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The aim of this work is to study a class of dynamic contact problems coupling adhesion and friction between two viscoelastic bodies with nonlinear viscosity operators. The boundary conditions concern relaxed unilateral contact, pointwise friction and adhesion including possible recoverable behavior. A mixed variational formulation of these problems is given as a five-field evolution implicit equation coupled with a differential inclusion describing the evolution of the intensity of adhesion. Based on several estimates and a classical fixed point theorem for multivalued functions, the existence of a strong variational solution is proved.

International audience; The aim of this work is to study a dynamic problem that constitutes a unified approach to describe some rate-depending interactions between the boundaries of two viscoelastic bodies, including relaxed unilateral contact, pointwise friction or adhesion conditions. The classical formulation of the problem is presented and two variational formulations are given as three and four-field evolution implicit equations. Based on some approximation results and an equivalent fixed point problem for a multivalued function, we prove the existence of solutions to these variational evolution problems.

International audience; The aim of this work is to study a class of nonsmooth dynamic contact problem which model several surface interactions, including relaxed unilateral contact conditions, adhesion and Coulomb friction laws, between two viscoelastic bodies of Kelvin-Voigt type. An abstract formulation which generalizes these problems is considered and the existence of a solution is proved by using Ky Fan's fixed point theorem, suitable approximation properties, several estimates and compactness arguments.

International audience; The aim of this paper is to study the existence of solutions and some approximations for a class of implicit evolution variational inequalities that represents a generalization of several quasistatic contact problems in elasticity. Using appropriate estimates for the incremental solutions, the existence of a continuous solution and convergence results are proved for some corresponding internal approximation and backward difference scheme. To solve the fully discrete problems, general additive subspace correction algorithms are considered, for which global convergence is proved and some error estimates are established.

This work deals with the mathematical analysis of a dynamic unilateral contact problem with friction for a cracked viscoelastic body. We consider here a Kelvin-Voigt viscoelastic material and a nonlocal friction law. To prove the existence of a solution to the unilateral problem with friction, an auxiliary penalized problem is studied. Several estimates on the penalized solutions are given, which enable us to pass to the limit by using compactness results.

In the present paper, we consider a thermodynamic model using the contact kinematics developed by A. Curnier, Q.C. He and J.J. Telega [C. R. Acad. Sci. Paris Ser. II 314 (1992) 1] involving unilateral contact, adhesion and Coulomb friction between two homogeneous, isotropic and hyperelastic bodies. Adhesion is described by an internal state variable β ϕ introduced by M. Fremond [C. R. Acad. Sci. Paris Ser. II 295 (1982) 913; J. Theor. Appl. Mech. 6 (1987) 383]. Taking the case of contact between a hyperelastic solid and a plane support, we formulate the associated boundary value problem as a minimization problem when no friction is involved. When the intensity of the adhesion obeys a `static' law, we obtain an existence result for this problem.

International audience; A mixed finite element method is adopted to approximate the quasi-static unilateral contact problem with local Coulomb friction. The existence of a solution with bounds independent of the discretization parameter is obtained by an incremental scheme. This approach enables us to select a sequence of discrete solutions which converges strongly towards a solution of the quasi-static unilateral contact problem with Coulomb friction law.

International audience; This paper deals with the mathematical analysis and the subspace approximation of a system of variational inequalities representing a unified approach to several quasistatic contact problems in elasticity. Using an implicit time discretization scheme and some estimates, convergence properties of the incremental solutions and existence results are presented for a class of abstract implicit evolution variational inequalities involving a nonlinear operator. To solve the corresponding semi-discrete and the fully discrete problems, some general subspace correction algorithms are proposed, for which global convergence is analyzed and error estimates are established.

