical examples the adaptive process is able to detect complex collapse modes that are not captured by a first, even if fine, mesh. Consequently, adaptive strategies are found to be essential to detect the collapse mechanism and to assess the optimal location of the elements in the mesh.
Abstract
This paper focuses on the numerical simulation of strain softening mechanical problems. Two problems arise: (1) the constitutive model has to be regular and (2) the numerical [...]
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Error estimation including pollution assessment for nonlinear finite element analysis
A. Huerta, P. Diez

Comput. Methods Appl. Mech. Engrg., (2000). Vol. 181 (1-3), pp. 21-41

Abstract
A residual type error estimator for nonlinear finite element analysis is introduced. This error estimator solves local problems avoiding both the computation of the flux jumps and the associated flux splitting procedure. Pollution errors are taken into account by a feedback strategy, that is, an error estimate based on local computations is used as the input of the pollution analysis. This estimator is used in the frame of an adaptive procedure. Numerical examples show that the estimator is able to drive adaptive procedures leading to likely good solutions. Moreover, one of the examples demonstrates that adaptive procedures are essential for complex highly nonlinear mechanical problems because they may discover secondary collapse mechanisms.
Abstract
A residual type error estimator for nonlinear finite element analysis is introduced. This error estimator solves local problems avoiding both the computation of the flux jumps [...]
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Error estimation for adaptive computations on shell structures
P. Diez, A. Huerta

European Journal of Finite Elements (2000). Vol. 9 (1-3), pp. 49-66

Abstract
The finite element discretization of a shell structure introduces two kinds of errors: the error in the functional approximation and the error in the geometry approximation. The first is associated with the finite dimensional interpolation space and it is present in any finite element computation. The latter is associated with the piecewise polynomial approximation of a curved surface and is much more relevant in shell problems than in any other standard 2D or 3D computation. In the shells framework, formerly the quality control of the finite element solution has been carried out using flux projection a posteriori error estimators. This technique exhibits two main drawbacks: 1) the flux smoothing averages stress components over different elements that may have different physical meaning if the tangent planes are different and 2) the error estimation process uses only the approximate solution and hence, the discretized forces and the computational mesh: the data describing the real geometry and load is therefore not accounted for. In this work, a residual type error estimator introduced for standard 2D finite element analysis is generalized to shell problems. This allows to easily account for the real original geometry of the problem in the error estimation procedure and precludes the necessity of comparing generalized stress components between non coplanar elements. This estimator is based on approximating a reference error associated with a refined reference mesh. In order to build up the residual error equation the computed solution must be represented (projected) on the reference mesh. The use of thin shell finite elements requires a proper formulation in order to preclude shear locking. Following an idea of Donea and Lamain, the interpolation of the rotations is not unique and requires a particular technique to transfer the information from the computational mesh to the reference mesh. This technique is also developed in this work and may be used in any adaptive evolution problem where the solution must be transferred from one mesh to another.
Abstract
The finite element discretization of a shell structure introduces two kinds of errors: the error in the functional approximation and the error in the geometry approximation. [...]
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Stabilization of incompressibility and convection through orthogonal sub-scale in finite element methods
R. Codina

Comput. Methods Appl. Mech. Engrg., (2000). Vol. 190 (13-14), pp. 1579-1599

Abstract
Two apparently different forms of dealing with the numerical instability due to the incompressibility constraint of the stokes problem are analyzed in this paper. The first of them is the stabilization thought the pressure gradient projection, which consists of adding a certain least-squares form of the difference between the pressure gradient and its L² projection onto the discrete velocity space in the variational equations of the problem. The second is a sub-grid scale method, whose stabilization effect is very similar to that of the Galerkin/least-squares method for the Stokes problem. It is shown here that the first method can also be recast in the framework of sub-grid scale method with a particular choice for the space of sub-scales. This leads to a new stabilization procedure, whose applicability to stabilize convection is also studied in this paper.
Abstract
Two apparently different forms of dealing with the numerical instability due to the incompressibility constraint of the stokes problem are analyzed in this paper. The first [...]
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Analysis of a pressure-stabilized finite element approximation of the stationary Navier-Stokes equations
R. Codina, J. Blasco

Numerische Mathematik (2000). Vol. 87 (1), pp. 59-81

Abstract
The purpose of this paper is to analyze a finite element approximation of the stationary Navier-Stokes equations that allows the use of equal velocity-pressure interpolation. The idea is to introduce as unknown of the discrete problem the projection of the pressure gradient (multiplied by suitable algorithmic parameters) onto the space of continuous vector fields. The difference between these two vectors (pressure gradient and projection) is introduced in the continuity equation. The resulting formulation is shown to be stable and optimally convergent, both in a norm associated to the problem and in the L2 norm for both velocities and pressure. This is proved first for the Stokes problem, and then it is extended to the nonlinear case. All the analysis relies on an inf-sup condition that is much weaker than for the standard Galerkin approximation, in spite of the fact that the present method is only a minor modification of this.
Abstract
The purpose of this paper is to analyze a finite element approximation of the stationary Navier-Stokes equations that allows the use of equal velocity-pressure interpolation. [...]
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Fourier analysis of an equal‐order incompressible flow solver stabilized by pressure gradient projection
G. Buscaglia, F. Basombrío, R. Codina

Int. J. Numer. Meth. Fluids (2000). Vol. 34 (1), pp. 65-92

Abstract
Fourier analysis techniques are applied to the stabilized finite element method (FEM) recently proposed by Codina and Blasco for the approximation of the incompressible Navier–Stokes equations, here denoted by pressure gradient projection (SPGP) method. The analysis is motivated by spurious waves that pollute the computed pressure in start‐up flow simulation. An example of this spurious phenomenon is reported. It is shown that Fourier techniques can predict the numerical behaviour of stabilized methods with remarkable accuracy, even though the original Navier–Stokes setting must be significantly simplified to apply them. In the steady state case, good estimates for the stabilization parameters are obtained. In the transient case, spurious long waves are shown to be persistent when the element Reynolds number is large and the Courant number is small. This can be avoided by treating the pressure gradient projection implicitly, though this implies additional computing effort. Standard extrapolation variants are unfortunately unstable. Comparisons with Galerkin–least‐squares (GLS) method and Chorin's projection method are also addressed
Abstract
Fourier analysis techniques are applied to the stabilized finite element method (FEM) recently proposed by Codina and Blasco for the approximation of the incompressible Navier–Stokes [...]
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A nodal-based implementation of a stabilized Finite Element Method for Incompressible Flow Problems
R. Codina

Int. J. Numer. Meth. Fluids (2000). Vol. 33 (5), pp. 737-766

Abstract
The objective of this paper is twofold. First, a stabilized finite element method for the incompressible Navier-Stokes is presented, and several numerical experiments are conducted to check its performance. This method is able to deal with all the instabilities that the standard Galerkin method presents, namely, the pressure instability, the instability arising in convection dominated situations and also the less popular instabilities found when the Navier-Stokes equations have a dominant Coriolis force, or there is a dominant absorption term arising from the small permeability of the medium where the flow takes place. The second objective is to describe a nodal-based implementation of the finite element formulation introduced. This implementation is based on an a priori calculation of the integrals appearing in the formulation and then the construction of the matrix approximations, this matrix and this vector can be constructed directly for each nodal point, without the need to loop over element and thus making the calculations much faster. In order to be able to do this, all the variables have to be defined at the nodes of the finite element mesh, not on the elements. This is also so for the stabilization parameters of the formulation. However, doing this given rise to questions regarding the consistency and the conservation properties of the final scheme that are addressed in this paper.
Abstract
The objective of this paper is twofold. First, a stabilized finite element method for the incompressible Navier-Stokes is presented, and several numerical experiments are [...]
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On stabilized finite element methods for linear systems of convection-diffusion-reaction equations
R. Codina

Comput. Methods Appl. Mech. Engrg., (2000). Vol. 188 (200), pp. 61-82

Abstract
A stabilized finite element method for solving systems of convection-diffusion-reaction equations is studied in this paper. The method is based on the subgrid scale approach and an algebraic approximation to the subscales. After presenting the formulation of the method, it is analyzed how it behaves under changes of variables, showing that it relies on the law of change of the matrix of stabilization parameters associated to the method. An expression for this matrix is proposed for the case of general coupled systems of equations that is an extension of the expression proposed for a 1D model problem. Applications of the stabilization technique to the Stokes problem with convection and to the bending of Reissner-Mindlin plates are discussed next. The design of the matrix of stabilization parameters is based on the identification of the stability deficiencies of the standard Galerkin method applied to these two problems.
Abstract
A stabilized finite element method for solving systems of convection-diffusion-reaction equations is studied in this paper. The method is based on the subgrid scale approach [...]
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Stabilized finite element method for the transient Navier–Stokes equations based on a pressure gradient projection
R. Codina, J. Blasco

Comput. Methods Appl. Mech. Engrg., (2000). Vol. 182 (3-4), pp. 277-300

Abstract
In this paper we present a stabilized finite element formulation for the transient incompressible Navier–Stokes equations. The main idea is to introduce as a new unknown of the problem the projection of the pressure gradient onto the velocity space and to add to the incompresibility equation the difference between the Laplacian of the pressure and the divergence of this new vector field. This leads to a pressure stabilization effect that allows the use of equal interpolation for both velocities and pressures. In the case of the transient equations, we consider the possibility of treating the pressure gradient projection either implicitly or explicity. In the first case, the number of unknowns of the problem is substantially increased with respect to the standard Galerkin formulation. Nevertheless, iterative techniques may be used in order to uncouple the calculation of the pressure gradient projection from the rest of unknowns (velocity and pressure). When this vector field is treated explicitly, the increment of computational cost of the stabilized formulation with respect to the Galerkin method is very low. We provide a stability estimate for the case of the simple backward Euler time integration scheme for both the implicit and the explicit treatment of the pressure gradient projection.
Abstract
In this paper we present a stabilized finite element formulation for the transient incompressible Navier–Stokes equations. The main idea is to introduce as a new unknown [...]
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Simulation of Construction of RCC Dams. II: Stress and Damage
M. Cervera, T. Prato, J. Oliver

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

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

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

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

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

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

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

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

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

Abstract
A stabilized finite point method (FPM) for the meshless analysis of incompressible fluid flow problems is presented. The stabilization approach is based in the finite increment calculus (FIC) procedure developed by Oñate [14]. An enhanced fractional step procedure allowing the semi-implicit numerical solution of incompressible fluids using the FPM is described. Examples of application of the stabilized FPM to the solution of two incompressible flow problems are presented.
Abstract
A stabilized finite point method (FPM) for the meshless analysis of incompressible fluid flow problems is presented. The stabilization approach is based in the finite increment [...]
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Numerical aerodynamic analysis of large buildings using a finite element model with application to a telescope building
R. Codina, C. Morton, E. Oñate, O. Soto

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

Abstract
Presents a numerical strategy for the aerodynamic analysis of large buildings, with an application to the simulation of the air flow within a telescope building. The finite element formulation is presented first, and then the methodology followed to obtain significant data from the calculations is described. The quality of the ventilation of the building is defined by the average residence times, and the feasibility of this ventilation by the actions created on the instruments and the general flow pattern.
Abstract
Presents a numerical strategy for the aerodynamic analysis of large buildings, with an application to the simulation of the air flow within a telescope building. The finite [...]
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A simple method for automatic update of finite element meshes
G. Chiandussi, G. Bugeda, E. Oñate

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

Abstract
A simple method to automatically update the finite element mesh of the analysis domain is proposed. The method considers the mesh as a fictitious elastic body subjected to prescribed displacements at selected boundary points. The mechanical properties of each mesh element are appropriately selected in order to minimize the deformation and the distortion of the mesh elements. Different selection strategies have been used and compared in their application to simple examples. The method avoids the use of remeshing in the solution of shape optimization problems and reduces the number of remeshing steps in the solution of coupled fluid–structure interaction problems
Abstract
A simple method to automatically update the finite element mesh of the analysis domain is proposed. The method considers the mesh as a fictitious elastic body subjected to [...]
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Finite element solution of free‐surface ship‐wave problems
S. Idelsohn, E. Oñate, C. Sacco

Int. J. Numer. Meth. Engng. (1999). Vol. 45 (5), pp. 503-528

Abstract
An unstructured finite element solver to evaluate the ship‐wave problem is presented. The scheme uses a non‐structured finite element algorithm for the Euler or Navier–Stokes flow as for the free‐surface boundary problem. The incompressible flow equations are solved via a fractional step method whereas the non‐linear free‐surface equation is solved via a reference surface which allows fixed and moving meshes. A new non‐structured stabilized approximation is used to eliminate spurious numerical oscillations of the free surface.
Abstract
An unstructured finite element solver to evaluate the ship‐wave problem is presented. The scheme uses a non‐structured finite element algorithm for the Euler or Navier–Stokes [...]
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Solving structural optimization problems with genetic algorithms and simulated annealing
S. Botello, J. Marroquín, E. Oñate

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

Abstract
In this paper we study the performance of two stochastic search methods: Genetic Algorithms and Simulated Annealing, applied to the optimization of pin‐jointed steel bar structures. We show that it is possible to embed these two schemes into a single parametric family of algorithms, and that optimal performance (in a parallel machine) is obtained by a hybrid scheme. Examples of applications to the optimization of several real steel bar structures are presented.
Abstract
In this paper we study the performance of two stochastic search methods: Genetic Algorithms and Simulated Annealing, applied to the optimization of pin‐jointed steel bar [...]
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A homogeneous constitutive model for masonry
J. Lopez, S. Oller, E. Oñate, J. Lubliner

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

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

Int. J. Numer. Meth. Engng. (1999). Vol. 46 (10), pp. 1595-1607

Abstract
A geometrically non‐linear formulation for composites and the resulting explicit dynamic finite element algorithm are presented. The proposed formulation assumes that small elastic and large plastic strains, being the anisotropy considered using tensors which map the model variables at each time step into an equivalent isotropic space, where the integration of the rate constitutive equations is performed. The evolution of the internal variables is calculated in the auxiliary spaces, taking into account the material non‐linear behaviour, and the results mapped back to the real stress space. The updating of the mapping tensors for each new spatial configuration allows the treatment of general anisotropic materials under large strain and can be extended to treat multiphase composite materials using the mixing theory. The behaviour of the composite is dictated by the mechanical response of each substance, and the resultant model allows a fully non‐linear analysis combining different material models, such as damage in one compounding substance, elastoplastic behaviour in the other, while a third substance behaves elastically.
Abstract
A geometrically non‐linear formulation for composites and the resulting explicit dynamic finite element algorithm are presented. The proposed formulation assumes that small [...]
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A generalized streamline finite element approach for the analysis of incompressible flow problems including moving surfaces
M. Cruchaga, E. Oñate

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

Abstract
In the present work a generalized streamline finite element formulation able to deal with incompressible flow problems is presented. In the finite element framework, this technique allows the use of equal order interpolation for the unknowns of the problem: velocity and pressure. In this context, stable and convergent solutions can be obtained without requiring tuning parameters defined outside this model. The tracking of moving surfaces is also included in the numerical model. This formulation has been checked in 21) and 3D tests.
Abstract
In the present work a generalized streamline finite element formulation able to deal with incompressible flow problems is presented. In the finite element framework, this [...]
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Adaptive finite element strategies based on error assessment
A. Huerta, A. Rodríguez-Ferran, P. Diez, J. Sarrate

Int. J. Numer. Meth. Engng. (1999). Vol. 46 (10), pp. 1803-1818

Abstract
Two main ingredients are needed for adaptive finite element computations. First, the error of a given solution must be assessed, by means of either error estimators or error indicators. After that, a new spatial discretization must be defined via h, p or r-adaptivity. In principle, any of the approaches for error assessment may be combined with any of the procedures for adapting the discretization. However, some combinations are clearly preferable. The advantages and limitations of the various alternatives are discussed. The most adequate strategies are illustrated by means of several applications in solid mechanics.
Abstract
Two main ingredients are needed for adaptive finite element computations. First, the error of a given solution must be assessed, by means of either error estimators or error [...]
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A unified approach to remeshing strategies for finite element h-adaptivity
P. Diez, A. Huerta

Comput. Methods Appl. Mech. Engrg., (1999). Vol. 176 (1-4), pp. 215-229

Abstract
In h-adaptivity, a remeshing strategy is needed to compute the distribution of required element size using the estimated error distribution. Several authors have introduced different remeshing strategies yielding very different results. In this work these methods are included in a unified framework, emphasizing the role of the underlying hypotheses. Moreover, an objective tool to evaluate the accuracy of the resulting finite element solution is presented. Thus, a new remeshing strategy is introduced to optimize the accuracy of the adapted solutions. The different remeshing strategies are compared with well-known numerical examples.
Abstract
In h-adaptivity, a remeshing strategy is needed to compute the distribution of required element size using the estimated error distribution. Several authors have introduced [...]
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Finite element simulation of the filling of thin moulds
R. Codina, O. Soto

Int. J. Numer. Meth. Engng. (1999). Vol. 46 (9), pp. 1559-1573

Abstract
In this work we present a finite element formulation to simulate the filling of thin moulds. The model has as starting point a 3‐D approach using either div‐stable elements, such as the Q2/P1 element (tri‐quadratic velocities and piecewise linear, discontinuous pressures) or stabilized finite element formulations. The tracking of the free surface is based on the Volume‐Of‐Fluid (VOF) method. The velocity profile is assumed to be parabolic in the direction normal to the mid‐plane, so that one element along the width of the mould is enough to reproduce this profile if this element is quadratic. The velocity is prescribed to zero on the upper and lower surfaces and the normal to the mid‐plane is also prescribed to zero. In the case of div‐stable elements, the pressure profile is prescribed to be constant along the width of the mould. This can be achieved by using as interpolation degrees of freedom the pressure values at the element centroid and its derivatives in the directions tangent and normal to the mid‐plane, and prescribing the latter to zero. No modifications are needed when stabilized formulations are employed. To advance in time the function used in the VOF technique, we use a constant velocity across the width of the mould, which is taken as the projection on the tangent plane of each element of the nodal velocities. This is needed in order to have mass conservation.
Abstract
In this work we present a finite element formulation to simulate the filling of thin moulds. The model has as starting point a 3‐D approach using either div‐stable elements, [...]
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The characteristic‐based‐split procedure: an efficient and accurate algorithm for fluid problems
O. Zienkiewicz, P. Nithiarasu, R. Codina, M. Vázquez, P. Ortiz

Int. J. Numer. Meth. Fluids (1999). Vol. 31 (1), pp. 359-392

Abstract
In 1995 the two senior authors of the present paper introduced a new algorithm designed to replace the Taylor–Galerkin (or Lax–Wendroff) methods, used by them so far in the solution of compressible flow problems. The new algorithm was applicable to a wide variety of situations, including fully incompressible flows and shallow water equations, as well as supersonic and hypersonic situations, and has proved to be always at least as accurate as other algorithms currently used. The algorithm is based on the solution of conservation equations of fluid mechanics to avoid any possibility of spurious solutions that may otherwise result. The main aspect of the procedure is to split the equations into two parts, (1) a part that is a set of simple scalar equations of convective–diffusion type for which it is well known that the characteristic Galerkin procedure yields an optimal solution; and (2) the part where the equations are self‐adjoint and therefore discretized optimally by the Galerkin procedure. It is possible to solve both the first and second parts of the system explicitly, retaining there the time step limitations of the Taylor–Galerkin procedure. But it is also possible to use semi‐implicit processes where in the first part we use a much bigger time step generally governed by the Peclet number of the system while the second part is solved implicitly and is unconditionally stable. It turns out that the characteristic‐based‐split (CBS) process allows equal interpolation to be used for all system variables without difficulties when the incompressible or nearly incompressible stage is reached. It is hoped that the paper will help to make the algorithm more widely available and understood by the profession and that its advantages can be widely realised.
Abstract
In 1995 the two senior authors of the present paper introduced a new algorithm designed to replace the Taylor–Galerkin (or Lax–Wendroff) methods, used by them [...]
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Finite element implementation of two‐equation and algebraic stress turbulence models for steady incompressible flows
R. Codina, O. Soto

