C. Agelet de Saracibar

A stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations

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

On the formulation of coupled thermoplastic problems with phase-change

This paper deals with a numerical formulation for coupled thermoplastic problems including phase-change phenomena. The final goal is to get an accurate, eAcient 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 diAerential 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 phasechange 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. # 1999 Elsevier Science Ltd. All rights reserved.

On the numerical modeling of frictional wear phenomena

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 Archards 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.

Numerical analysis of coupled thermomechanical frictional contact problems. Computational model and applications

SummaryIn 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.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.

A new frictional time integration algorithm for large slip multi-body frictional contact problems☆

In this paper a new frictional time integration 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 of the local surface finite 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 completely bypassed. Remarkably, the algorithm is defined on the sole 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.

On the constitutive modeling of coupled thermomechanical phase-change problems

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.

A Computational Model for the Numerical Simulation of FSW Processes

In this paper a computational model for the numerical simulation of Friction Stir Welding (FSW) processes is presented. FSW is a new method of welding in solid state in which a shouldered tool with a profile probe is rotated and slowly plunged into the joint line between two pieces of sheet or plate material which are butted together. Once the probe has been completely inserted, it is moved with a small tilt angle in the welding direction. Here a quasi‐static, thermal transient, mixed multiscale stabilized Eulerian formulation is used. Norton‐Hoff and Sheppard‐Wright rigid thermo‐viscoplastic material models have been considered. A staggered solution algorithm is defined such that for any time step, the mechanical problem is solved at constant temperature and then the thermal problem is solved keeping constant the mechanical variables. A pressure multiscale stabilized mixed linear velocity/linear pressure finite element interpolation formulation is used to solve the mechanical problem and a convection mul...

A novel stress-accurate FE technology for highly non-linear analysis with incompressibility constraint: application to the numerical simulation of the FSW process

In this work a novel finite element technology based on a three-field mixed formulation is presented. The Variational Multi Scale (VMS) method is used to circumvent the LBB stability condition allowing the use of linear piece-wise interpolations for displacement, stress and pressure fields, respectively. The result is an enhanced stress field approximation which enables for stress-accurate results in nonlinear computational mechanics. The use of an independent nodal variable for the pressure field allows for an adhoc treatment of the incompressibility constraint. This is a mandatory requirement due to the isochoric nature of the plastic strain in metal forming processes. The highly non-linear stress field typically encountered in the Friction Stir Welding (FSW) process is used as an example to show the performance of this new FE technology. The numerical simulation of the FSW process is tackled by means of an Arbitrary-Lagrangian-Eulerian (ALE) formulation. The computational domain is split into three different zones: the work.piece (defined by a rigid visco-plastic behaviour in the Eulerian framework), the pin (within the Lagrangian framework) and finally the stirzone (ALE formulation). A fully coupled thermo-mechanical analysis is introduced showing the heat fluxes generated by the plastic dissipation in the stir-zone (Sheppard rigid-viscoplastic constitutive model) as well as the frictional dissipation at the contact interface (Norton frictional contact model). Finally, tracers have been implemented to show the material flow around the pin allowing a better understanding of the welding mechanism. Numerical results are compared with experimental evidence.

Current developments on the coupled thermomechanical computational modeling of metal casting processes

The coupled thermomechanical computational modeling of metal casting processes has been one of the research topics of great interest over the last years. However, despite the considerable advances achieved in computational mechanics, the large-scale numerical simulation of these processes continues to be nowadays a very complex task. This is mainly due to the highly nonlinear nature of the problem, involving nonlinear material models, liquid-solid phase change, nonlinear thermomechanical boundary conditions and thermomechanical contact, among others. In this paper, current developments to deal with an accurate, efficient and robust coupled thermomechanical computational simulation of metal casting processes is presented. A thermodynamically consistent constitutive material model is derived from a thermoviscoplastic free energy function. A continuous transition between the initial fluid-like and the final solid-like is modeled by considering a J2 thermoviscoplastic model. Thus, an thermoelastoviscoplastic model, suitable for the solid-like phase, degenerates into a pure thermoviscous model, suitable for the liquid-like phase, according to the evolution of the solid fraction function [1-2]. A thermomechanical contact model, taking into account the insulated effects of the air-gap due to thermal shrinkage of the part during solidification and cooling, is introduced [1-2]. A fractional step method, arising from an operator split of the governing differential equations, is considered to solve the coupled problem using a staggered scheme [1-2]. Within a finite element setting, using low-order interpolation elements, a multiscale stabilization technique is introduced as a convenient framework to overcome the Babuska-Brezzi condition and avoid volumetric locking and pressure instabilities arising in incompressible or quasi-incompressible problems [3-4]. Computational simulation of industrial castings show the good performance of the model.