The present paper is devoted to the modeling of finite deformations of hyperelastic bodies described by the Yeoh model under contact/impact conditions. A total Lagrangian formulation is adopted to describe the geometrically nonlinear behavior. A first order algorithm is applied to integrate the equations of motion. For the finite element implementation, an explicit expression of the tangent operator is derived. Two numerical examples are presented to show the applicability of the developed approach.

In this paper, we present a comparative study of the boundary element method (BEM) and the finite element method (FEM) for analysis of Signorini contact problems in elastostatics with Coulomb's friction law. Particularities of each method and comparison with the penalty method are discussed. Numerical examples are included to demonstrate the present formulations and to highlight its performance. IntroductionThe analysis of contact problems with friction is of great importance in many engineering applications. The numerical treatment of the unilateral contact with dry friction is certainly one of the non smooth mechanics topics for which many efforts have been made in the past. In the literature, many attempts have been developed to deal with such problems using the finite element method (FEM), these include the penalty function method [1][2][3][4], the flexibility method [5,6], the mathematical programming method [7-9], the Lagrangian multiplier method [10,11] and the augmented Lagrangian method [12][13][14][15][16][17]. A large literature base is available for a variety of numerical algorithms (See the monographs of Zhong [18] and Wriggers [19]). However, the modeling of frictional contact problems by the boundary element method (BEM) remains limited. At first a trial and error algorithm has been developed [20]. Then numerical procedures based on an incremental approach [21,22], on the flexibility method [23] or on mathematical programming [24] have been proposed. For elastoplastic materials in the presence of frictionless contact conditions, a formulation characterized by two variational principles based on boundary integral equation method has been presented [25].The aim of the present paper is to present a comparative study of BEM and FEM for analysis of Signorini contact problems in two-dimensional elastostatics with Coulomb's friction law. After a definition of contact kinematics, we outline the penalty method for comparison reason. We present then the BEM and FEM developed for contact modeling. Two numerical examples are performed in this study to show the validity of the developed models. The performance of present methods is reported as compared to the general purpose finite element code ANSYS in which the penalty method is used for contact modeling. Contact kinematicsIn this section, the geometric and kinematic quantities found suitable for describing the contact compatibility of deformable bodies are defined. First of all, some basic definitions and notations are set up. For the sake of simplicity, let us consider contact between two bodies X 1 and X 2 , one of which may be a rigid foundation. In order to state the contact constraints, we have to find the minimum distance of a point P of one body with respect to the other one. The displacements of the particles of X 1 and X 2 being respectively u 1 and u 2 , the relative displacement is: u ¼ u 1 À u 2 . Let r be the contact traction acting at P from X 2 onto X 1 . Then X 2 is subjected to the traction Àr, acting from X 1 . Let n denote the normal unit ...

Pour déterminer les déformations et les contraintes au sein de tissus biologiques tels que les ligaments, les tendons ou les parois artérielles, les lois de comportements hyperélastiques anisotropes sont souvent utilisées dans le cadre de la méthode des éléments finis [J.A. Weiss, B.N. Maker, S. Govindjee, Finite element implementation of incompressible, transversely isotropic hyperelasticity, Comp. Meth. Appl. Mech. Engng. 135 (1996) 107-128]. Dans cet article, on se propose de réaliser une telle étude en parallèle avec une analyse analytique. Cette analyse complémentaire permet de comprendre pourquoi la correspondance n'est pas biunivoque entre la déformation principale λ 2 et le quatrième invariant de la matrice de dilatation pour un modèle usuel tel que celui proposé par Holzapfel, Gasser et Ogden [

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The power density of a proton exchange membrane fuel cell (PEMFC) depends on several parameters. The contact resistance between the bipolar plate (BPP) and the gas diffusion layer (GDL) and the porosity of the GDL are two main parameters involved in the performance of the PEMFC. The purpose of this work is to develop a numerical model to describe the contact behavior (contact zone, contact force) on the interfaces between the different layers in order to propose an optimal structure for the high performance of PEM fuel cells. Numerical results can help to increase the knowledge of fuel cell's performance and to determine the optimal structure which can be used in the design of fuel cells.