Int. J. Numer. Meth. Fluids (1999). Vol. 30 (3), 309-334

Abstract
The main purpose of this paper is to describe a finite element formulation for solving the equations for k and ε of the classical k–ε turbulence model, or any other two‐equation model. The finite element discretization is based on the SUPG method together with a discontinuity capturing technique to deal with sharp internal and boundary layers. The iterative strategy consists of several nested loops, the outermost being the linearization of the Navier–Stokes equations. The basic k–ε model is used for the implementation of an algebraic stress model that is able to account for the effects of rotation. Some numerical examples are presented in order to show the performance of the proposed scheme for simulating directly steady flows, without the need of reaching the steady state through a transient evolution.
Abstract
The main purpose of this paper is to describe a finite element formulation for solving the equations for k and ε of the classical k–ε [...]
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A fractional-step finite-element method for the Navier–Stokes equations applied to magma-chamber withdrawal
R. Folch, M. Vázquez, R. Codina, J. Martí i Castell

Computers and Geotechnics (1999). Vol. 25 (3), pp. 263-275

Abstract
We develop an algorithm to solve numerically the Navier–Stokes equations using a finite element method. The algorithm uses a fractional step approach that allows the use of equal interpolation spaces for the pressure and velocity fields and can be used to solve both compressible and incompressible flows. The standard Galerkin method is used to space-discretize the equations in which convective terms are dominant because the equations are reformulated in a characteristics co-moving frame providing thus the required artificial diffusion in a consistent way. The algorithm depends on four different parameters. Depending on their values, a fully implicit, a semi-implicit or a fully explicit solution can be obtained. The proposed algorithm may be useful in solving a wide spectrum of problems in geology, engineering and geosciences. Several flows frequently encountered in practical applications such as incompressible, slightly compressible or perfect gas are taken into account. As an example, we use it to model the withdrawal of magma from shallow chambers during explosive volcanic eruptions. Our model constitutes a first attempt to characterize the temporal evolution of the most revelant physical parameters during such a process.
Abstract
We develop an algorithm to solve numerically the Navier–Stokes equations using a finite element method. The algorithm uses a fractional step approach that allows [...]
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Numerical solution of the incompressible Navier–Stokes equations with Coriolis forces based on the discretization of the total time derivative.
R. Codina

Journal of Computational Physics (1999). Vol. 148 (2), pp. 467-496

Abstract
In this paper we present a numerical formulation to solve the incompressible Navier–Stokes equations written in a rotating frame of reference. The method is based on a finite difference discretization in time and a finite element discretization in space. When the viscosity is very small, numerical oscillations may appear due both to the high Reynolds number and to the presence of the Coriolis forces. To overcome these oscillations, a special discretization in time is proposed. The idea is to discretize the total time derivative in an inertial basis rather than only the partial time derivative in the rotating reference system. After this is done, a further high-order approximation is introduced, leading to a problem posed in the rotating frame of reference and in spatial coordinates. In contrast with the straightforward discretization of the original equations, some additional terms appear that enhance the stability of the numerical scheme. In the absence of Coriolis forces, the method is a generalization of the characteristic Galerkin technique for convection-dominated flows.
Abstract
In this paper we present a numerical formulation to solve the incompressible Navier–Stokes equations written in a rotating frame of reference. The method is based on [...]
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On the numerical modeling of frictional wear phenomena
C. Agelet de Saracibar, M. Chiumenti

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Abstract
An unstructured grid-based, parallel-free surface solver is presented. The overall scheme combines a finite-element, equal-order, projection-type 3-D incompressible flow solver with a finite element, 2-D advection equation solver for the free surface equation. For steady-state applications, the mesh is not moved every timestep, in order to reduce the cost of geometry recalculations and surface repositioning. A number of modifications required for efficient processing on shared-memory, cache-based parallel machines are discussed, and timings are shown that indicate scalability to a modest number of processors. The results show good quantitative comparison with experiments and the results of other techniques. The present combination of unstructured grids (enhanced geometrical flexibility) and good parallel performance (rapid turnaround) should make the present approach attractive to hydrodynamic design simulations.
Abstract
An unstructured grid-based, parallel-free surface solver is presented. The overall scheme combines a finite-element, equal-order, projection-type 3-D incompressible flow solver [...]
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A layer-wise triangle for analysis of laminated composite plates and shells
S. Botello, E. Oñate, J. Miquel

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

Abstract
The paper presents a new triangle for analysis of laminate plates and shells. The in-plane degrees of freedom are interpolated quadratically whereas a linear layer-wise approximation is chosen for the normal displacement. A substructuring technique is used to eliminate the in-plane degrees of freedom during the assembly process thus reducing substantially the computationed costs. The element performance is evaluated in the static and dynamic analysis of dierent laminate plate and shell structures
Abstract
The paper presents a new triangle for analysis of laminate plates and shells. The in-plane degrees of freedom are interpolated quadratically whereas a linear layer-wise approximation [...]
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A mesh-free finite point method for advective-diffusive transport and fluid flow problems
E. Oñate, S. Idelsohn

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

Abstract
The finite point method (FPM) is a gridless numerical procedure based on the combination of weighted least square interpolations on a cloud of points with point collocation for evaluating the approximation integrals. In the paper, details of a procedure for stabilizing the numerical solution for advective-diffusive transport and fluid flow problems using the FPM are given. The method is based on a consistent introduction of the stabilizing terms in the governing differential equations. One example showing the applicability of the FPM is given.
Abstract
The finite point method (FPM) is a gridless numerical procedure based on the combination of weighted least square interpolations on a cloud of points with point collocation [...]
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A general procedure for deriving symmetric expressions for the secant and tangent stiffness matrices in finite element analysis
A. Morán, E. Oñate, J. Miquel

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

Abstract
The paper presents a general and straightforward procedure based on the use of the strain energy density for deriving symmetric expressions of the secant and tangent stiffness matrices for finite element analysis of geometrically non‐linear structural problems. The analogy with previously proposed methods for deriving secant and tangent matrices is detailed. The simplicity of the approach is shown in an example of application
Abstract
The paper presents a general and straightforward procedure based on the use of the strain energy density for deriving symmetric expressions of the secant and tangent stiffness [...]
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A hierarchical finite element method based on the partition of unity
R. Taylor, O. Zienkiewicz, E. Oñate

Comput. Methods Appl. Mech. Engrg., (1998). Vol. 152, pp. 73-84

Abstract
In this paper we consider the application of hierarchical functions to base approximations which are a partition of unity. The particular hierarchical functions used are added to base finite element interpolations which, for Co approximations, are a particular case of the partition of unity. We also show how the functions may be constructed to preserve the interpolation property of the base finite element functions. An application to linear elasticity is used to illustrate the properties and stability of the approximation.
Abstract
In this paper we consider the application of hierarchical functions to base approximations which are a partition of unity. The particular hierarchical functions used are added [...]
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Derivation of stabilized equations for numerical solution of advective-diffusive transport and fluid flow problems
E. Oñate

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

Abstract
The concept of the so called “artificial or balancing diffusion” used to stabilize the numerical solution of advective–diffusive transport and fluid flow problems is revised in this paper. It is shown that the standard forms of the balancing diffusion terms, usually chosen in a heuristic manner, can be naturally found by introducing higher order approximations in the derivation of the governing differential equations via standard conservation (or equilibrium) principles. This allows us to reinterprete many stabilization algorithms and concepts used in every day practice by numerical analysts and also provides an expression for computing the stabilization parameter.
Abstract
The concept of the so called “artificial or balancing diffusion” used to stabilize the numerical solution of advective–diffusive transport and fluid flow [...]
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ED-Elas2D: An Educational Program for Computer-aided Training in Structural Analysis Using the Finite Element Method
B. Suarez, E. Blanco, L. Gil, P. Zapata, E. Oñate

European Journal of Engineering Education (1998). Vol. 23 (2), pp. 243-254

Abstract
In this paper, a methodology for computer-aided training of structural problems by the finite element method is presented. The resulting educational program, named ED-Elas2D, has been developed by a group of researchers at the School of Civil Engineering at the Technical University of Catalonia (UPC) in Barcelona, UPC. The program combines the standard concept which appears in the traditional teaching of finite element methods for structural analysis, such as the introduction to the basic structural theory, data definition (pre-processor), description of the analysis procedure (processor) and interpretation of results (post-processor). The program is addressed to both students who enrol in the study on finite element methods and to academic and technical staff in universities and companies who wish to update their knowledge of finite element techniques. The educational program ED-Elas2D works in the Windows system and it is characterized by its interactivity and graphic utilities.
Abstract
In this paper, a methodology for computer-aided training of structural problems by the finite element method is presented. The resulting educational program, named ED-Elas2D, [...]
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A posteriori error estimation for standard finite element analysis
P. Díez, J. Egozcue, A. Huerta

Comput. Methods Appl. Mech. Engrg., (1998). Vol. 163 (1-4), pp. 141-157

Abstract
A new residual type estimator based on projections of the error on subspaces of locally-supported functions is presented. The estimator is defined by a standard element-by-element refinement. First, an approximation of the energy norm of the error is obtained solving local problems with homogeneous Dirichlet boundary conditions. A later enrichment of the estimation is performed by adding the contributions of projections on a new family of subspaces. This estimate is a lower bound of the measure of the actual error. The estimator does not need to approximate local boundary conditions for the error equation. Therefore, computation of flux jumps is not necessary. Moreover, the estimator can be applied in mixed meshes containing elements of different shapes and its implementation in a standard finite element code is straightforward. The presented results show the effectiveness of the estimator approximating both the distribution and the global measure of the error, as well as its usefulness in adaptive procedures.
Abstract
A new residual type estimator based on projections of the error on subspaces of locally-supported functions is presented. The estimator is defined by a standard element-by-element [...]
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Shock capturing viscosities for the general fluid mechanics algorithm
P. Nithiarasu, O. Zienkiewicz, B. Sai, K. Morgan, R. Codina, M. Vázquez

Int. J. Numer. Meth. Fluids (1998). Vol. 28 (9), pp. 1325-1353

Abstract
The performance of different shock capturing viscosities has been examined using our general fluid mechanics algorithm. Four different schemes have been tested, both for viscous and inviscid compressible flow problems. Results show that the methods based on the second gradient of pressure give better performance in all situations. For instance, the method constructed from the nodal pressure values and consistent and lumped mass matrices is an excellent choice for inviscid problems. The method based on L2 projection is better than any other method in viscous flow computations. The residual based anisotropic method gives excellent performance in the supersonic range and gives better results in the hypersonic regime if a small amount of residual smoothing is used
Abstract
The performance of different shock capturing viscosities has been examined using our general fluid mechanics algorithm. Four different schemes have been tested, both for viscous [...]
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A fractional-step method for the incompressible navier-stokes equations related to a predictor-multicorrector algorithm
J. Blasco, R. Codina, A. Huerta

Int. J. Numer. Meth. Fluids (1998). Vol. 28 (10), pp. 1391-1419

Abstract
An implicit fractional-step method for the numerical solution of the time-dependent incompressible Naiver-Stokes equations in primitive variables is developed and studied in this paper. The method, which is first order accurate in the time-step, is shown to convergence to an exact solution of the equations. By adequately splitting the viscous term, it allows to enforce full Dirichlet boundary conditions on the velocity in all substeps of the scheme, while needing no boundary condition at all for the pressure. It is also shown to be related to an iterative predictor-multicorrector algorithm for evolution equations, when this is applied to the incompressible Naiver-Stokes system. A new derivation of the algorithm in a general setting is provided. Two different finite element interpolations are considered for the implementation of the algorithm; numerical results obtained with them for standard benchmark cases are presented.
Abstract
An implicit fractional-step method for the numerical solution of the time-dependent incompressible Naiver-Stokes equations in primitive variables is developed and studied [...]
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A numerical model for temporal variations during explosive central vent eruptions
R. Folch, J. Marti, R. Codina, M. Vázquez

Journal of Geophysical Research: Solid Earth (1998). Vol. 103, 20883-20899

Abstract
An axisymmetrical numerical model has been developed in order to find the temporal evolution of pressure, the position of the exsolution level, the velocity field, the eruption rate, and the amount of erupted material of a shallow, volatile‐rich, felsic magma chamber during a Plinian central vent eruption. The overpressure necessary to trigger the eruption is assumed to result from crystallization‐driven volatile oversaturation. We solve the resulting set of equations using a finite element method. The results obtained show that the pressure at the conduit entrance decreases exponentially as the eruption proceeds. This produces a shifting of the exsolution level, so that deeper parts of the chamber become progressively volatile oversaturated during the eruption. We assess the influence of chamber geometry and the physical properties of the magma on the computed parameters using several numerical examples. The results are also compared with those predicted by previous models from the literature and are found to be in good agreement with documented eruptions. The model constitutes a first attempt to numerically model the dynamics and the temporal evolution of the most relevant physical parameters during withdrawal from a closed magma chamber.
Abstract
An axisymmetrical numerical model has been developed in order to find the temporal evolution of pressure, the position of the exsolution level, the velocity field, the eruption [...]
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Comparison of some finite element methods for solving the diffusion-convection-reaction equation
R. Codina

Comput. Methods Appl. Mech. Engrg., (1998). Vol. 156, (1-4), pp. 185-210

Abstract
In this paper we describe several finite element methods for solving the diffusion-convection-reaction equation. None of them is new, although the presentation is non-standard in an effort to emphasize the similarities and differences between them. In particular, it is shown that the classical SUPG method is very similar to an explicit version of the Characteristic-Galerkin method, whereas the Taylor-Galerkin method has a stabilization effect similar to a sub-grid scale model, which is un turn related to the introduction of bubbles functions.
Abstract
In this paper we describe several finite element methods for solving the diffusion-convection-reaction equation. None of them is new, although the presentation is non-standard [...]
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A general algorithm for compressible and incompressible flows. Part III: The semi‐implicit form
R. Codina, M. Vázquez, O. Zienkiewicz

Int. J. Numer. Meth. Fluids (1998). Vol. 27 (1-4), 13-32

Abstract
In this paper we consider some particular aspects related to the semi‐implicit version of a fractional step finite element method for compressible flows that we have developed recently. The first is the imposition of boundary conditions. We show that no boundary conditions at all need to be imposed in the first step where an intermediate momentum is computed. This allows us to impose the real boundary conditions for the pressure, a point that turns out to be very important for compressible flows. The main difficulty of the semi‐implicit form of the scheme arises in the solution of the continuity equation, since it involves both the density and the pressure. These two variables can be related through the equation of state, which in turn introduces the temperature as a variable in many cases. We discuss here the choice of variables (pressure or density) and some strategies to solve the continuity equation. The final point that we study is the behaviour of the scheme in the incompressible limit. It is shown that the method has an inherent pressure dissipation that allows us to reach this limit without having to satisfy the classical compatibility conditions for the interpolation of the velocity and the pressure
Abstract
In this paper we consider some particular aspects related to the semi‐implicit version of a fractional step finite element method for compressible flows that we have developed [...]
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Numerical analysis of coupled thermomechanical frictional contact problems. Computational model and applications
C. Agelet de Saracibar

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

Abstract
In this paper a numerical model for the analysis of coupled thermomechanical multi-body frictional contact problems at finite deformations is presented. The multi-body frictional contact formulation is fully developed on the continuum setting and then a spatial (Galerkin projection) and temporal (time-stepping algorithm) discretization is applied. A contact pressure and temperature dependent thermal contact model has been used. A fractional step method arising from an operator split of the governing equations has been used to solve the coupled nonlinear system of equations, leading to a staggered solution algorithm. The numerical model has been implemented into an enhanced version of the computational finite element program FEAP. Numerical examples and simulation of industrial metal forming processes show the performance of the numerical model in the analysis of coupled thermomechanical frictional contact problems.
Abstract
In this paper a numerical model for the analysis of coupled thermomechanical multi-body frictional contact problems at finite deformations is presented. The multi-body frictional [...]
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A strain-based plastic viscous-damage model for massive concrete structures
R. Faria, M. Cervera, J. Oliver

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

Abstract
Within the framework of continuum damage mechanics, a new constitutive damage model for massive concrete is presented, mainly intended for the seismic analysis of gravity and arch dams. Consistent with thermodynamic requirements, a straindriven formalism is adopted, improving the algorithmic efficiency as much as required for the analysis of large scale problems to become feasible. Two scalar damage variables are introduced as internal variables, as well as a plastic-strain tensor. An extension to account for the concrete strain-rate dependency, suitable for seismic analysis, is presented at the end. The efficiency of numerical predictions from the constitutive model is illustrated through numerical applications and algorithmic implementation is also detailed.
Abstract
Within the framework of continuum damage mechanics, a new constitutive damage model for massive concrete is presented, mainly intended for the seismic analysis of gravity [...]
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Algebraic Discrete Nonlocal (DNL) Absorbing Boundary Condition for the Ship Wave Resistance Problem
M. Storti, J. D'ELIA, S. Idelsohn

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

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

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

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

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

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

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

Abstract
A finite element formulation for solving incompressible flow problems is presented. In this paper, the generalized streamline operator presented by Hughes et al. (Comput. Methods Appl. Mech. Engrg. (1986) 58 305-328) for compressible flows is adapted to the incompressible Navier-Stokes equations. This new methodology allows the use of equal order interpolation for the unknowns of the problem: velocity and pressure. In this context, the definition of the ‘upwinding tensor’ does not require parameters defined outside this model. This formulation has been checked in classical tests with satisfactory results. Finally, a moving surface problem (Cruchaga et al., Comput. Numer. Methods Engrg. (1986) 59: 85-99) is also presented.
Abstract
A finite element formulation for solving incompressible flow problems is presented. In this paper, the generalized streamline operator presented by Hughes et al. (Comput. [...]
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Vulnerabilidad sísmica y toma de decisiones
J. Egozcue, G. Grande, P. Diez

Revista Internacional de Cálculo de Estructuras (1997). Vol. 2 (1), pp. 35-58

Abstract
Vulnerability of civil structures and systems under seismic actions have been extensively used and studied in the last decade. However, the goals of those studies are very diverse and it have caused some confusion on the meaning and definition of vulnerability. Naturally, different scopes of vulnerability lead to different methodologies in its study which may be incompatible. The present aim is to analyse the definition of seismic vulnerability in the framework of Bayesian decision making. Three different examples of decision making related to seismic vulnerability, which are qualitatively different, guide the discussion. They have an increasing complexity: decisions on normative seismic design; decisions on insurances against seismic risk and, finally, those decisions that should be taken to lead alarm, mitigation and rescue systems for seismic disasters. The three analised examples correspond to three different decision making schemes, respectively named: a priori, a posteriori and preposterior. In each case the definition of seismic vulnerability depends on the concept of considered utility (cost-benefit), on the involved random states and the scale in which the phenomena are to be considered. Most of the concepts associated with seismic vulnerability are reviewed through these three examples. A conclusion is that seismic vulnerability studies should consider the associated decision making problem. Simultaneously, the study of methodological and estimation aspects on vulnerability are remarked in order to improve both guidelines for seismic design and disaster mitigation.
Abstract
Vulnerability of civil structures and systems under seismic actions have been extensively used and studied in the last decade. However, the goals of those studies are very [...]
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Finite element solution of the Stokes problem with dominating Coriolis force
R. Codina, O. Soto

Comput. Methods Appl. Mech. Engrg., (1997). Vol. 142 (3-4), pp. 215-234

Abstract
The objective of this paper is to present a finite element formulation to solve the Stokes problem with Coriolis force. This force results in a skew-symmetric term in the weak formulation of the problem that deteriorates the stability of the standard Galerkin finite element method when the viscosity is small. We show that the stability is worsened due to the presence of the pressure gradient to enforce the incompressibility of the flow. The relevance of this effect depends on the relative importance of the viscous force and the Coriolis force, which is measured by the Ekman number. When it is small, oscillations occur using the Galerkin approach. To overcome them, we propose two different methods based on a consistent modification of the basic Galerkin formulation. Both methods eliminate the oscillations, keeping the accuracy of the formulation and enhancing its numerical stability.
Abstract
The objective of this paper is to present a finite element formulation to solve the Stokes problem with Coriolis force. This force results in a skew-symmetric term in the [...]
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A finite element formulation for Stokes proble allowing equal velocity-pressure interpolation
R. Codina, J. Blasco

Comput. Methods Appl. Mech. Engrg., (1997). Vol. 143 (3–4), pp. 373-391

Abstract
In this paper we study a variational formulation of the Stokes problem that accommodates the use of equal velocity-pressure finite element interpolations. The motivation of this method relies on the analysis of a class of fractional-step methods for the Navier-Stokes equations for which it is known that equal interpolations yield good numerical results. The reason for this turns out to be the difference between two discrete Laplacian operators computed in a different manner. The formulation of the Stokes problem considered here aims to reproduce this effect. From the analysis of the finite element approximation of the problem we obtain stability and optimal error estimates using velocity-pressure interpolations satisfying of the standard formulation. In particular, this condition is fulfilled by the most common equal order interpolations.
Abstract
In this paper we study a variational formulation of the Stokes problem that accommodates the use of equal velocity-pressure finite element interpolations. The motivation of [...]
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A new frictional time integration algorithm for large slip multi-body frictional contact problems
C. Agelet de Saracibar

Comput. Methods Appl. Mech. Engrg., (1997). Vol. 142 (3-4), pp. 303-334

Abstract
In this paper a new frictional time integration algorithm suitable for large slip multibody frictional contact problems is presented. The algorithm is introduced within the simple context of a model problem: the sliding motion of a particle onto a rough surface. Time integration of frictional traction is performed introducing a new slip path parametrization, which is defined independently traction is performed introducing element parametrization used in the spatial triangularization. The key point of the algorithm is that now, in presence of large slips, problems associated with slip motions such that a full incremental slip path is not within a single surface element, are completed bypassed. Remarkably, the algorithm is defined on the solely basis of the unit outward normal field to the surface without any appeal to the underlying local surface finite element triangularization. Geometrically, the assumed slip path can be viewed as an approximation to the geodesic passing throughout the initial and final points of each incremental slip path. The algorithm is amenable to exact linearization and asymptotic quadratic rate of convergence can be achieved within a Newton-Raphson iterative solution scheme. The algorithm can easily be extended to large slip multi-body frictional contact problems, involving finite strains.
Abstract
In this paper a new frictional time integration algorithm suitable for large slip multibody frictional contact problems is presented. The algorithm is introduced within the [...]
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Boundary conditions for finite element simulations of convective flows with artificial boundaries
J. Heinrich, S. Idelsohn, E. Oñate, C. Vionnet

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

Abstract
We examine the use of natural boundary conditions and conditions of the Sommerfeld type for finite element simulations of convective transport in viscous incompressible flows. We show that natural boundary conditions are superior in the sense that they always provide a correct boundary condition, as opposed to the Sommerfeld‐type conditions, which can lead to a singular formulation and a great loss of accuracy. For the Navier–Stokes equations, the natural boundary conditions must be combined with a simple method to eliminate perturbations on the pressure at the open boundary, which is the source of most errors.
Abstract
We examine the use of natural boundary conditions and conditions of the Sommerfeld type for finite element simulations of convective transport in viscous incompressible flows. [...]
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Petrov-Galerkin methods for the transient advective-diffusive equation with sharp gradients
S. Idelsohn, J. Heinrich, E. Oñate

Int. J. Numer. Meth. Engng. (1996). Vol. 39 (9), pp. 1455-1473

Abstract
A Petrov–Galerkin formulation based on two different perturbations to the weighting functions is presented. These perturbations stabilize the oscillations that are normally exhibited by the numerical solution of the transient advective–diffusive equation in the vicinity of sharp gradients produced by transient loads and boundary layers. The formulation may be written as a generalization of the Galerkin Least‐Square method.
Abstract
A Petrov–Galerkin formulation based on two different perturbations to the weighting functions is presented. These perturbations stabilize the oscillations that are normally [...]
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A critical displacement approach for predicting structural instability
E. Oñate, W. Matias

Comput. Methods Appl. Mech. Engrg., (1996). Vol. 134 (1-2), pp. 135-161

Abstract
A new technique for predicting structural instability points using the finite element method is presented. The approach is based on the estimation of the critical displacement pattern by writing an approximation of the tangent stiffness singularity condition at the instability point. The critical load is subsequently computed by using a secant load-displacement relationship. Details of this procedure are given together with explicit forms of the secant stiffness matrix for finite element analysis of solids and trusses. The accuracy and effectiveness of the method are clearly shown in a number of examples of two- and three-dimensional bar structures.
Abstract
A new technique for predicting structural instability points using the finite element method is presented. The approach is based on the estimation of the critical displacement [...]
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A stabilized finite point method for analysis of fluid mechanics problems
E. Oñate, S. Idelsohn, O. Zienkiewicz, R. Taylor, C. Sacco

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

Abstract
flow type problems is presented. The method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation integrals. Some examples of application to convective trasport and compressible flow problems are presented.
Abstract
flow type problems is presented. The method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation [...]
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Split, characteristic based semi‐implicit algorithm for laminar/turbulent incompressible flows
O. Zienkiewicz, B. Sai, K. Morgan, R. Codina

Int. J. Numer. Meth. Fluids (1996). Vol. 23, 787-809

Abstract
In an earlier paper, Zienkiewicz and Codina (Int. j. numer. methods fluids, 20, 869–885 (1995)) presented a general algorithm for the solution of both compressible and incompressible Navier–Stokes equations. The algorithm, based on operator splitting, permits arbitrary interpolation functions to be used while avoiding the Babŭska–Brezzi restriction. In addition, its characteristic based approach introduces a form of rational dissipation. Zienkiewicz et al. (Int. j. numer. methods fluids, 20, 887–913 (1995)) presented the application of this algorithm in its fully explicit form to various inviscid compressible flow problems. They also presented two incompressible flow problems solved by the fully explicit form, employing a pseudo compressibility. The present work deals with the application of the above algorithm it its semi‐implicit form to some incompressible flow benchmark problems. Further, it extends the methodology to turbulent flows by employing both one, and two equation turbulence models. A comparison of results with earlier investigations is presented. Other issues addressed in this study include the effect of additional diffusion terms present in the scheme for both laminar and turbulent flow problems and some practical difficulties associated with local time stepping.
Abstract
In an earlier paper, Zienkiewicz and Codina (Int. j. numer. methods fluids, 20, 869–885 (1995)) presented a general algorithm for the solution of both compressible [...]
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A rate-dependent isotropic damage model for the seismic analysis of concrete dams
M. Cervera, O. Manzoli, J. Oliver

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

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

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

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

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

Abstract
The paper presents a fully meshless procedure fo solving partial differential equations. The approach termed generically the ‘finite point method’ is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals. Some examples showing the accuracy of the method for solution of adjoint and non‐self adjoint equations typical of convective‐diffusive transport and also to the analysis of compressible fluid mechanics problem are presented.
Abstract
The paper presents a fully meshless procedure fo solving partial differential equations. The approach termed generically the ‘finite point method’ is based on [...]
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Industrial applications of sheet stamping simulation using new finite element models
J. Rojek, J. Jovicevic, E. Oñate

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

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

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

Abstract
A general constitutive model adequate for analysis of the thermomechanical response of composite materials is presented. The model is based on the mixture of the basic substances of the composite and allows the evaluation of the interdependence between the constitutive behaviour of different compounding materials. The behaviour of the each compound is modelled by a general anisotropic thermo‐elasto‐plastic model, termed the ‘base model’. The different base models for each compound are combined using mixing theory to simulate the behaviour of the multiphase material.
Abstract
A general constitutive model adequate for analysis of the thermomechanical response of composite materials is presented. The model is based on the mixture of the basic substances [...]
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A 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

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

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

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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On the derivation and possibilities of the secant stiffness matrix for non linear finite element analysis
E. Oñate

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

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

Computational Mechanics (1995). Vol. 17 (1-2), pp. 107-114

Abstract
A comparison between new and existing triangular finite elements based on the shell theory proposed by Juan Carlos Simo and co-workers is presented. Particular emphasis is put on the description of new triangles which show a promising behaviour for linear and non linear shell analysis.
Abstract
A comparison between new and existing triangular finite elements based on the shell theory proposed by Juan Carlos Simo and co-workers is presented. Particular emphasis is [...]
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A general algorithm for compressible and incompressible flow—Part II. tests on the explicit form
O. Zienkiewicz, K. Morgan, B. Sai, R. Codina, M. Vasquez

Int. J. Numer. Meth. Fluids (1995). Vol. 20 (8-9), pp. 887-913

Abstract
The algorithm introduced in Part I of this paper is applied in its explicit form to a variety of problems in order to demonstrate its wide range of applicability and excellent performance. Examples range from nearly incompressible, viscous, flows through transonic applications to high speed flows with shocks. In most examples linear triangular elements are used in the finite element approximation, but some use of quadratic approximation, again in triangles, indicates satisfactory performance even in the case of severe shocks.
Abstract
The algorithm introduced in Part I of this paper is applied in its explicit form to a variety of problems in order to demonstrate its wide range of applicability and excellent [...]
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A general algorithm for compressible and incompressible flow—Part I. the split, characteristic‐based scheme
O. Zienkiewicz, R. Codina

Int. J. Numer. Meth. Fluids (1995). Vol. 20, 869-885

Abstract
The paper outlines the formulation of a novel algorithm which can be used for the solution of both compressible and incompressible Navier‐Stokes or Euler equations. Full incompressibility can be dealt with if the algorithm is used in its semi‐explicit form and its structure permits arbitrary interpolation functions to be used avoiding the Babuška‐Brezzi restriction. In a fully explicit version it introduces a rational form of balancing dissipation avoiding the use of arbitrary parameters and forms for this.
Abstract
The paper outlines the formulation of a novel algorithm which can be used for the solution of both compressible and incompressible Navier‐Stokes or Euler equations. Full [...]
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Optimum aerodynamic shape design including mesh adaptivity
G. Bugeda, E. Oñate

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

Abstract
This paper presents a methodology for solving shape optimization problems in the context of fluid flow problems including adaptive remeshing. The method is based on the computation of the sensitivities of the geometrical design parameters, the mesh, the flow variables and the error estimator to project the refinement parameters from one design to the next. This sensitivity analysis is described for the incompressible potential equations and the Euler equations. The efficiency of the proposed method is checked by means of two 2D inverse problems.
Abstract
This paper presents a methodology for solving shape optimization problems in the context of fluid flow problems including adaptive remeshing. The method is based on the computation [...]
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Seismic evaluation of concrete dams via continuum damage models
M. Cervera, R. Faria, J. Oliver

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

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

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

Abstract
Stereolithography (SLA) is one of the most important techniques used in rapid prototyping processes. It has a great industrial interest because it allows for dramatic time savings with respect to traditional manufacturing processes. One of the main sources of error in the final dimensions of the prototype is the curl distortion effect owing to the shrinkage of the resin during the SLA process. Presents a study of the influence of different constructive and numerical parameters in the curl distortion, an analysis which was made using the computer code stereolithography analysis program, developed to model SLA processes using the finite element method. Also briefly presents this code.
Abstract
Stereolithography (SLA) is one of the most important techniques used in rapid prototyping processes. It has a great industrial interest because it allows for dramatic time [...]
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NUMISTAMP: a research project for assessment of finite-element models for stamping processes
E. Oñate, J. Rojek, C. Garino

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

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

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

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

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

Abstract
A consistent formulation for unilateral contact problems including frictional work hardening or softening is proposed. The approach is based on an augmented Lagrangian approach coupled to an implicit quasi‐static Finite Element Method. Analogous to classical work hardening theory in elasto‐plasticity, the frictional work is chosen as the internal variable for formulating the evolution of the friction convex. In order to facilitate the implementation of a wide range of phenomenological models, the friction coefficient is defined in a parametrised form in terms of Bernstein polynomials. Numerical simulation of a 3D deep‐drawing operation demonstrates the performance of the methods for predicting frictional contact phenomena in the case of large sliding paths including high curvatures.
Abstract
A consistent formulation for unilateral contact problems including frictional work hardening or softening is proposed. The approach is based on an augmented Lagrangian approach [...]
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An anisotropic elastoplastic model based on an isotropic formulation
S. Oller, S. Botello, J. Canet, E. Oñate

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

Abstract
This paper shows a generalization of the classic isotropic plasticity theory to be applied to orthotropic or anisotropic materials. This approach assumes the existence of a real anisotropic space, and other fictitious isotropic space where a mapped fictitious problem is solved. Both spaces are related by means of a linear transformation using a fourth order transformation tensor that contains all the information concerning the real anisotropic material. The paper describes the basis of the spaces transformation proposed and the expressions of the resulting secant and tangent constitutive equations. Also details of the numerical integration of the constitutive equation are provided. Examples of application showing the good performance of the model for analysis of orthotropic materials and fibre‐reinforced composites are given.
Abstract
This paper shows a generalization of the classic isotropic plasticity theory to be applied to orthotropic or anisotropic materials. This approach assumes the existence of [...]
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Finite volumes and finite elements: Two ‘good friends’
E. Oñate, S. Idelsohn

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

Abstract
In this paper a comparison between the finite element and the finite volume methods is presented in the context of elliptic, convective–diffusion and fluid flow problems. The paper shows that both procedures share a number of features, like mesh discretization and approximation. Moreover, it is shown that in many cases both techniques are completely equivalent.
Abstract
In this paper a comparison between the finite element and the finite volume methods is presented in the context of elliptic, convective–diffusion and fluid flow problems. [...]
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A temperature‐based formulation for finite element analysis of generalized phase‐change problems
D. Celentano, E. Oñate, S. Oller

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

Abstract
A finite element formulation for solving multidimensional phase‐change problems is presented. The formulation considers the temperature as the unique state variable, it is conservative in the weak form sense and it preserves the moving interface condition. In this work, an approximate jacobian matrix that preserves numerical convergence and stability is also derived. Furthermore, a comparative analysis with other different phase‐change finite element techniques is performed. Finally, several numerical examples are analysed in order to show the performance of the proposed methodology.
Abstract
A finite element formulation for solving multidimensional phase‐change problems is presented. The formulation considers the temperature as the unique state variable, it [...]
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A simple triangular element for thick and thin plate and shell analysis
E. Oñate, F. Zárate, F. flores

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

Abstract
A new plate triangle based on Reissner–Mindlin plate theory is proposed. The element has a standard linear deflection field and an incompatible linear rotation field expressed in terms of the mid‐side rotations. Locking is avoided by introducing an assumed linear shear strain field based on the tangential shear strains at the mid‐sides. The element is free of spurious modes, satisfies the patch test and behaves correctly for thick and thin plate and shell situations. The element degenerates in an explicit manner to a simple discrete Kirchhoff form.
Abstract
A new plate triangle based on Reissner–Mindlin plate theory is proposed. The element has a standard linear deflection field and an incompatible linear rotation field [...]
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A finite volume format for structural mechanics
E. Oñate, M. Cervera, O. Zienkiewicz

Int. J. Numer. Meth. Engng. (1994). Vol. 37 (2), pp. 181-201

Abstract
A general Finite Volume Method (FVM) for the analysis of structural problems is presented. It is shown that the FVM can be considered to be a particular case of finite elements with a non‐Galerkin weighting. For structural analysis this can readily be interpreted as equivalent to the unit displacement method which involves mainly surface integrals. Both displacement and mixed FV formulations are presented for static and dynamic problems.
Abstract
A general Finite Volume Method (FVM) for the analysis of structural problems is presented. It is shown that the FVM can be considered to be a particular case of finite elements [...]
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A methodology for adaptive mesh refinement in optimum shape design problems
G. Bugeda, E. Oñate

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

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

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

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

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

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

Journal of Physique IV (1993). Vol. 3 (C7), pp. 1171-1180

Abstract
This paper summarizes the recent work of the authors in the numerical simulation of casting processes. In particular, a coupled thermomechanical model to simulate the solidification problem in casting has been developed [7,8,9]. The model, based on a general isotropic thermoelasto-plasticity theory and formulated in a macroscopical point of view, includes generalized phase-change effects and considers the different thermomechanical behaviour of the solidifying material during its evolution from liquid to solid. For this purpose, a phase-change variable, plastic evolution equations and a temperature-dependent material constitutive law have been defined. Some relevant aspects of this model are presented here. Full thermomechanical coupling terms have been considered as well as variable thermal and mechanical boundary conditions : the first are due to air gap formation, while the second involve a contact formulation. Particular details concerning the numerical implementation of this model are also mentioned. An enhanced staggered scheme, used to solve the highly non-linear fully coupled finite element equations, is proposed. Furthermore, a proper convergence criterion to stop the iteration process is adopted and, although the quadratic convergence of Newton-Rapshon's method is not achieved, several numerical experiments demonstrate reasonable convergence rates [9]. Finally, an experimental cylindrical casting test problem, including phase-change phenomena, temperature-dependent constitutive properties and contact effects, is analyzed. Numerical results are compared with some laboratory measurements.
Abstract
This paper summarizes the recent work of the authors in the numerical simulation of casting processes. In particular, a coupled thermomechanical model to simulate the solidification [...]
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A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation
R. Codina

Comput. Methods Appl. Mech. Engrg., (1993). Vol. 110 (3-4), pp. 325-342

Abstract
To avoid the local oscillations that still remain using the streamline-upwind/Petrov-Galerkin formulation for the scalar convection-diffusion equation, the introduction of a nonlinear crosswind dissipation is proposed. It is shown that the method is less overdiffusive than other discontinuity-capturing techniques and has better numerical behavior. The design of the crosswind diffusion is based on the study of the discrete maximum principle for some simple cases.
Abstract
To avoid the local oscillations that still remain using the streamline-upwind/Petrov-Galerkin formulation for the scalar convection-diffusion equation, the introduction of [...]
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Stability analysis of the forward Euler scheme for the convection‐diffusion equation using the SUPG formulation in space
R. Codina

Int. J. Numer. Meth. Engng. (1993). Vol. 36, 1445-1464

Abstract
The stability and accuracy of the forward Euler scheme for the semidiscrete problem arising from the space discretization of the convection‐diffusion equation using the SUPG formulation are analysed. Both linear and quadratic finite elements are considered. The stability limits are derived for the one‐dimensional problem and a heuristic criterion is proposed for the multidimensional equation. Some numerical experiments are conducted in order to assess the performance of different finite elements
Abstract
The stability and accuracy of the forward Euler scheme for the semidiscrete problem arising from the space discretization of the convection‐diffusion equation using the [...]
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An iterative penalty method for the finite element solution of the stationary Navier-Stokes equations
R. Codina

Comput. Methods Appl. Mech. Engrg., (1993). Vol. 110 (3-4), pp. 237-262

Abstract
The objective of this paper is to analyse an iterative procedure for the finite element solution of the Stokes and Navier-Stokes stationary problems. For the latter case, the usual condition on the viscosity and the data that ensures uniqueness is assumed. The method is based on the iterative imposition of the incompressibility condition via penalization. Theoretical and numerical results show that this constraint can be approximated iteratively within the same iterative loop used to deal with the nonlinear term of the equations. Two particular iterative schemes are analysed, namely those based on the Picard and Newton-Raphson algorithms.
Abstract
The objective of this paper is to analyse an iterative procedure for the finite element solution of the Stokes and Navier-Stokes stationary problems. For the latter case, [...]
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Derivation of thin plate bending elements with one degree of freedom per node: a simple three node triangle
E. Oñate, M. Cervera

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

Abstract
A general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented. The formulation is based on the combination of a standard C0 finite element interpolation for the deflection field with an independent approximation of the curvatures which are expressed in terms of the deflection gradient along the sides using a finite volume‐like approach. The formulation is particularized for the simplest element of the family, i.e. the three node triangle with three degrees of freedom. The potential of the new element is shown through different examples of application.
Abstract
A general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented. The formulation is based on the combination of a standard C0 [...]
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A study of mesh optimality criteria in adaptive finite element analysis
E. Oñate, G. Bugeda

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

Abstract
The concepts of solution error and optimal mesh in adaptive finite element analysis are revisited. It is shown that the correct evaluation of the convergence rate of the error norms involved in the error measure and the optimal mesh criteria chosen are essential to avoid oscillations in the refinement process. Two mesh optimality criteria based on: (a) the equal distribution of global error, and (b) the specific error over the elements are studied and compared in detail through some examples of application.
Abstract
The concepts of solution error and optimal mesh in adaptive finite element analysis are revisited. It is shown that the correct evaluation of the convergence rate of the error [...]
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A general methodology for deriving shear constrained Reissner-Mindlin plate elements
E. Oñate, O. Zienkiewicz, B. Suarez, R. Taylor

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

Abstract
In this paper the necessary requirements for the good behaviour of shear constrained Reissner–Mindlin plate elements for thick and thin plate situations are re‐interpreted and a simple explicit form of the substitute shear strain matrix is obtained. This extends the previous work of the authors presented in References 18 and 31. The general methodology is applied to the re‐formulation of some well known quadrilateral plate elements and some new triangular and quadrilateral plate elements which show promising features. Some examples of the good behaviour of these elements are given.
Abstract
In this paper the necessary requirements for the good behaviour of shear constrained Reissner–Mindlin plate elements for thick and thin plate situations are re‐interpreted [...]
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The intrinsic time for the streamline upwind Petrov-Galerkin formulation using quadratic elements
R. Codina, E. Oñate, M. Cervera

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

Abstract
In this paper the functions of the Péclet number that appear in the intrinsic time of the streamline upwind/Petrov-Galerkin (SUPG) formulation are analyzed for quadratic elements. Some related issues such as the computation of the characteristic element length and the introduction of source terms in the one-dimensional model problem are also addressed.
Abstract
In this paper the functions of the Péclet number that appear in the intrinsic time of the streamline upwind/Petrov-Galerkin (SUPG) formulation are analyzed for quadratic [...]
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Numerical Analysis of Dams with Extensive Cracking due to Concrete Hydration: Simulation of a Real Case
M. Cervera, M. Galindo, J. Oliver

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

Abstract
The paper presents the computational model developed to study an existing large gravity dam suffering from observed "pathological behavior" resulting concrete hydration. The combined effect of water intrusion and chemical and numerical studies. The present study was undertaken to simulate numerically the observed phenomenon and to predict future developments. Concrete is modelled using an isotropic continuum damage model including visco-elastic effects. The triggering of the volumetric expansion resulting from water intrusion is linked to the onset of damage at each a point, assuming that water enters dam mostly through the damaged areas. Transversal construction joints are modelled using smeared joints. Temperature and porewater pressure effects are included using assumed distributions based on available field data. Results are presented which match reasonably well with the available filed measurements.
Abstract
The paper presents the computational model developed to study an existing large gravity dam suffering from observed "pathological behavior" resulting concrete hydration. [...]
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Comparative study on sheet metal forming processes by numerical modelling and experiment
W. Sosnowski, E. Oñate, C. Agelet de Saracibar

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

Abstract
In this paper some results of a wide experimental program are presented and compared with some finite element solution of sheet metal forming problems using a viscous shell formulation.
Abstract
In this paper some results of a wide experimental program are presented and compared with some finite element solution of sheet metal forming problems using a viscous shell [...]
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Finite element analysis of sheet metal forming problems using a selective viscous bending/membrane formulation
E. Oñate, C. Agelet de Saracibar

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

Abstract
In this paper the possibilities of the viscous voided shell approach for deriving bending/membrane finite elements for sheet metal forming problems are presented. These elements can be selectively used for membrane or full bending analysis of some parts of the sheet according to the nature of the deformation. Numerical aspects of this approach are discussed and some examples of application are also given.
Abstract
In this paper the possibilities of the viscous voided shell approach for deriving bending/membrane finite elements for sheet metal forming problems are presented. These elements [...]
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Finite element nonlinear analysis of concrete structures using a “plastic-damage model”
S. Oller, E. Oñate, J. Oliver, J. Lubliner

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

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

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

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

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

Abstract
In recent years a series of elements based on Reissner-Mindlin assumptions and using discrete (collocation type) constraints has been introduced. These elements have proved to be very effective, however their relation to straightforward mixed approximations has not been clear. In this paper this relationship is discussed and the reasons for their success explained. This allows new and effective triangular elements to be developed. The presentation shows the close relationships with the DKT (Discrete Kirchhoff Theory) element previously available only for thin plates and allows extension of their applications.
Abstract
In recent years a series of elements based on Reissner-Mindlin assumptions and using discrete (collocation type) constraints has been introduced. These elements have [...]
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A plastic-damage model for concrete
J. Lubliner, J. Oliver, S. Oller, E. Oñate

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

Abstract
In this paper a constitutive model based on an internal variable-formulation of plasticity theory for the non-linear analysis of concrete is presented. The model uses a new yield criterion which matches experimental data quite well and it accounts for both elastic and plastic stiffness degradations effects. Onset and amount of cracking can be studied by a simple postprocessing of the finite-element plasticity solution. The accuracy of the model is checked with some examples of application.
Abstract
In this paper a constitutive model based on an internal variable-formulation of plasticity theory for the non-linear analysis of concrete is presented. The model uses a new [...]
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Dynamic analysis of structures using a Reissner-Mindlin finite strip formulation
J. Canet, B. Suarez, E. Oñate

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

Abstract
In this paper a finite strip formulation based on Reissner-Mindlin plate theory for dynamic analysis of prismatic shell type structure is presented. Detailed expressions of the relevant strip matrices for a variety of structures using the simple two node linear strip element are given. Examples of the good performance of the linear strip element for free and forced vibration analysis of plates, bridges and axisymmetric shells are presented.
Abstract
In this paper a finite strip formulation based on Reissner-Mindlin plate theory for dynamic analysis of prismatic shell type structure is presented. Detailed expressions of [...]
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Plastic and viscoplastic flow of void‐containing metals. Applications to axisymmetric sheet forming problems
E. Oñate, M. Kleiber, C. Agelet de Saracibar

Int. J. Numer. Meth. Engng. (1988). Vol. 25 (1), pp. 227-251

Abstract
A formal analogy between the equations of pure plastic and viscoplastic flow theory for void‐containing metals and those of standard non‐linear elasticity is presented. The formulation is particularized for the analysis of axisymmetric sheet metal forming problems using simple two node linear finite elements. Details of the treatment of friction and strain hardening phenomena, time increment computation and elastic effects are also given. Examples of the effect of void porosity on the hemispherical stretching of a circular sheet are presented.
Abstract
A formal analogy between the equations of pure plastic and viscoplastic flow theory for void‐containing metals and those of standard non‐linear elasticity is presented. [...]
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On a non‐linear formulation for curved Timoshenko beam elements considering large displacement/rotation increments
E. Dvorkin, E. Oñate, J. Oliver

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

Abstract
An incremental Total Lagrangian Formulation for curved beam elements that includes the effect of large rotation increments is developed. A complete and symmetric tangent stiffness matrix is obtained and the numerical results show, in general, an improvement over the standard formulation where the assumption of infinitesimal rotation increments is made in the derivation of the tangent stiffness matrix.
Abstract
An incremental Total Lagrangian Formulation for curved beam elements that includes the effect of large rotation increments is developed. A complete and symmetric tangent stiffness [...]
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Benchmarks for geotechnical modeling
E. Alarcón, E. Alonso, D. Aubry, K. Axelsson, E. Oñate

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

Abstract
This letter represents an initiative started by a number of researchers signed below who are working in the field of numerical modelling of soil mechanics problems. We belive that the type of approach outlined is important in a serious numerical study of all problems in geomechanics and indeed is valid in other areas.
Abstract
This letter represents an initiative started by a number of researchers signed below who are working in the field of numerical modelling of soil mechanics problems. We belive [...]
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Free vibration analysis of plates, bridges and axisymmetric shells using a thick finite strip method
B. Suarez, J. Canet, E. Oñate

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

Abstract
A unified approach for the vibration analysis of curved or straight prismatic plates and bridges and axisymmetric shells using a finite strip method based in Reissner—Mindlin shell theory is presented. Details of obtaining all relevant strip matrices and vectors are given. It is also shown how the use of the simple linear two node strip with reduced integration leads to direct explicit forms of all relevant matrices. Examples of application which show the accuracy of the linear strip for free vibration analysis of structures are presented.
Abstract
A unified approach for the vibration analysis of curved or straight prismatic plates and bridges and axisymmetric shells using a finite strip method based in Reissner—Mindlin [...]
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A constitutive model for cracking of concrete based on the incremental theory of plasticity
E. Oñate, S. Oller, J. Oliver, J. Lubliner

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

Abstract
A constitutive model based on classical plasticity theory for non‐linear analysis of concrete structures using finite elements is presented. The model uses the typical parameters of non‐associated plasticity theory for frictional materials and a modified Mohr‐Coulomb yield surface is suggested. Onset and amount of cracking at a point are controlled by the values of the effective plastic strain and thus it can be studied by a posteriori postprocessing of numerical results. The accuracy and objectivity of the model is checked out with some examples of application.
Abstract
A constitutive model based on classical plasticity theory for non‐linear analysis of concrete structures using finite elements is presented. The model uses the typical parameters [...]
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Nonlinear analysis of reinforced concrete plate and shell structures using 20-noded isoparametric brick elements
M. Cervera, E. Hinton, O. Hassan

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

Abstract
This paper describes an efficient and accurate, 3-D finite element model which may be adopted in the nonlinear analysis of reinforced concerete plate and shell structures. Benchmark tests are undertaken to check the computational model.
Abstract
This paper describes an efficient and accurate, 3-D finite element model which may be adopted in the nonlinear analysis of reinforced concerete plate and shell structures. [...]
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A total Lagrangian formulation for the geometrically nonlinear-analysis of structures using finite-elements. Part II: arches, frames and axisymmetric shells
J. Oliver, E. Oñate

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

Abstract
A geometrically nonlinear finite element formulation based on a total Lagrangian approach for axisymmetric shells, arches and frames has been presented. The formulation allows for large displacement-large rotations of the structure. Shear deformation effects have also been taken into account. It has been shown how the formulation can be presented in a unified manner to treat simultaneously the three types of structures.
Abstract
A geometrically nonlinear finite element formulation based on a total Lagrangian approach for axisymmetric shells, arches and frames has been presented. The formulation allows [...]
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Preconditioned conjugate gradient method for the non‐linear finite element analysis with particular reference to 3D reinforced concrete structures
M. Cervera, Y. Liu, E. Hinton

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

Abstract
A hierarchically preconditioned conjugate gradient (PCG) method for finite element analysis is presented. Its use is demonstrated for the difficult problem of the non‐linear analysis of 3D reinforced concrete structures. Examples highlight the dramatic savings in computer storage and more modest savings in solution times obtained using PCG especially for large problems.
Abstract
A hierarchically preconditioned conjugate gradient (PCG) method for finite element analysis is presented. Its use is demonstrated for the difficult problem of the non‐linear [...]
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Análisis no lineal de tanques criogénicos bajo cargas térmicas
J. Oliver, E. Oñate, J. Peraire, R. Chueca

Hormigón y Acero (1985). Vol. 155, pp. 99-123
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A finite element formulation for the analysis of marine pipelines during laying operations
J. Oliver, E. Oñate

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

Abstract
In this paper a finite element formulation for the deformation analysis of submarine pipelines during laying operations is presented. The formation allows for large displacement/rotations and the effect of nonconservative water loads. An iterative procedure to deal with the changing boundary conditions at the seafloor is also presented. Numerical results for two pipeline laying cases, obtained using three noded isoparametrical one-dimensional curved elements, are given.
Abstract
In this paper a finite element formulation for the deformation analysis of submarine pipelines during laying operations is presented. The formation allows for large displacement/rotations [...]
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A total Lagrangian formulation for the geometrically nonlinear analysis of structures using finite elements. Part I. Two‐dimensional problems: Shell and plate structures
J. Oliver, E. Oñate

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

Abstract
A total Lagrangian finite element formulation for the geometrically nonlinear analysis (large displacement/large rotations) of shells is presented. Explicit expressions of all relevant finite element matrices are obtained by means of the definition of a local co‐ordinate system, based on the shell principal curvature directions, for the evaluation of strains and stresses. A series of examples of nonlinear analysis of shell and plate structures is given.
Abstract
A total Lagrangian finite element formulation for the geometrically nonlinear analysis (large displacement/large rotations) of shells is presented. Explicit expressions of [...]
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Estudio de la distribución transitoria del gas en redes urbanas por el método de los elementos finitos
B. Suárez, E. Oñate

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

Abstract
Se representa una formulación por elementos finitos que permite simular la distribución transitoria de presiones y caudales del gas en redes urbanas. Esta formulación, que parte de las ecuaciones básicas que proporciona la mecánica de fluidos para la circulación de un gas en régimen variable por conductos cilíndricos, utiliza elementos finitos unidimensionales parabólicos para discretizar los distintos tramos de la red y un esquema paso a paso de integración en el tiempo que supone una variación lineal de la presión del gas en cada intervalo de tiempo. La formulación se aplica al caso real de la red media presión de la ciudad de Barcelona utilizando algunos resultados experimentales para confirmar su eficiencia y aproximación.
Abstract
Se representa una formulación por elementos finitos que permite simular la distribución transitoria de presiones y caudales del gas en redes urbanas. Esta formulación, [...]
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Posibilidades de los ordenadores personales en el cálculo de estructuras por el método de los elementos finitos
E. Oñate, Á. Gaona, J. Oliver, B. Suarez

Revista de Obras Públicas (1983). Vol. 130 (3212), pp. 231-248
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Una formulación para el estudio, por el método de los elementos finitos, de la deformación de tuberías marinas durante su instalación
J. Oliver, E. Oñate

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

Abstract
La ejecución de emisarios submarinos para saneamiento y la instalación de tuberías para transporte de productos petrolíferos son ejemplos de la necesidad de conocer los esfuerzos y deformaciones que se producen en el tendido de tuberías submarinas, a cuyo estudio, mediante elementos finitos en diversas condiciones de instalación, se dedica este artículo, que permite la obtención de ábacos de cálculo o formulas sencillas aplicables en los distintos casos.
Abstract
La ejecución de emisarios submarinos para saneamiento y la instalación de tuberías para transporte de productos petrolíferos son ejemplos de la [...]
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A viscous shell formulation for the analysis of thin sheet metal forming
E. Oñate, O. Zienkiewicz

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

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

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

Abstract
The behaviour of the linear, quadratic and cubic elements of the Mindlin plate strip family for thick and very thin plate analysis is investigated in this paper. Selective integration techniques are used to ensure the good behaviour of the elements when dealing with thin plates. Numerical results showing the convergence and accuracy of the elements for the analysis of plates of a wide range of thicknesses are given. The general performance of the three elements is discussed in detail. In particular, the linear element with a single integration point seems to be the best value strip element for practical purposes.
Abstract
The behaviour of the linear, quadratic and cubic elements of the Mindlin plate strip family for thick and very thin plate analysis is investigated in this paper. Selective [...]
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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

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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El laboratorio de ensayo de estructuras en modelo reducido de la Escuela de Ingenieros de Caminos de Barcelona
J. Oliver, B. Suárez, E. Blanco, E. Oñate

Acero y Hormigón (1982). Vol. 145, pp. 65-78
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A general formulation for coupled thermal flow of metals using finite elements
O. Zienkiewicz, E. Oñate, J. Heinrich

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

Abstract
A finite element formulation to deal with the flow of metals coupled with thermal effects in presented. The deformation process of the metal is treated using the visco‐plastic flow approach and the solution technique for the coupled problem implies a simultaneous solution for velocities and temperatures. Some aspects of the numerical solution of the problem are given and in the last part of the paper some examples of steady‐state extrusion and rolling problems showing the applicability of the method are shown.
Abstract
A finite element formulation to deal with the flow of metals coupled with thermal effects in presented. The deformation process of the metal is treated using the visco‐plastic [...]
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La formulación del flujo viscoplástico y sus diversas aplicaciones prácticas por el método de los elementos finitos
E. Oñate

Revista de Obras Públicas (1980). Vol. 127 (3178), pp. 115-129
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Flow of solids during forming and extrusion: Some aspects of numerical solutions
O. Zienkiewicz, P. Jain, E. Oñate

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

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

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

Abstract
A two noded, straight element which includes shear deformation effects is presented and shown to be extremely efficient in the analysis of axisymmetric shells. A single point of numerical integration is essential for its success when applied to thin shells where the results compare favourably with those achieved with more complex curved elements.
Abstract
A two noded, straight element which includes shear deformation effects is presented and shown to be extremely efficient in the analysis of axisymmetric shells. A single point [...]
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Diseño óptimo de vasijas de presión usando el método de los elementos finitos y un optimizador no lineal
J. Middleton, E. Oñate

ETSIIT (1977). Vol. 11, pp. 309-325

Abstract
Se presenta un esquema de diseño para vasijas de presión metálicas de manera que se minimice la tensión tangencial en la vasija . La geometría final se establece mediante un procedimiento iterativo que optimiza un modelo matemático que expresa la variación de la tensión tangencial en la vasija. Los parámetros del modelo se calculan para cada interacción a partir de los valores de las tensiones tangenciales en la vasija, determinados por el método de los elementos finitos.
Abstract
Se presenta un esquema de diseño para vasijas de presión metálicas de manera que se minimice la tensión tangencial en la vasija . La geometría [...]
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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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Experiments on reinforced brick masonry vaulted light roofs
F. López-Almansa, P. Roca, V. Sarrablo, X. Cahís, J. Canet

Structural Journal (2010). Vol. 107 (3), pp. 355-363

Abstract
This paper describes structural tests of thin vaults made of reinforced brick masonry. The experiments consist of concentrated loading tests of 14 full-scale laboratory vaults. These vaults are designed to include common situations such as short- to midspan length, low-mid-high rise, rigid-flexible-sliding supports, instantaneous-sustained loading, low-high strength mortar, point-line loading, central-eccentric loading, point-line supports, hinged-clamped supports, symmetric-asymmetric shape, double layer versus single layer reinforcement, and uniaxial-biaxial bending, among others. The tests mainly aim to obtain the collapse loads and to characterize the pre- and post-peak response. The results show satisfactory structural performance, both in terms of ductility and strength. Moreover, it is possible to predict the structural response with numerical models developed specifically for this purpose. Flat specimens were also tested to determine the punching shear strength of the vaults. This work is part of a larger research project aimed at promoting innovative semi-prefabrication techniques for reinforced brick masonry vaulted light roofs.
Abstract
This paper describes structural tests of thin vaults made of reinforced brick masonry. The experiments consist of concentrated loading tests of 14 full-scale laboratory vaults. [...]
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A numerical-experimental method for characterizing recycled asphalt mixtures
R. Miró, F. Pérez, S. Oller, J. Canet, J. González

Road materials and pavement design (2008). Vol. 9 (4), pp. 711-730

Abstract
Experimental techniques usually employed in the characterization of conventional mixes are not able to clearly describe some specific properties of the recycled mixes, which are determinant in the material's mechanical response like cracking strength or tenacity. These new specific properties demands new methods of testing to know the really conditioning mechanical variables taking part in the process, so that being able to characterize and design new recycled mixes in an optimum way. In this paper, the direct tensile test is analyzed as a suitable method for evaluating the properties of recycled asphalt mixtures for different percentages of reclaimed asphalt pavement. A constitutive formulation has been developed to simulate the experimental results and can be used in conjunction with the experimental analysis of the recycled asphalt properties to provide an accurate characterization of the material.
Abstract
Experimental techniques usually employed in the characterization of conventional mixes are not able to clearly describe some specific properties of the recycled mixes, which [...]
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Limit analysis of reinforced masonry vaults
P. Roca, F. López-Almansa, J. Canet, A. Hanganu

Engineering Structures (2007). Vol. 23 (3), pp. 431-439

Abstract
Reinforced brick masonry has experienced only scarce use as a fully structural material due to, among other reasons, the lack of design criteria and calculation tools allowing a scientific, but also practical, engineering approach to design and assessment. Aiming at contributing to a more widespread use of this material, a simplified method for the ultimate analysis of reinforced masonry arches and cylindrical vaults, based on the lower-bound theorem (or static approach) of plasticity, has been developed. This approach has been satisfactorily validated by comparison with experimental and numerical results obtained by more accurate numerical models.
Abstract
Reinforced brick masonry has experienced only scarce use as a fully structural material due to, among other reasons, the lack of design criteria and calculation tools [...]
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A viscoplastic constitutive model with strain rate variables for asphalt mixtures—numerical simulation
J. González, J. Canet, S. Oller, R. Miró

Computational Materials Science (2007). Vol. 38 (4), pp. 543-560

Abstract
The study and development of recycling techniques for pavements is an increasing activity in engineering nowadays. This research line demands a more realistic characterization of the material properties with the aim of simulate the asphalt mixture’s response placed into a multilayered system over granular bases, under dynamic loads, considering also temperature variation or strength reduction for cyclic loads. In order to improve the current formulations, a new viscoplastic model has been developed assuming the strain rate dependency of the material’s response observed in the experimental tests. The strain rate variable affects in a significant way the Young modulus and the viscosity parameter of the model. According to this hypothesis a constitutive equations have been formulated. The mechanical variables involved have been calibrated according to experimental results, developing new expressions for the strain rate dependent parameters. The new viscoplastic model permits us to characterize the material’s response with a few mechanical values, easily obtained from standard laboratory tests. The results obtained show a good approximation to experimental laboratory curves for different rates of loading and temperatures. The model has been applied to simulate the response of a real flexible pavement structure conformed by two asphalt layers over two granular bases, that’s materials with different constitutive behaviors. Experimental tests in the recycled track have been made obtaining the horizontal strain evolution under dynamic load. Different loading rates and temperatures, as well as cracked and continuum pavement responses have been considered in the study. Strains were measured in the interface between the two asphalt layers and simulated using the here proposed model offering a fairly good approximation of the real response observed in the track, although the degree of variation even in the experimental curves is quite high. The results of this study represent a proper base for further developments in structural analysis of pavement layers, considering more complex phenomena, determinant in the long term material’s response, to develop a numerical tool for pavements’ design and lifetime prediction.
Abstract
The study and development of recycling techniques for pavements is an increasing activity in engineering nowadays. This research line demands a more realistic characterization [...]
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Composite material behavior using a homogenization double scale method
S. Oller, J. Canet, F. Zalamea

Journal of Engineering Mechanics (2005). Vol. 131 (1), pp. 65-79

Abstract
In this paper, we present a two-scale numerical method in which structures made up of composite materials are simulated. The method proposed lies within the context of homogenization theory and assumes the periodicity of the internal structure of the material. The problem is divided into two scales of different orders of magnitude: A macroscopic scale in which the body and structure of the composite material is simulated, and a microscopic scale in which an elemental volume called a “cell” simulates the material. In this work, the homogenized strain tensor is related to the transformation of the periodicity vectors. The problem of composite materials is posed as a coupled, two-scale problem, in which the constitutive equation of the composite material becomes the solution of the boundary-value problem in the cell domain. Solving various examples found in the bibliography on this subject demonstrates the validity of the method.
Abstract
In this paper, we present a two-scale numerical method in which structures made up of composite materials are simulated. The method proposed lies within the context of homogenization [...]
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Utilización de amortiguadores y conectores sísmicos en puentes
J. Forment, J. Canet, A. Aparicio

Hormigón y Acero (2000). Vol. 51 (217), pp. 81-100

Abstract
The earthquakes have always represented on of the most dread destructive phenomena, for they affect the last stability of the structures. The modern societies are not prepared any more to accept then as a fatility, and the trend is now to provide, for structures situated in critical seismic zones, specific devices which nullify, or at least reduce the effect of the earthquakes. In this paper we are going to present the effects that the establishment of two similar seismic devices - the dampers and the seismic connectors - produces in different kinds of bridges.
Abstract
The earthquakes have always represented on of the most dread destructive phenomena, for they affect the last stability of the structures. The modern societies are not prepared [...]
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Cool steam method for desalinating seawater
P. Arnau, N. Navarro, J. Soraluce, J. Martínez-Iglesias, J. Illas, E. Oñate

Water (2019). Vol. 11 (11), 16 pp.

Abstract
Cool steam is an innovative distillation technology based on low-temperature thermal distillation (LTTD), which allows obtaining fresh water from non-safe water sources with substantially low energy consumption. LTTD consists of distilling at low temperatures by lowering the working pressure and making the most of low-grade heat sources (either natural or artificial) to evaporate water and then condensate it at a cooler heat sink. To perform the process, an external heat source is needed that provides the latent heat of evaporation and a temperature gradient to maintain the distillation cycle. Depending on the available temperature gradient, several stages can be implemented, leading to a multi-stage device. The cool steam device can thus be single or multi-stage, being raw water fed to every stage from the top and evaporated in contact with the warmer surface within the said stage. Acting as a heat carrier, the water vapor travels to the cooler surface and condensates in contact with it. The latent heat of condensation is then conducted through the conductive wall to the next stage. Net heat flux is then established from the heat source until the heat sink, allowing distilling water inside every parallel stage.
Abstract
Cool steam is an innovative distillation technology based on low-temperature thermal distillation (LTTD), which allows obtaining fresh water from non-safe water sources with [...]
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A Proper Generalized Decomposition (PGD) approach to crack propagation in brittle materials: with application to random field material properties
H. Garikapati, S. Zlotnik, C. Verhoosel, E. Brummelen, P. Diez

Computational Mechanics (2019). (Preprint) pp. 1-23

Abstract
Understanding the failure of brittle heterogeneous materials is essential in many applications. Heterogeneities in material properties are frequently modeled through random fields, which typically induces the need to solve finite element problems for a large number of realizations. In this context, we make use of reduced order modeling to solve these problems at an affordable computational cost. This paper proposes a reduced order modeling framework to predict crack propagation in brittle materials with random heterogeneities. The framework is based on a combination of the Proper Generalized Decomposition (PGD) method with Griffith’s global energy criterion. The PGD framework provides an explicit parametric solution for the physical response of the system. We illustrate that a non-intrusive sampling-based technique can be applied as a postprocessing operation on the explicit solution provided by PGD.We first validate the framework using a global energy approach on a deterministic two-dimensional linear elastic fracture mechanics benchmark. Subsequently, we apply the reduced order modeling approach to a stochastic fracture propagation problem.
Abstract
Understanding the failure of brittle heterogeneous materials is essential in many applications. Heterogeneities in material properties are frequently modeled through random [...]
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A new 3D equilibrated residual method improving accuracy and efficiency of flux‐free error estimates
N. Parés, P. Diez

Comput. Methods Appl. Mech. Engrg., (2019). (Preprint) Vol. 120, pp. 391-432

Abstract
The paper presents a novel strategy providing fully computable upper bounds for the energy norm of the error in the context of three‐dimensional linear finite element approximations of the reaction‐diffusion equation. The upper bounds are guaranteed regardless the size of the finite element mesh and the given data, and all the constants involved are fully computable. The upper bound property holds if the shape of the domain is polyhedral and the Dirichlet boundary conditions are piecewise‐linear. The new approach is an extension of the flux‐free methodology introduced by Parés and Díez in the paper “A new equilibrated residual method improving accuracy and efficiency of flux‐free error estimates”, which introduces a guaranteed, low‐cost, and efficient flux‐free method substantially reducing the computational cost of obtaining guaranteed bounds using flux‐free methods while retaining the good quality of the bounds. Besides extending the 2D methodology, specific new modifications are introduced to further reduce the computational cost in the three‐dimensional setting. The presented methodology also provides a new strategy to obtain equilibrated boundary tractions, which improves the quality of standard techniques while having a similar computational cost.
Abstract
The paper presents a novel strategy providing fully computable upper bounds for the energy norm of the error in the context of three‐dimensional linear finite element approximations [...]
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Sampling-based stochastic analysis of the PKN model for hydraulic fracturing
H. Garikapati, C. Verhoosel, E. Brummelen, S. Zlotnik, P. Diez

Computational Geosciences (2019). (Preprint) Vol. 23 (1), pp. 81-105

Abstract
Hydraulic fracturing processes are surrounded by uncertainty, as available data is typically scant. In this work, we present a sampling-based stochastic analysis of the hydraulic fracturing process by considering various system parameters to be random. Our analysis is based on the Perkins-Kern-Nordgren (PKN) model for hydraulic fracturing. This baseline model enables computation of high fidelity solutions, which avoids pollution of our stochastic results by inaccuracies in the deterministic solution procedure. In order to obtain the desired degree of accuracy of the computed solution, we supplement the employed time-dependent moving-mesh finite element method with two new enhancements: (i) global conservation of volume is enforced through a Lagrange multiplier; (ii) the weakly singular behavior of the solution at the fracture tip is resolved by supplementing the solution space with a tip enrichment function. This tip enrichment function enables the computation of the tip speed directly from its associated solution coefficient. A novel incremental-iterative solution procedure based on a backward-Euler time-integrator with sub-iterations is employed to solve the PKN model. Direct Monte-Carlo sampling is performed based on random variable and random field input parameters. The presented stochastic results quantify the dependence of the fracture evolution process—in particular the fracture length and fracture opening—on variations in the elastic properties and leak-off coefficient of the formation, and the height of the fracture.
Abstract
Hydraulic fracturing processes are surrounded by uncertainty, as available data is typically scant. In this work, we present a sampling-based stochastic analysis of the hydraulic [...]
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Algebraic and parametric solvers for the power flow problem: towards real-time and accuracy-guaranteed simulation of electric systems
R. García-Blanco, P. Diez, D. Borzacchiello, F. Chinesta

Archives of Comp. Meths. Engng. (2018). (Preprint) Vol. 25 (4), pp. 1003-1026

Abstract
The power flow model performs the analysis of electric distribution and transmission systems. With this statement at hand, in this work we present a summary of those solvers for the power flow equations, in both algebraic and parametric version. The application of the Alternating Search Direction method to the power flow problem is also detailed. This results in a family of iterative solvers that combined with Proper Generalized Decomposition technique allows to solve the parametric version of the equations. Once the solution is computed using this strategy, analyzing the network state or solving optimization problems, with inclusion of generation in real-time, becomes a straightforward procedure since the parametric solution is available. Complementing this approach, an error strategy is implemented at each step of the iterative solver. Thus, error indicators are used as an stopping criteria controlling the accuracy of the approximation during the construction process. The application of these methods to the model IEEE 57-bus network is taken as a numerical illustration.
Abstract
The power flow model performs the analysis of electric distribution and transmission systems. With this statement at hand, in this work we present a summary of those solvers [...]
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Algebraic PGD for tensor separation and compression: An algorithmic approach
P. Diez, S. Zlotnik, A. García-González, A. Huerta

Comptes Rendus Mécanique (2018). (Preprint) Vol. 346 (7), pp. 501-514

Abstract
Proper Generalized Decomposition (PGD) is devised as a computational method to solve high-dimensional boundary value problems (where many dimensions are associated with the space of parameters defining the problem). The PGD philosophy consists in providing a separated representation of the multidimensional solution using a greedy approach combined with an alternated directions scheme to obtain the successive rank-one terms. This paper presents an algorithmic approach to high-dimensional tensor separation based on solving the Least Squares approximation in a separable format of multidimensional tensor using PGD. This strategy is usually embedded in a standard PGD code in order to compress the solution (reduce the number of terms and optimize the available storage capacity), but it stands also as an alternative and highly competitive method for tensor separation.
Abstract
Proper Generalized Decomposition (PGD) is devised as a computational method to solve high-dimensional boundary value problems (where many dimensions are associated [...]
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Numerical estimation of the bearing capacity of resistance spot welds in martensitic boron steels using a J-integral fracture criterion
D. Dorribo, L. Greve, P. Diez, I. Arias, X. Larráyoz-Izcara

Theoretical and Applied Fracture Mechanics (2018). (Preprint) Vol. 96, pp. 497-508

Abstract
Predicting the bearing capacity of resistance spot welds (RSW) during vehicle crash tests has become a crucial task for the automotive industry, since the recent introduction of advanced high strength steels (AHSS) such as martensitic boron steels (e.g. 22MnB5). The spot weld joints of these steels exhibit relatively low bearing strengths, compared to those of more ductile high strength steels. Currently, the bearing capacity of spot weld joints is characterized through extensive experimental campaigns. In this article, a model for quantification of the bearing capacity of RSW using a finite-element J-integral fracture criterion is presented. The model takes into account geometric and mechanical features of the spot weld, namely the weld diameter and the mechanical properties distribution resulting from the welding process. An experimental loading test campaign is carried out for calibration and validation purposes, considering multiple sheet thickness combinations, loading angles and weld sizes. Experimental observations of the failed spot welds and preliminary simulations show that failure is caused mostly by stress concentration around the sharp weld notch. Consequently, the J-integral obtained from detailed finite element simulations is used to asses the stress/strain concentration along the first crack advance direction predicted by the acoustic tensor. The computed J-integral values are compared to the material toughness to obtain the joint’s maximum force. The resulting simulated and experimental bearing capacities show a good agreement for all tested configurations.
Abstract
Predicting the bearing capacity of resistance spot welds (RSW) during vehicle crash tests has become a crucial task for the automotive industry, since the recent introduction [...]
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A non-intrusive proper generalized decomposition scheme with application in biomechanics
X. Zou, M. Conti, P. Diez, F. Auricchio

Int. J. Numer. Meth. Engng. (2018). (Preprint) Vol. 113 (2), pp. 230-251

Abstract
Proper generalized decomposition (PGD) is often used for multi-query and fast-response simulations. It is a powerful tool alleviating the curse of dimensionality affecting multi-parametric partial differential equations. Most implementations of PGD are intrusive extensions based on in-house developed finite element (FE) solvers. In this work, we propose a non-intrusive PGD scheme using off-the-shelf FE codes (such as certified commercial software) as an external solver. The scheme is implemented and monitored by in-house flow-control codes. A typical implementation is provided with downloadable codes. Moreover, a novel parametric separation strategy for the PGD resolution is presented. The parametric space is split into two- or three-dimensional subspaces, to allow PGD technique solving problems with constrained parametric spaces, achieving higher convergence ratio. Numerical examples are provided. In particular, a practical example in biomechanics is included, with potential application to patient-specific simulation.
Abstract
Proper generalized decomposition (PGD) is often used for multi-query and fast-response simulations. It is a powerful tool alleviating the curse of dimensionality affecting [...]
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Explicit parametric solutions of lattice structures with proper generalized decomposition (PGD)
A. Sibileau, A. García-González, F. Auricchio, S. Morganti, P. Diez

Computational Mechanics (2018). (Preprint) Vol. 62 (4), pp. 871-891

Abstract
Architectured materials (or metamaterials) are constituted by a unit-cell with a complex structural design repeated periodically forming a bulk material with emergent mechanical properties. One may obtain specific macro-scale (or bulk) properties in the resulting architectured material by properly designing the unit-cell. Typically, this is stated as an optimal design problem in which the parameters describing the shape and mechanical properties of the unit-cell are selected in order to produce the desired bulk characteristics. This is especially pertinent due to the ease manufacturing of these complex structures with 3D printers. The proper generalized decomposition provides explicit parametic solutions of parametric PDEs. Here, the same ideas are used to obtain parametric solutions of the algebraic equations arising from lattice structural models. Once the explicit parametric solution is available, the optimal design problem is a simple post-process. The same strategy is applied in the numerical illustrations, first to a unit-cell (and then homogenized with periodicity conditions), and in a second phase to the complete structure of a lattice material specimen.
Abstract
Architectured materials (or metamaterials) are constituted by a unit-cell with a complex structural design repeated periodically forming a bulk material with emergent mechanical [...]
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Numerical Modelling of Multi-Phase Multi-Component. Reactive Transport in the Earth’s interior
B. Oliveira, J. Afonso, S. Zlotnik, P. Diez

Geophysical Journal International (2018). (Preprint) Vol. 212 (1), pp. 345-388

Abstract
We present a conceptual and numerical approach to model processes in the Earth’s interior that involve multiple phases that simultaneously interact thermally, mechanically and chemically. The approach is truly multiphase in the sense that each dynamic phase is explicitly modelled with an individual set of mass, momentum, energy and chemical mass balance equations coupled via interfacial interaction terms. It is also truly multicomponent in the sense that the compositions of the system and its constituent phases are expressed by a full set of fundamental chemical components (e.g. SiO2, Al2O3, MgO, etc.) rather than proxies. These chemical components evolve, react with and partition into different phases according to an internally consistent thermodynamic model. We combine concepts from Ensemble Averaging and Classical Irreversible Thermodynamics to obtain sets of macroscopic balance equations that describe the evolution of systems governed by multiphase multicomponent reactive transport (MPMCRT). Equilibrium mineral assemblages, their compositions and physical properties, and closure relations for the balance equations are obtained via a ‘dynamic’ Gibbs free-energy minimization procedure (i.e. minimizations are performed on-the-fly as needed by the simulation). Surface tension and surface energy contributions to the dynamics and energetics of the system are taken into account. We show how complex rheologies, that is, visco-elasto-plastic, and/or different interfacial models can be incorporated into our MPMCRT ensemble-averaged formulation. The resulting model provides a reliable platform to study the dynamics and nonlinear feedbacks of MPMCRT systems of different nature and scales, as well as to make realistic comparisons with both geophysical and geochemical data sets. Several numerical examples are presented to illustrate the benefits and limitations of the model.
Abstract
We present a conceptual and numerical approach to model processes in the Earth’s interior that involve multiple phases that simultaneously interact thermally, mechanically [...]
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PFEM–DEM for particle-laden flows with free surface
A. Franci, I. de-Pouplana, G. Casas, M. Celigueta, J. González-Usúa, E. Oñate

Comp. Part. Mech (2019). pp. 1-20

Abstract
This work proposes a fully Lagrangian formulation for the numerical modeling of free-surface particle-laden flows. The fluid phase is solved using the particle finite element method (PFEM), while the solid particles embedded in the fluid are modeled with the discrete element method (DEM). The coupling between the implicit PFEM and the explicit DEM is performed through a sub-stepping staggered scheme. This work only considers suspended spherical particles that are assumed not to affect the fluid motion. Several tests are presented to validate the formulation. The PFEM–DEM results show very good agreement with analytical solutions, laboratory tests and numerical results from alternative numerical methods.
Abstract
This work proposes a fully Lagrangian formulation for the numerical modeling of free-surface particle-laden flows. The fluid phase is solved using the particle finite element [...]
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A finite element reduced order model based on adaptive mesh refinement and artificial neural networks
J. Baiges, R. Codina, I. Castañar, E. Castillo

Comput. Methods Appl. Mech. Engrg., (2019). (prepint) pp. 1-14

Abstract
In this work a reduced order model based on adaptive finite element meshes and a correction term obtained by using an artificial neural network (FAN-ROM) is presented. The idea is to run a high-fidelity simulation by using an adaptively refined finite element mesh, and compare the results obtained with those of a coarse mesh finite element model. From this comparison, a correction forcing term can be computed for each training configuration. A model for the correction term is built by using an artificial neural network, and the final reduced order model is obtained by putting together the coarse mesh finite element model, plus the artificial neural network model for the correction forcing term. The methodology is applied to non-linear solid mechanics problems, transient quasi-incompressible flows, and a fluid-structure interaction problem. The results of the numerical examples show that the FAN-ROM is capable of improving the simulation results obtained in coarse finite element meshes at a reduced computational cost.
Abstract
In this work a reduced order model based on adaptive finite element meshes and a correction term obtained by using an artificial neural network (FAN-ROM) is presented. The [...]
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A bonded discrete element method for modeling ship–ice interactions in broken and unbroken sea ice fields
O. Jou Devesa, M. Celigueta, S. Latorre, F. Arrufat, E. Oñate

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

Abstract
This work investigates the failure patterns of ice cakes and floe-icewhen loaded by amoving and sloping structure (ice-breaking ships and cones). In the paper, we introduce the most frequently encountered ice infested scenarios, the main characteristics of ice-breaking ships and the predicted failure modes of floe-ice depending on the loading conditions, the structure type and the ice feature dimensions and thickness. For the simulations, a local bonded discrete element method (DEM) is used to model sea ice and its fractures. The packing of bonded spherical particles which reproduce the ice continuum can break due to ship–ice interactions and the failure modes are studied. A set of validation simulations are first carried out. A level ice sheet breaking against an installed ice-breaking cone with different slope angles is studied, and the results are compared with other DEM simulations. Then, a group of bonded DEM simulations are performed to predict the different failure modes produced when an ice-breaking ship bow contacts with ice cakes and floe-ice of different dimensions and thickness, typical in broken ice fields. Finally, the study of breaking a continuous level ice sheet is carried out by modeling with the bonded DEM an “infinite” large domain of sea ice and loaded by a single-degree-of-freedom model of an ice-breaking ship.
Abstract
This work investigates the failure patterns of ice cakes and floe-icewhen loaded by amoving and sloping structure (ice-breaking ships and cones). In the paper, we introduce [...]
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Chebyshev spectral collocation method approximations of the Stokes eigenvalue problem based on penalty techniques
Ö. Türk, R. Codina

Applied Numerical Mathematics (2019). (preprint) Vol. 145, pp. 188-200

Abstract
Numerical solution strategies for the Stokes eigenvalue problem based on the use of penalty formulations are investigated in this study. It is shown that the penalty method approach can successfully be adapted for the eigenproblem to rectify the associated problems such as the existence of zero diagonal entries in the resulting algebraic system. Two different schemes, namely, the standard penalisation with a small penalty parameter, and the iterative penalisation that enables relatively large parameters, are implemented. The employment of the latter leads to a so-called inhomogeneous generalised eigenvalue problem which requires a special attention. A feasible solution strategy is presented which is adapted from a procedure based on Newton's method proposed for the corresponding standard (inhomogeneous) eigenvalue problems. Concerning the spatial discretisation, among other possible options, the Chebyshev spectral collocation method based on expanding the unknown fields in tensor product of Chebyshev polynomials is employed. It is shown that the method constitutes a novel way of efficiently examining the approximate eigensolutions of the Stokes operator with the use of Chebyshev spectral collocation method directly, without a decoupling of velocity and pressure.
Abstract
Numerical solution strategies for the Stokes eigenvalue problem based on the use of penalty formulations are investigated in this study. It is shown that the penalty method [...]
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Logarithmic conformation reformulation in viscoelastic flow problems approximated by a VMS-type stabilized finite element formulation
L. Moreno García, R. Codina, J. Baiges, E. Castillo

Comput. Methods Appl. Mech. Engrg., (2019). Vol. 354, pp. 706-731

Abstract
The log-conformation reformulation, originally proposed by Fattal and Kupferman (2004), allows computing incompressible viscoelastic problems with high Weissenberg numbers which are impossible to solve with the typical three-field formulation. By following this approach, in this work we develop a new stabilized finite element formulation based on the logarithmic reformulation using the Variational Multiscale (VMS) method as stabilization technique, together with a modified log-conformation formulation. Our approach follows the term-by-term stabilization proposed by Castillo and Codina (2014) for the standard formulation, which is more effective when there are stress singularities. The formulation can be used when the relaxation parameter is set to zero, and permits a direct steady numerical resolution. The formulation is validated in the classical benchmark flow past a cylinder and in the well-known planar contraction 4:1, achieving very accurate, stable and mesh independent results for highly elastic fluids.
Abstract
The log-conformation reformulation, originally proposed by Fattal and Kupferman (2004), allows computing incompressible viscoelastic problems with high Weissenberg numbers [...]
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Dynamic term-by-term stabilized finite element formulation using orthogonal subgrid-scales for the incompressible Navier–Stokes problem
E. Castillo, R. Codina

Comput. Methods Appl. Mech. Engrg., (2019). Vol. 349, pp. 701-721

Abstract
In this paper, we propose and analyze the stability and the dissipative structure of a new dynamic term-by-term stabilized finite element formulation for the Navier–Stokes problem that can be viewed as a variational multiscale (VMS) method under some assumptions. The essential point of the formulation is the time dependent nature of the subscales and, contrary to residual-based formulations, the introduction of two velocity subscale components. They represent the components of the convective and the pressure gradient terms, respectively, of the momentum equation that cannot be captured by the finite element mesh. A key idea of the proposed method is that the convective subscale is close to a solenoidal field and the pressure gradient subscale is close to a potential field. The method ensures stability in anisotropic space–time discretizations, which is proved using numerical analysis for a linearized problem and demonstrated in classical numerical tests. The work includes a detailed description of the proposed formulation and several numerical examples that serve to justify our claims.
Abstract
In this paper, we propose and analyze the stability and the dissipative structure of a new dynamic term-by-term stabilized finite element formulation for [...]
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Time-dependent semidiscrete analysis of the viscoelastic fluid flow problem using a variational multiscale stabilized formulation
G. Barrenechea, E. Castillo, R. Codina

Journal of Numerical Analysis (2019). Vol. 39 (2), pp. 792-819

Abstract
In this article we analyse a stabilized finite element formulation recently proposed to approximate viscoelastic fluid flows. The formulation has shown to have accuracy and robustness in the different benchmarks tested in the viscoelastic framework, and permitting the use of equal interpolation of the unknown fields. We first present results about a linearized subproblem, for which well-posedness and stability results can be proved. Then, the semidiscrete nonlinear time-dependent case is addressed using a fixed point theorem, which allows us to prove existence of a semidiscrete solution, along with error estimates.
Abstract
In this article we analyse a stabilized finite element formulation recently proposed to approximate viscoelastic fluid flows. The formulation has shown to have accuracy and [...]
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Solution of low Mach number aeroacoustic flows using a Variational Multi-Scale finite element formulation of the compressible Navier–Stokes equations written in primitive variables
C. Bayona, J. Baiges, R. Codina

Comput. Methods Appl. Mech. Engrg., (2019). Vol. 344, pp. 1073-1103

Abstract
In this work we solve the compressible Navier–Stokes equations written in primitive variables in order to simulate low Mach number aeroacoustic flows. We develop a Variational Multi-Scale formulation to stabilize the finite element discretization by including the orthogonal, dynamic and non-linear subscales, together with an implicit scheme for advancing in time. Three additional features define the proposed numerical scheme: the splitting of the pressure and temperature variables into a relative and a reference part, the definition of the matrix of stabilization parameters in terms of a modified velocity that accounts for the local compressibility, and the approximation of the dynamic stabilization matrix for the time dependent subscales. We also include a weak imposition of implicit non-reflecting boundary conditions in order to overcome the challenges that arise in the aeroacoustic simulations at low compressibility regimes. The order of accuracy of the method is verified for two- and three-dimensional linear and quadratic elements using steady manufactured solutions. Several benchmark flow problems are studied, including transient examples and aeroacoustic applications.
Abstract
In this work we solve the compressible Navier–Stokes equations written in primitive variables in order to simulate low Mach number aeroacoustic [...]
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Computational aeroacoustics to identify sound sources in the generation of sibilant /s/
A. Pont, O. Guasch, J. Baiges, R. Codina, A. Hirtum

Int. J. Numer. Meth. Biomed. Engng (2019). Vol. 35 (1), e3153

Abstract
A sibilant fricative /s/ is generated when the turbulent jet in the narrow channel between the tongue blade and the hard palate is deflected downwards through the space between the upper and lower incisors and then impinges the space between the lower incisors and the lower lip. The flow eddies in that region become a source of direct aerodynamic sound, which is also diffracted by the speech articulators and radiated outwards. The numerical simulation of these phenomena is complex. The spectrum of an /s/ typically peaks between 4 and 10 kHz, which implies that very fine computational meshes are needed to capture the eddies producing such high frequencies. In this work, a large‐scale computation of the aeroacoustics of /s/ has been performed for a realistic vocal tract geometry, resorting to two different acoustic analogies. A stabilized finite element method that acts as a large eddy simulation model has been adopted to solve the flow dynamics. Also, a numerical strategy has been implemented that allows the determination, in a single computational run, of the separate contribution of the sound diffracted by the upper incisors from the overall radiated sound. Results are presented for points located close to the lip opening showing the relative influence of the upper teeth depending on frequency.
Abstract
A sibilant fricative /s/ is generated when the turbulent jet in the narrow channel between the tongue blade and the hard palate is deflected downwards through the space between [...]
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Finite element modeling of nonlinear reaction-diffusion-advection systems of equations
S. Komala, R. Codina

Int. J. Numer. Meth. Heat and Fluid Flows (2018). Vol. 28 (11), pp. 2688-2715

Abstract
Purpose This paper aims to present a finite element formulation to approximate systems of reaction–diffusion–advection equations, focusing on cases with nonlinear reaction. The formulation is based on the orthogonal sub-grid scale approach, with some simplifications that allow one to stabilize only the convective term, which is the source of potential instabilities. The space approximation is combined with finite difference time integration and a Newton–Raphson linearization of the reactive term. Some numerical examples show the accuracy of the resulting formulation. Applications using classical nonlinear reaction models in population dynamics are also provided, showing the robustness of the approach proposed. Design/methodology/approach A stabilized finite element method for advection–diffusion–reaction equations to the problem on nonlinear reaction is adapted. The formulation designed has been implemented in a computer code. Numerical examples are run to show the accuracy and robustness of the formulation. Findings The stabilized finite element method from which the authors depart can be adapted to problems with nonlinear reaction. The resulting method is very robust and accurate. The framework developed is applicable to several problems of interest by themselves, such as the predator–prey model. Originality/value A stabilized finite element method to problems with nonlinear reaction has been extended. Original contributions are the design of the stabilization parameters and the linearization of the problem. The application examples, apart from demonstrating the validity of the numerical model, help to get insight in the system of nonlinear equations being solved.
Abstract
Purpose This paper aims to present a finite element formulation to approximate systems of reaction–diffusion–advection equations, focusing on cases with nonlinear [...]
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Stationary and time-dependent numerical approximation of the lid-driven cavity problem for power-law fluid flows at high Reynolds numbers using a stabilized finite element formulation of the VMS type
A. Aguirre, E. Castillo, M. Cruchaga, R. Codina, J. Baiges

Journal of Non-Newtonian Fluid Mechanics (2018). Vol. 257, pp. 22-43

Abstract
In this work, a variational multiscale finite element formulation is used to approximate numerically the lid-driven cavity flow problem for high Reynolds numbers. For Newtonian fluids, this benchmark case has been extensively studied by many authors for low and moderate Reynolds numbers (up to Re=10,000), giving place to steady flows, using stationary and time-dependent approaches. For more convective flows, the solution becomes unstable, describing an oscillatory behavior. The critical Reynolds number which gives place to this time-dependent fluid dynamics has been defined over a wide range 7, 300 ≲ Re ≲ 35, 000, using different numerical approaches. In the non-Newtonian case, the cavity problem has not been studied deeply for high Reynolds number (Re > 10, 000), specifically, in the oscillatory time-dependent case. A VMS formulation is presented to be validated using existing results, to determine flow conditions at which the instability appears, and lastly, to establish new benchmark solutions for high-Reynolds numbers fluid flows using the power-law model. Obtained results show a good agreement with those reported in the references, and new data related with the oscillatory behavior of the flow has been found for the non-Newtonian case. In this regard, time-dependent flows show dependence on both Reynolds number and power-law index, and the unsteady starting point has been determined for all studied cases. It is determined that the critical Reynolds number (Rec) that defines the first Hopf bifurcation for Newtonian fluid flow is ranged between 8,100 ≲ Rec ≲ 8, 250, whereas for power-law indexes n=0.5 and n=1.5, it is 7,100 ≲ Rec ≲ 7,200 and 18,250 ≲ Rec ≲ 18,500, respectively.
Abstract
In this work, a variational multiscale finite element formulation is used to approximate numerically the lid-driven cavity flow problem for high Reynolds numbers. For Newtonian [...]
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On hp convergence of stabilized finite element methods for the convection–diffusion equation
R. Codina

Sociedad Española de Matemática Aplicada (2018). Vol. 75 (4), pp. 591-606

Abstract
This work analyzes some aspects of the hp convergence of stabilized finite element methods for the convection-diffusion equation when diffusion is small. The methods discussed are classical-residual based stabilization techniques and also projection-based stabilization methods. The theoretical impossibility of obtaining an optimal convergence rate in terms of the polynomial order p for all possible Péclet numbers is explained. The key point turns out to be an inverse estimate that scales as p2. The use of this estimate is not needed in a particular case of (H1-)projection-based methods, and therefore the theoretical lack of convergence described does not exist in this case.
Abstract
This work analyzes some aspects of the hp convergence of stabilized finite element methods for the convection-diffusion equation when diffusion is small. The methods [...]
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Variational multiscale error estimators for the adaptive mesh refinement of compressible flow simulations
C. Bayona, R. Codina, J. Baiges

Comput. Methods Appl. Mech. Engrg., (2018). Vol. 337, pp. 501-526

Abstract
This article investigates an explicit a-posteriori error estimator for the finite element approximation of the compressible Navier–Stokes equations. The proposed methodology employs the Variational Multi-Scale framework, and specifically, the idea is to use the variational subscales to estimate the error. These subscales are defined to be orthogonal to the finite element space, dynamic and non-linear, and both the subscales in the interior of the element and on the element boundaries are considered. Another particularity of the model is that we define some norms that lead to a dimensionally consistent measure of the compressible flow solution error inside each element; a scaled L2-norm, and the calculation of a physical entropy measure, are both studied in this work. The estimation of the error is used to drive the adaptive mesh refinement of several compressible flow simulations. Numerical results demonstrate good accuracy of the local error estimate and the ability to drive the adaptative mesh refinement to minimize the error through the computational domain.
Abstract
This article investigates an explicit a-posteriori error estimator for the finite element approximation of the compressible Navier–Stokes equations. [...]
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Unified solver for fluid dynamics and aeroacoustics in isentropic gas flows
A. Pont, R. Codina, J. Baiges, O. Guasch

Journal of Computational Physics (2018). Vol. 363, pp. 11-29

Abstract
The high computational cost of solving numerically the fully compressible Navier–Stokes equations, together with the poor performance of most numerical formulations for compressible flow in the low Mach number regime, has led to the necessity for more affordable numerical models for Computational Aeroacoustics. For low Mach number subsonic flows with neither shocks nor thermal coupling, both flow dynamics and wave propagation can be considered isentropic. Therefore, a joint isentropic formulation for flow and aeroacoustics can be devised which avoids the need for segregating flow and acoustic scales. Under these assumptions density and pressure fluctuations are directly proportional, and a two field velocity-pressure compressible formulation can be derived as an extension of an incompressible solver. Moreover, the linear system of equations which arises from the proposed isentropic formulation is better conditioned than the homologous incompressible one due to the presence of a pressure time derivative. Similarly to other compressible formulations the prescription of boundary conditions will have to deal with the backscattering of acoustic waves. In this sense, a separated imposition of boundary conditions for flow and acoustic scales which allows the evacuation of waves through Dirichlet boundaries without using any tailored damping model will be presented.
Abstract
The high computational cost of solving numerically the fully compressible Navier–Stokes equations, together with the poor performance of most numerical formulations [...]
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Stabilized mixed finite element method for the M1 radiation model
Q. Schmid, Y. Mesri, E. Hachem, R. Codina

Comput. Methods Appl. Mech. Engrg., (2018). Vol. 335, pp. 69-90

Abstract
In this work, we present a computational approach for the numerical simulation of thermal radiation. Radiation is modeled by solving a set of two coupled partial differential equations, the so-called M1 model. A Variational Multiscale method is developed for this system, and tested on some illustrative benchmarks. The question of dealing with heterogeneous physical properties is also considered, and treated by means of an immersed method. It combines a level-set approach for representation of interfaces, mixing laws to build effective physical properties and an anisotropic mesh adaptation process, all these ingredients leading to an accurate description of the interface.
Abstract
In this work, we present a computational approach for the numerical simulation of thermal radiation. Radiation is modeled by solving a set of two coupled partial [...]
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Variational multiscale approximation of the one‐dimensional forced Burgers equation: The role of orthogonal subgrid scales in turbulence modeling
C. Bayona, J. Baiges, R. Codina

Int. J. Numer. Meth. Fluids (2018). Vol. 86 (5), pp. 313-328

Abstract
A numerical approximation for the one‐dimensional Burgers equation is proposed by means of the orthogonal subgrid scales–variational multiscale (OSGS‐VMS) method. We evaluate the role of the variational subscales in describing the Burgers “turbulence” phenomena. Particularly, we seek to clarify the interaction between the subscales and the resolved scales when the former are defined to be orthogonal to the finite‐dimensional space. Direct numerical simulation is used to evaluate the resulting OSGS‐VMS energy spectra. The comparison against a large eddy simulation model is presented for numerical discretizations in which the grid is not capable of solving the small scales. An accurate approximation to the phenomena of turbulence is obtained with the addition of the purely dissipative numerical terms given by the OSGS‐VMS method without any modification of the continuous problem.
Abstract
A numerical approximation for the one‐dimensional Burgers equation is proposed by means of the orthogonal subgrid scales–variational multiscale (OSGS‐VMS) method. [...]
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Shockwaves in spillways with the particle finite element method
F. Salazar, J. San-Mauro, M. Celigueta, E. Oñate

Comp. Part. Mech. (2019).

Abstract
Changes in direction and cross section in supercritical hydraulic channels generate shockwaves which result in an increase in flow depth with regard to that for uniform regime. These disturbances are propagated downstream and need to be considered in the design of the chute walls. In dam spillways, where flow rates are often high, this phenomenon can have significant implications for the cost and complexity of the solution. It has been traditionally analysed by means of reduced-scale experimental tests, as it has a clear three-dimensional character and therefore cannot be approached with two-dimensional numerical models. In this work, the ability of the particle finite element method (PFEM) to reproduce this phenomenon is analysed. PFEM has been successfully applied in previous works to problems involving high irregularities in free surface. First, simple test cases available in the technical bibliography were selected to be reproduced with PFEM. Subsequently, the method was applied in two spillways of real dams. The results show that PFEM is capable of capturing the shockwave fronts generated both in the contractions and in the expansions that occur behind the spillway piers. This suggests that the method may be useful as a complement to laboratory test campaigns for the design and hydraulic analysis of dam spillways with complex geometries.
Abstract
Changes in direction and cross section in supercritical hydraulic channels generate shockwaves which result in an increase in flow depth with regard to that for uniform regime. [...]
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An investigation on thermal performance of wollastonite and bentonite reinforced intumescent fire-retardant coating for steel structures
F. Ahmad, S. Ullah, N. Merican, E. Oñate, A. Al-Sehemi, G. Yeoh

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

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

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

Abstract
The computational modeling and numerical simulation of Friction Stir Welding (FSW) processes is an extremely challenging task due to the highly nonlinear and coupled nature of the physical problem and the complex computational issues that need to be properly tackled in the numerical model.
Abstract
The computational modeling and numerical simulation of Friction Stir Welding (FSW) processes is an extremely challenging task due to the highly nonlinear and coupled nature [...]
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An accurate non-local bonded discrete element method for non linear analysis of solids. Application to concrete fracture tests
M. Celigueta, S. Latorre, F. Arrufat, E. Oñate

Computational Particle Mechanics (2019). (prepint), 10.1007/s40571-019-00278-5

Abstract
We present a numerical procedure for elastic and non linear analysis (including fracture situations) of solid materials and structures using the Discrete Element Method (DEM). It can be applied to strongly cohesive frictional materials such as concrete and rocks. The method consists on defining the non-local constitutive equations at the contact interfaces between discrete particles using the information provided by the stress tensor over the neighbour particles. The method can be used with different yield surfaces and in the paper it is applied to the analysis of fracture of concrete samples. Good comparison with experimental results is obtained.
Abstract
We present a numerical procedure for elastic and non linear analysis (including fracture situations) of solid materials and structures using the Discrete Element Method (DEM). [...]
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An implicit unsteady hydraulic solver for suspended cuttings transport in managed pressure wells
R. Flores, R. Ortega, A. Ilin, D. Simpkins, E. Oñate

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

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

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

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

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

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

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

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

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

Abstract
Several theoretical contributions in order to establish a particle packing methodology are presented. In this respect, a generic formulation of a new method for packing particles based on a constructive advancing front method, which uses Monte Carlo techniques for the generation of particle dimensions, is also shown. The method can be used to obtain virtual dense packings of particles with several geometrical shapes. It employs continuous, discrete and empirical statistical distributions in order to generate the dimensions of particles. The packing algorithm is very flexible and allows alternatives for: 1- The direction of the advancing front (inwards or outwards), 2- The selection of the local advancing front, 3- The method for placing a mobile particle in contact with others and 4- The overlap checks. The algorithm also allows obtaining highly porous media when it is slightly modified. Practical applications of the formulations are presented in the end of this paper.
Abstract
Several theoretical contributions in order to establish a particle packing methodology are presented. In this respect, a generic formulation of a new method for packing [...]
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Residual stress and distortion of rectangular and S-shaped Ti-6Al-4V parts by Directed Energy Deposition: Modelling and experimental calibration
X. Lu, X. Lin, M. Chiumenti, M. Cervera, Y. Hu, X. Ji, L. Ma, H. Yang, W. Huang

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

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

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

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

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

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

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

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

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

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

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

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

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

Abstract
AM processes are characterized by complex thermal cycles that have a deep influence on the microstructural transformations of the deposited alloy. In this work, a general model for the prediction of microstructure evolution during solid state transformations of Ti6Al4V is presented. Several formulations have been developed and employed for modeling phase transformations in other manufacturing processes and, particularly, in casting. The proposed model is mainly based on the combination and modification of some of these existing formulations, leading to a new overall model specifically dedicated to AM. The accuracy and suitability of the integrated model is enhanced, introducing new dedicated features. In fact the model is designed to deal with fast cooling and re-heating cycles typical of AM processes because: (a) it is able to consider incomplete transformations and varying initial content of phases and (b) it can take into account simultaneous transformations.The model is implemented in COMET, an in-house Finite Element (FE)-based framework for the solution of thermo-mechanical engineering problems. The validation of the microstructural model is performed by comparing the simulation results with the data available in the literature. The sensitivity of the model to the variation of material parameters is also discussed.
Abstract
AM processes are characterized by complex thermal cycles that have a deep influence on the microstructural transformations of the deposited alloy. In this work, a general [...]
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Numerical analysis of the manufacturing processes of a mock-up of the ITER NHF First Wall Panel
J. González, M. Chiumenti, M. Cervera, C. Agelet de Saracibar, F. Samaniego, I. Cobo

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

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

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

Abstract
In this work we put the method proposed by van Hinsberg et al. to the test, highlighting its accuracy and efficiency in a sequence of benchmarks of increasing complexity. Furthermore, we explore the possibility of systematizing the way in which the method's free parameters are determined by generalizing the optimization problem that was considered originally. Finally, we provide a list of worked-out values, ready for implementation in large-scale particle-laden flow simulations.
Abstract
In this work we put the method proposed by van Hinsberg et al. to the test, highlighting its accuracy and efficiency in a sequence of benchmarks of increasing complexity. [...]
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Triangular prismatic solid-shell element with generalised deformation description
V. Mataix Ferrándiz, F. Flores, R. Rossi, E. Oñate

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

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

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

Abstract
A new computational technique for the simulation of 2D and 3D fracture propagation processes in saturated porous media is presented. A non-local damage model is conveniently used in conjunction with interface elements to predict the degradation pattern of the domain and insert new fractures followed by remeshing. FIC-stabilized elements of equal order interpolation in the displacement and the pore pressure have been successfully used under complex conditions near the undrained-incompressible limit. A bilinear cohesive fracture model describes the mechanical behaviour of the joints. A formulation derived from the cubic law models the fluid flow through the crack. Examples in 2D and 3D, using 3-noded triangles and 4-noded tetrahedra respectively, are presented to illustrate the accuracy and robustness of the proposed methodology.
Abstract
A new computational technique for the simulation of 2D and 3D fracture propagation processes in saturated porous media is presented. A non-local damage model [...]
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A Phenomenological Model for the Solidification of Eutectic and Hypoeutectic Alloys Including Recalescence and Undercooling
M. Chiumenti, M. Cervera, E. Salsi, A. Zonato

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

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

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

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

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

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

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

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

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

Abstract
The asymmetric tensile/compressive material behavior and microcracks closure-reopening (MCR) effects exhibited by quasi-brittle solids are of significant importance to the nonlinear responses of engineering structures under cyclic loading, e.g., earthquake excitations. Based on our previous work (Cervera et al., 1995; Faria et al., 1998; Wu et al., 2006) this work addresses a novel thermodynamically consistent unilateral damage model for concrete. In particular, the positive/negative projection (PNP) of the effective stress tensor and the additive bi-scalar damage constitutive relation are maintained owing to the conceptual simplicity and computational efficiency. It is found that the classical PNP widely adopted in the literature is not optimal for this damage model, since the resulting stiffness is not always of major symmetry. Consequently, a well-defined free energy potential does not exist in general cases and the model cannot be cast into the framework of thermodynamics with internal variables. Furthermore, the damage induced anisotropy cannot be captured, exhibiting excessive lateral deformationsunder uniaxial tension. To overcome the above issues, a novel PNP, variationally interpreted as the closest point projection of the effective stress in energy norm, is proposed with closed-form solution. With the novel PNP, the secant stiffness tensorof the proposed unilateral damage model always possesses major symmetry and exhibits orthotropic behavior under uniaxial tension and mixed tension/compression. The corresponding thermodynamics framework is then given, resulting in an energy release rate based rounded-Rankine type damage criterion appropriate for tensile failure in quasi-brittle solids. Several numerical examples of single-point verifications and benchmark tests are presented. It is demonstrated that the proposed model is capable of characterizing localized failureof concrete under proportional and non-proportional static loading, as well as the MCR effects under seismic cyclic loading.
Abstract
The asymmetric tensile/compressive material behavior and microcracks closure-reopening (MCR) effects exhibited by quasi-brittle solids are of significant [...]
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A Finite Element Model for the Simulation of the UL-94 Burning Test
J. Marti, S. Idelsohn, E. Oñate

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

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

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

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

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

Abstract
In this paper we present a collection of techniques used to formulate a projection-based reduced order model (ROM) for zero Mach limit thermally coupled Navier–Stokes equations. The formulation derives from a standard proper orthogonal decomposition (POD) model reduction, and includes modifications to improve the drawbacks caused by the inherent non-linearity of the used Navier–Stokes equations: a hyper-ROM technique based on mesh coarsening; an implicit ROM subscales formulation based on a variational multi-scale (VMS) framework; and a Petrov–Galerkin projection necessary in the case of non-symmetric terms. At the end of the article, we test the proposed ROM formulation using 2D and 3D versions of the same example: a differentially heated cavity.
Abstract
In this paper we present a collection of techniques used to formulate a projection-based reduced order model (ROM) for zero Mach limit thermally coupled Navier–Stokes [...]
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A second-order in time and space particle-based method to solve flow problems on arbitrary meshes
J. Gimenez, H. Aguerre, S. Idelsohn, N. Nigro

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

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

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

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

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

Abstract
This paper presents the basic concepts and application of the strategy that combines finite element methods (FEM) and discrete elements (DEM)for the study of the propagation of fractures in concrete structures. The calculation of the structure, modeled as a continuum, begins with the FEMand the DEM is used to start and grow the cracks that may appear in the structure. This methodology has been proposed by the authors in two andthree dimensions. Recently, the use of one-dimensional steel elements embedded in the continuum has been added to model the reinforcement inconcrete structures. The work presents different examples of application to the study of the breakage of parts and structures of concrete in massand armed, as well as the multiple breakage of a historic structure of masonry due to an earthquake.
Abstract
This paper presents the basic concepts and application of the strategy that combines finite element methods (FEM) and discrete elements (DEM)for the study of the propagation [...]
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A coupled fluid FEM-DEM technique for predicting blasting operations in tunnels
F. Zarate, J. Gonzalez, J. Miquel, R. Lohner, E. Oñate

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

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

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

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

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

Abstract
This paper extends to three dimensions (3D) the computational technique developed by the authors in 2D for predicting the onset and evolution of fracture in a finite element mesh in a simple manner based on combining the finite element method (FEM) and the discrete element method (DEM) approach Zarate2D. Once a crack is detected at an element edge, discrete elements are generated at the adjacent element vertexes and a simple DEM mechanism is considered in order to follow the evolution of the crack. The combination of the DEM with simple 4-noded linear tetrahedron elements correctly captures the onset of fracture and its evolution, as shown in several 3D examples of application.
Abstract
This paper extends to three dimensions (3D) the computational technique developed by the authors in 2D for predicting the onset and evolution of fracture in a finite element [...]
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Real-time micro-modelling of city evacuations
R. Löhner, E. Haug, C. Zinggerling, E. Oñate

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

Abstract
A methodology to integrate geographical information system (GIS) data with large-scale pedestrian simulations has been developed. Advances in automatic data acquisition and archiving from GIS databases, automatic input for pedestrian simulations, as well as scalable pedestrian simulation tools have made it possible to simulate pedestrians at the individual level for complete cities in real time. An example that simulates the evacuation of the city of Barcelona demonstrates that this is now possible. This is the first step towards a fully integrated crowd prediction and management tool that takes into account not only data gathered in real time from cameras, cell phones or other sensors, but also merges these with advanced simulation tools to predict the future state of the crowd.
Abstract
A methodology to integrate geographical information system (GIS) data with large-scale pedestrian simulations has been developed. Advances in automatic data acquisition and [...]
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Virtual modeling of polycrystalline structures of materials using particle packing algorithms and Laguerre cells
C. Recarey Morfa, M. Farias, I. Pérez, E. Oñate

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

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

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

Abstract
A methodology that comprises several characterization properties for particle packings is proposed in this paper. The methodology takes into account factors such as dimension and shape of particles, space occupation, homogeneity, connectivity and isotropy, among others. This classification and integration of several properties allows to carry out a characterization process to systemically evaluate the particle packings in order to guarantee the quality of the initial meshes in discrete element simulations, in both the micro- and the macroscales. Several new properties were created, and improvements in existing ones are presented. Properties from other disciplines were adapted to be used in the evaluation of particle systems. The methodology allows to easily characterize media at the level of the microscale (continuous geometries—steels, rocks microstructures, etc., and discrete geometries) and the macroscale. A global, systemic and integral system for characterizing and evaluating particle sets, based on fuzzy logic, is presented. Such system allows researchers to have a unique evaluation criterion based on the aim of their research. Examples of applications are shown.
Abstract
A methodology that comprises several characterization properties for particle packings is proposed in this paper. The methodology takes into account factors such as dimension [...]
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General advancing front packing algorithm for the discrete element method
C. Recarey Morfa, I. Pérez, M. Farías, E. Oñate, R. Valera, H. Casañas

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

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

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

Abstract
In this work a stabilized mixed formulation for the solution of non-linear solid mechanics problems in nearly-incompressible conditions is presented. In order to deal with high material deformation, an implicit Material Point Method is chosen. Such choice allows avoiding the classical limitations of the Finite Element Method, e.g., element tangling and extreme mesh distortion. The proposed mixed formulation, with displacement and pressure as primary variables, is tested through classical benchmarks in solid and geo-mechanics where a Neo-Hookean, a J2 and a Mohr-Coulomb plastic law are employed. Further, the stabilized mixed formulation is compared with a displacement-based formulation to demonstrate how the proposed approach gets better results in terms of accuracy, not only when incompressible materials are simulated, but also in the case of compressible ones.
Abstract
In this work a stabilized mixed formulation for the solution of non-linear solid mechanics problems in nearly-incompressible conditions is presented. In order to deal with [...]
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A unified Lagrangian formulation for solid and fluid dynamics and its possibility for modelling submarine landslides and their consequences
X. Zhang, E. Oñate, S. Galindo, J. Bleyer

Comput. Methods Appl. Mech. Engrg., (2018). (prepint) Vol. 343, pp. 314-338

Abstract
Consequences of submarine landslides include both their direct impact on offshore infrastructure, such as subsea electric cables and gas/oil pipelines, and their indirect impact via the generated tsunami. The simulation of submarine landslides and their consequences has been a long-standing challenge majorly due to the strong coupling among sliding sediments, seawater and infrastructure as well as the induced extreme material deformation during the complete process. In this paper, we propose a unified finite element formulation for solid and fluid dynamics based on a generalised Hellinger–Reissner variational principle so that the coupling of fluid and solid can be achieved naturally in a monolithic fashion. In order to tackle extreme deformation problems, the resulting formulation is implemented within the framework of the particle finite element method. The correctness and robustness of the proposed unified formulation for single-phase problems (e.g. fluid dynamics problems involving Newtonian/Non-Newtonian flows and solid dynamics problems) as well as for multi-phase problems (e.g. two-phase flows) are verified against benchmarks. Comparisons are carried out against numerical and analytical solutions or experimental data that are available in the literature. Last but not least, the possibility of the proposed approach for modelling submarine landslides and their consequences is demonstrated via a numerical experiment of an underwater slope stability problem. It is shown that the failure and post-failure processes of the underwater slope can be predicted in a single simulation with its direct threat to a nearby pipeline and indirect threat by generating tsunami being estimated as well.
Abstract
Consequences of submarine landslides include both their direct impact on offshore infrastructure, such as subsea electric cables and gas/oil pipelines, and their indirect [...]
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3D numerical simulation of free-surface Bingham Fluids interacting with structures using the PFEM
A. Franci, X. Zhang

Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE) (2019). 12

Abstract
This paper presents a purely Lagrangian approach for the 3D simulation of Bingham free-surface uids and their interaction with deformable solid structures. In the proposed numerical strategy, the fluid is handled using the Particle Finite Element Method (PFEM) to tackle the issues resulting from extreme changes of geometry, such as mesh distortion and free-surface evolution. Additionally, the Papanastasiou model is employed as a regularization technique to overcome the computational difficulties associated with the classical Bingham model. The solid structure, on the other hand, is represented by the hypoelastic constitutive model and simulated using the conventional Finite Element Method (FEM). The coupling between the fluid and the structure is achieved via a monolithic approach, called Unified formulation. Several numerical examples are presented to illustrate the correctness and the robustness of the proposed formulation, in 2D and in 3D. Special attention is devoted to the analysis of the convergence behavior of the proposed computational framework, the effect of the regularization on the numerical results and the 3D effects. Moreover, detailed comparisons between the simulated results and experimental data are performed so that the concerned problems and results can serve as benchmarks.
Abstract
This paper presents a purely Lagrangian approach for the 3D simulation of Bingham free-surface uids and their interaction with deformable solid structures. In the proposed [...]
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Dynamic modelling of retrogressive landslides with emphasis on the role of clay sensitivity
X. Zhang, S. Sloan, E. Oñate

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

Abstract
This paper presents a detailed numerical study of the retrogressive failure of landslides in sensitive clays. The dynamic modelling of the landslides is carried out using a novel continuum approach, the particle finite element method, complemented with an elastoviscoplastic constitutive model. The multiwedge failure mode in the collapse is captured successfully, and the multiple retrogressive failures that have been widely observed in landslides in sensitive clays are reproduced with the failure mechanism, the kinematics, and the deposition being discussed in detail. Special attention has been paid to the role of the clay sensitivity on each retrogressive failure as well as on the final retrogression distance and the final run‐ out distance via parametric studies. Moreover, the effects of the viscosity of sensitive clays on the failure are also investigated for different clay sensitivities.
Abstract
This paper presents a detailed numerical study of the retrogressive failure of landslides in sensitive clays. The dynamic modelling of the landslides is carried out [...]
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Data-MSCA-IF: Collapse Velocity
X. Zhang

Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE) (2018). 7

Abstract
Variations of horizontal and vertical velocities of retrogressive landslides
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Data-MSCA-IF: Sensitive clays
X. Zhang

Papers Repository of the International Centre for Numerical Methods in Engineering (CIMNE) (2018). 6

Abstract
Properties of Norwegian clays, Canadian clays and offshore clays
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Particle finite element modelling of retrogressive slope failure in sensitive clays
X. Zhang, D. Sloan

15th IACMAG (2017). paper no 868

Abstract
In this paper, the slope failure in sensitive clays is studied numerically using the particle finite element method which is a novel approach capable of tackling extreme deformation problems. The sensitive clay is described using an elastoviscoplastic model with strain softening. This model can be considered a mixture of the Tresca model with strain softening and the classical Bingham model. The former is used to capture the solid-like behaviour, for example when the clay is intact, whereas the latter is to describe the semi-fluid behaviour of the fully remolded clay. The complete process of the collapse of a sensitive clay deposit is captured successfully and the widely-observed retrogressive failure mode is reproduced. The mechanism behind the failure is also discovered.
Abstract
In this paper, the slope failure in sensitive clays is studied numerically using the particle finite element method which is a novel approach capable of tackling extreme deformation [...]
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A non-linear finite element method on unstructured meshes for added resistance in waves
J. García-Espinosa, B. Servan Camas

Ships and offshore structures (2018). 14:2, 153-164 (preprint)

Abstract
In this work a finite element method (FEM) is proposed to solve the problem of estimating the added resistance of a ship in waves in the time domain and using unstructured meshes. Two different schemes are used to integrate the corresponding free surface kinematic and dynamic boundary conditions: the first one based on streamlines integration (SLI); and the second one based on the Streamline-Upwind Petrov-Galerking (SUPG) stabilization. The proposed numerical schemes have been validated in different test cases, including towing tank tests with monochromatic waves. The results obtained in this work show the suitability of the present method to estimate added resistance in waves in a computationally affordable manner.
Abstract
In this work a finite element method (FEM) is proposed to solve the problem of estimating the added resistance of a ship in waves in the time domain and using unstructured [...]
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A finite element model for fluid–structure interaction problems involving closed membranes, internal and external fluids
P. Ryzhakov, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2017). Vol. 326, pp. 422-445

Abstract
In this paper we propose a Finite Element model for analyzing closed membranes (“bags”) interacting with internal and external (surrounding) fluids. The approach is based on embedding a Lagrangian monolithic model describing the membrane containing an internal fluid into an Eulerian external fluid model. The combination of kinematic frameworks allows us to accurately track the location of the membrane and naturally represent flow variables discontinuities across it. In order to obtain stable coupling for membrane materials with low density, a slight fluid compressibility is assumed. The coupling between the membrane and the internal fluid is automatically accounted for by a monolithic set-up. The filled membrane and the external fluid are coupled in a Dirichlet–Neumann fashion. The model is validated in several numerical examples and its potential application to a civil engineering problem of coast protection via water-filled bag reefs is shown.
Abstract
In this paper we propose a Finite Element model for analyzing closed membranes (“bags”) interacting with internal and external (surrounding) fluids. The approach [...]
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PFEM formulation for thermo-coupled FSI analysis. Application to nuclear core melt accident
A. Franci, E. Oñate, J. Carbonell, M. Chiumenti

Comput. Methods Appl. Mech. Engrg., (2017). Vol. 325, pp. 711-732

Abstract
The aim of this paper is to present a Lagrangian formulation for thermo-coupled fluid–structure interaction (FSI) problems and to show its applicability to the simulation of hypothetical scenarios of a nuclear core melt accident. During this emergency situation, an extremely hot and radioactive lava-like material, the corium, is generated by the melting of the fuel assembly. The corium may induce collapse of the nuclear reactor devices and, in the worst case, breach the reactor containment and escape into the environment. This work shows the capabilities of the proposed formulation to reproduce the structural failure mechanisms induced by the corium that may occur during a meltdown scenario. For this purpose, a monolithic method for FSI problems, the so-called Unified formulation, is here enhanced in order to account for the thermal field and to model phase change phenomena with the Particle Finite Element Method (PFEM). Several numerical examples are presented. First, the convergence of the thermo-coupled method and phase change algorithm is shown for two academic problems. Then, two complex simulations of hypothetical nuclear meltdown situations are studied in 2D as in 3D.
Abstract
The aim of this paper is to present a Lagrangian formulation for thermo-coupled fluid–structure interaction (FSI) problems and to show its applicability [...]
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A FIC-based stabilized finite element formulation for turbulent flows
J. Cotela-Dalmau, R. Rossi, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2017). (preprint) Vol. 315, pp. 607-631

Abstract
We present a new stabilized finite element (FEM) formulation for incompressible flows based on the Finite Increment Calculus (FIC) framework (Oñate, 1998). In comparison to existing FIC approaches for fluids, this formulation involves a new term in the momentum equation, which introduces non-isotropic dissipation in the direction of velocity gradients. We also follow a new approach to the derivation of the stabilized mass equation, inspired by recent developments for quasi-incompressible flows (Oñate et al., 2014). The presented FIC-FEM formulation is used to simulate turbulent flows, using the dissipation introduced by the method to account for turbulent dissipation in the style of implicit large eddy simulation.
Abstract
We present a new stabilized finite element (FEM) formulation for incompressible flows based on the Finite Increment Calculus (FIC) framework (Oñate, [...]
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Generalized parametric solutions in Stokes flow
P. Diez, S. Zlotnik, A. Huerta

Comput. Methods Appl. Mech. Engrg. (2017). (Preprint) Vol. 326, pp. 223-240

Abstract
Design optimization and uncertainty quantification, among other applications of industrial interest, require fast or multiple queries of some parametric model. The Proper Generalized Decomposition (PGD) provides a separable solution, a computational vademecum explicitly dependent on the parameters, efficiently computed with a greedy algorithm combined with an alternated directions scheme and compactly stored. This strategy has been successfully employed in many problems in computational mechanics. The application to problems with saddle point structure raises some difficulties requiring further attention. This article proposes a PGD formulation of the Stokes problem. Various possibilities of the separated forms of the PGD solutions are discussed and analyzed, selecting the more viable option. The efficacy of the proposed methodology is demonstrated in numerical examples for both Stokes and Brinkman models.
Abstract
Design optimization and uncertainty quantification, among other applications of industrial interest, require fast or multiple queries of some parametric model. The Proper [...]
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A semi‐analytical scheme for highly oscillatory integrals over tetrahedra
R. Hospital-Bravo, J. Sarrate, P. Diez

Comput. Methods Appl. Mech. Engrg., (2017). (Preprint) Vol. 111 (8), pp. 703-723

Abstract
This paper details a semi‐analytical procedure to efficiently integrate the product of a smooth function and a complex exponential over tetrahedral elements. These highly oscillatory integrals appear at the core of different numerical techniques. Here, the partition of unity method enriched with plane waves is used as motivation. The high computational cost or the lack of accuracy in computing these integrals is a bottleneck for their application to engineering problems of industrial interest. In this integration rule, the non‐oscillatory function is expanded into a set of Lagrange polynomials. In addition, Lagrange polynomials are expressed as a linear combination of the appropriate set of monomials, whose product with the complex exponentials is analytically integrated, leading to 16 specific cases that are developed in detail. Finally, we present several numerical examples to assess the accuracy and the computational efficiency of the proposed method, compared with standard Gauss–Legendre quadratures.
Abstract
This paper details a semi‐analytical procedure to efficiently integrate the product of a smooth function and a complex exponential over tetrahedral elements. These highly [...]
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Monitoring a PGD solver for parametric power flow problems with goal-oriented error assessment
R. García-Blanco, D. Borzacchiello, F. Chinesta, P. Diez

Int. J. Numer. Meth. Engng. (2017). Vol. 111 (6), pp. 529-552

Abstract
The parametric analysis of electric grids requires carrying out a large number of Power Flow computations. The different parameters describe loading conditions and grid properties. In this framework, the Proper Generalized Decomposition (PGD) provides a numerical solution explicitly accounting for the parametric dependence. Once the PGD solution is available, exploring the multidimensional parametric space is computationally inexpensive. The aim of this paper is to provide tools to monitor the error associated with this significant computational gain and to guarantee the quality of the PGD solution. In this case, the PGD algorithm consists in three nested loops that correspond to 1) iterating algebraic solver, 2) number of terms in the separable greedy expansion and 3) the alternated directions for each term. In the proposed approach, the three loops are controlled by stopping criteria based on residual goal-oriented error estimates. This allows one for using only the computational resources necessary to achieve the accuracy prescribed by the end- user. The paper discusses how to compute the goal-oriented error estimates. This requires linearizing the error equation and the Quantity of Interest to derive an efficient error representation based on an adjoint problem. The efficiency of the proposed approach is demonstrated on benchmark problems.
Abstract
The parametric analysis of electric grids requires carrying out a large number of Power Flow computations. The different parameters describe loading conditions and grid properties. [...]
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Enhanced goal-oriented error assessment and computational strategies in adaptive reduced basis solver for stochastic problems
K. Serafin, B. Magnain, E. Florentin, N. Parés, P. Diez

Int. J. Numer. Meth. Engng. (2017). (Preprint) Vol. 110 (5), pp. 440-466

Abstract
This work focuses on providing accurate low-cost approximations of stochastic finite elements simulations in the framework of linear elasticity. In [E. Florentin, P. Diez, Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems, Comput. Methods Appl. Mech. Engrg. 225-228 (2012) 116-127], an adaptive strategy has been introduced as an improved Monte-Carlo method for multi-dimensional large stochastic problems. We provide here a complete analysis of the method including a new enhanced goal-oriented error estimator and estimates of CPU cost gain. Technical insight of these two topics are presented in details and numerical examples show the interest of these new developments.
Abstract
This work focuses on providing accurate low-cost approximations of stochastic finite elements simulations in the framework of linear elasticity. In [E. Florentin, P. Diez, [...]
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Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems
M. Signorini, S. Zlotnik, P. Diez

Int. J. Numer. Meth. Engng. (2017). (Preprint) Vol. 109, (8), pp. 1085-1102

Abstract
The identification of the geological structure from seismic data is formulated as an inverse problem. The properties and the shape of the rock formations in the subsoil are described by material and geometric parameters, which are taken as input data for a predictive model. Here, the model is based on the Helmholtz equation, describing the acoustic response of the system for a given wave length. Thus, the inverse problem consists in identifying the values of these parameters such that the output of the model agrees the best with observations. This optimization algorithm requires multiple queries to the model with different values of the parameters. Reduced order models are especially well suited to significantly reduce the computational overhead of the multiple evaluations of the model. In particular, the proper generalized decomposition produces a solution explicitly stating the parametric dependence, where the parameters play the same role as the physical coordinates. A proper generalized decomposition solver is devised to inexpensively explore the parametric space along the iterative process. This exploration of the parametric space is in fact seen as a post‐process of the generalized solution. The approach adopted demonstrates its viability when tested in two illustrative examples.
Abstract
The identification of the geological structure from seismic data is formulated as an inverse problem. The properties and the shape of the rock formations in the subsoil are [...]
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A new equilibrated residual method improving accuracy and efficiency of flux-free error estimates
N. Parés, P. Diez

Comput. Methods Appl. Mech. Engrg., (2017). (Preprint) Vol. 313 (1), pp. 785-816

Abstract
This paper presents a new methodology to compute guaranteed upper bounds for the energy norm of the error in the context of linear finite element approximations of the reaction-diffusion equation. The new approach revisits the ideas in [20, 18] with the goal of substantially reducing the com- putational cost of the flux-free method while retaining the good quality of the bounds. The new methodology provides also a technique to compute equilibrated boundary tractions improving the quality of standard equilibration strategies. The zeroth-order equilibration conditions are imposed using an alternative less restrictive form of the first-order equilibration conditions, along with a new efficient minimization criterion. This new equilibration strategy provides much more accurate up- per bounds for the energy and requires only doubling the dimension of the local linear systems of equations to be solved.
Abstract
This paper presents a new methodology to compute guaranteed upper bounds for the energy norm of the error in the context of linear finite element approximations of the reaction-diffusion [...]
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Variational Multiscale error estimators for solid mechanics adaptive simulations: An Orthogonal Subgrid Scale approach
J. Baiges, R. Codina

Comput. Methods Appl. Mech. Engrg., (2017). Vol. 325, pp. 37-55

Abstract
In this work we present a general error estimator for the finite element solution of solid mechanics problems based on the Variational Multiscale method. The main idea is to consider a rich model for the subgrid scales as an error estimator. The subscales are considered to belong to a space orthogonal to the finite element space (Orthogonal Subgrid Scales) and we take into account their contribution both in the element interiors and on the element boundaries (Subscales on the Element Boundaries). A simple analysis shows that the upper bound for the obtained error estimator is sharper than in other error estimators based on the Variational Multiscale Method. Numerical examples show that the proposed error estimator is an accurate approximation for the energy norm error and can be used both in simple linear constitutive models and in more complex non-linear cases.
Abstract
In this work we present a general error estimator for the finite element solution of solid mechanics problems based on the Variational Multiscale method. [...]
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Interpolation with restrictions between finite element meshes for flow problems in an ALE setting
A. Pont, R. Codina, J. Baiges

Comput. Methods Appl. Mech. Engrg., (2017). Vol. 110 (13), pp. 1203-1226

Abstract
The need for remeshing when computing flow problems in domains suffering large deformations has motivated the implementation of a tool that allows the proper transmission of information between finite element meshes. Because the Lagrangian projection of results from one mesh to another is a dissipative method, a new conservative interpolation method has been developed. A series of constraints, such as the conservation of mass or energy, are applied to the interpolated arrays through Lagrange multipliers in an error minimization problem, so that the resulting array satisfies these physical properties while staying as close as possible to the original interpolated values in the L2 norm. Unlike other conservative interpolation methods that require a considerable effort in mesh generation and modification, the proposed formulation is mesh independent and is only based on the physical properties of the field being interpolated. Moreover, the performed corrections are neither coupled with the main calculation nor with the interpolation itself, for which reason the computational cost is very low.
Abstract
The need for remeshing when computing flow problems in domains suffering large deformations has motivated the implementation of a tool that allows the proper transmission [...]
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Numerical analysis of a stabilized finite element approximation for the three-field linearized viscoelastic fluid problem using arbitrary interpolations
E. Castillo, R. Codina

Mathematical Models and Methods in Applied Sciences (2017). Vol. 51 (4), pp. 1407-1427

Abstract
In this paper we present the numerical analysis of a three-field stabilized finite element formulation recently proposed to approximate viscoelastic flows. The three-field viscoelastic fluid flow problem may suffer from two types of numerical instabilities: on the one hand we have the two inf-sup conditions related to the mixed nature problem and, on the other, the convective nature of the momentum and constitutive equations may produce global and local oscillations in the numerical approximation. Both can be overcome by resorting from the standard Galerkin method to a stabilized formulation. The one presented here is based on the subgrid scale concept, in which unresolvable scales of the continuous solution are approximately accounted for. In particular, the approach developed herein is based on the decomposition into their finite element component and a subscale, which is approximated properly to yield a stable formulation. The analyzed problem corresponds to a linearized version of the Navier–Stokes/Oldroyd-B case where the advection velocity of the momentum equation and the non-linear terms in the constitutive equation are treated using a fixed point strategy for the velocity and the velocity gradient. The proposed method permits the resolution of the problem using arbitrary interpolations for all the unknowns. We describe some important ingredients related to the design of the formulation and present the results of its numerical analysis. It is shown that the formulation is stable and optimally convergent for small Weissenberg numbers, independently of the interpolation used.
Abstract
In this paper we present the numerical analysis of a three-field stabilized finite element formulation recently proposed to approximate viscoelastic flows. The three-field [...]
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An adaptive Fixed-Mesh ALE method for free surface flows
J. Baiges, R. Codina, A. Pont, E. Castillo

Comput. Methods Appl. Mech. Engrg., (2017). Vol. 313, pp. 159-188

Abstract
In this work we present a Fixed-Mesh ALE method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background domain. This mesh is successively refined and unrefined at each time step in order to focus the computational effort on the spatial regions where it is required. Some of the main ingredients of the formulation are the use of an Arbitrary-Lagrangian–Eulerian formulation for computing temporal derivatives, the use of stabilization terms for stabilizing convection, stabilizing the lack of compatibility between velocity and pressure interpolation spaces, and stabilizing the ill-conditioning introduced by the cuts on the background finite element mesh, and the coupling of the algorithm with an adaptive mesh refinement procedure suitable for running on distributed memory environments. Algorithmic steps for the projection between meshes are presented together with the algebraic fractional step approach used for improving the condition number of the linear systems to be solved. The method is tested in several numerical examples. The expected convergence rates both in space and time are observed. Smooth solution fields for both velocity and pressure are obtained (as a result of the contribution of the stabilization terms). Finally, a good agreement between the numerical results and the reference experimental data is obtained.
Abstract
In this work we present a Fixed-Mesh ALE method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background [...]
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Finite element approximation of the viscoelastic flow problem: A non-residual based stabilized formulation
E. Castillo, R. Codina

Computers & Fluids (2017). Vol. 142, pp. 72-78

Abstract
In this paper, a three-field finite element stabilized formulation for the incompressible viscoelastic fluid flow problem is tested numerically. Starting from a residual based formulation, a non-residual based one is designed, the benefits of which are highlighted in this work. Both formulations allow one to deal with the convective nature of the problem and to use equal interpolation for the problem unknowns σ−u−p (deviatoric stress, velocity and pressure). Additionally, some results from the numerical analysis of the formulation are stated. Numerical examples are presented to show the robustness of the method, which include the classical 4: 1 planar contraction problem and the flow over a confined cylinder case, as well as a two-fluid formulation for the planar jet buckling problem.
Abstract
In this paper, a three-field finite element stabilized formulation for the incompressible viscoelastic fluid flow problem is tested numerically. Starting from a residual based [...]
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Conserving algorithms for frictionless and full stick friction contact dynamic problems using the direct elimination method
C. Agelet de Saracibar, D. Di Capua

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

Abstract
In this paper, conserving time‐stepping algorithms for frictionless and full stick friction dynamic contact problems are presented. Time integration algorithms for frictionless and full stick friction dynamic contact problems have been designed to preserve the conservation of key discrete properties satisfied at the continuum level. Energy and energy‐momentum–preserving algorithms for frictionless and full stick friction dynamic contact problems, respectively, have been designed and implemented within the framework of the direct elimination method, avoiding the drawbacks linked to the use of penalty‐based or Lagrange multipliers methods. An assessment of the performance of the resulting formulation is shown in a number of selected and representative numerical examples, under full stick friction and slip frictionless contact conditions. Conservation of key discrete properties exhibited by the time‐stepping algorithm is shown.
Abstract
In this paper, conserving time‐stepping algorithms for frictionless and full stick friction dynamic contact problems are presented. Time integration algorithms for frictionless [...]
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A coupled FEM-DEM procedure for predicting blasting operations in tunnels
F. Zarate, J. Gonzalez, J. Miquel, R. Lohner, E. Oñate

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

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 technique 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 with an embedded fluid-structure interaction method. This allows us to accurately predicting the progressive multi-fracture of the rock accounting for the penetration of the gas in the fractured domain modelled with the FEM-DEM procedure. 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 correctly captures the onset of fractures and their evolution [1].
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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Early detection of anomalies in dam performance: A methodology based on boosted regression trees
F. Salazar, M. Toledo, J. González, E. Oñate

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

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

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

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

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

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

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

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

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

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