This work is concerned with the study of a class of dynamic problems, coupling unilateral contact, adhesion and nonlocal friction for viscoelastic bodies of Kelvin-Voigt type. We consider a model for the dynamic frictional contact with reversible adhesion, where the coefficient of friction depends on the slip velocity and the evolution of the intensity of adhesion is nonlinear. A corresponding variational formulation is given as a system of coupled implicit variational inequalities, including a nonlinear parabolic inequality which describes the evolution, possibly reversible, of the adhesion field. An abstract problem is considered in order to study the approximation of variational solutions by a penalty method and also to analyse other problems including normal compliance laws. Based on incremental techniques together with a fixed point method, a general result is presented and is applied to show the existence and uniqueness of the penalized solutions. Using several estimates on the penalized solutions and some compactness arguments, one can obtain a variational solution of the initial problem.

International audience; The aim of this paper is to study an interaction law coupling recoverable adhesion, friction and unilateral contact between two viscoelastic bodies of Kelvin–Voigt type. A dynamic contact problem with adhesion and nonlocal friction is considered and its variational formulation is written as the coupling between an implicit variational inequality and a parabolic variational inequality describing the evolution of the intensity of adhesion. The existence and approximation of variational solutions are analysed, based on a penalty method, some abstract results and compactness properties. Finally, some numerical examples are presented.

In this paper, the interface law coupling adhesion, friction and unilateral contact, proposed in [5] for elastic bodies in a quasistatic evolution, is extended and considered in the case of dynamic contact for viscoelastic bodies.

In this paper, we extend the existence results obtained in [1], for a dynamic unilateral contact problem with nonlocal friction between a Kelvin-Voigt viscoelastic body and a rigid obstacle, to the contact between two viscoelastic bodies and to a cracked viscoelastic body. We give classical and primal variational formulations for the problems. Penalized formulations are investigated by using an abstract existence and uniqueness result. Several estimates on the penalized solutions are established which allow to pass to the limit and to prove the existence of solutions for these dynamic unilateral contact problems with friction.

In this paper we study a dynamic unilateral contact problem with friction for a cracked viscoelastic body. The viscoelastic model is characterized by Kelvin–Voigt's law and a nonlocal friction law is investigated here. The existence of a solution to the problem is obtained by using a penalty method. Several estimates are obtained on the solution to the penalized problem, which enable us to pass to the limit by using compactness results. To cite this article: M. Cocou, G. Scarella, C. R. Acad. Sci. Paris, Ser. I 338 (2004).

The approximation of the quasistatic two-body unilateral contact problem with local Coulomb friction by a mixed finite element method is studied. Continuous and discrete variational formulations are stated. Using a regularity result for the normal component of the stress vector for an auxiliary problem with given friction and some error estimates, convergence to the continuous quasistatic solution is proved when the discretization parameters tend to zero.

International audience; A dynamic unilateral contact problem with nonlocal friction for a viscoelastic body satisfying a Kelvin-Voigt law is studied. Using a penalty method and compactness results, the existence of a weak solution of this problem is proved.

Many problems encountered in industry are concerned with interface evolutions, where contact, friction and adhesion are fundamental topics. This PhD thesis contributes to the development of a model involving adhesion and friction and allowing the healing of the adhesive bonds when the bodies are again pushed closer together after their separation. This model is called model of healing adhesion. In this work the applications concern specifically the contact glass/rubber. The formation of the the adhesion neck, jump-on and jump-off phenomena and the formation and the propagation of the Schallamach waves are investigated. A modelling of the adhesive contact is thus proposed, based on thermodynamic considerations and surface interactions concepts. In addition to the possible healing of the adhesives bonds, the originality of the model is that healing process and damage process are both related to the rate of the solicitation at the interface. According to the applications, the approch allows to consider two potential sources of dissipation. One is called surface dissipation and linked to the behaviour of the interface. The second is called bulk dissipation and linked to the behaviour of the bodies. The dynamic formulation is done within the framework of the non-smooth mechanic. Implementations of appropriate numerical methods and simulations are done in LMGC90 (Montpellier - Marseille). The model is tested with Benchmark and validated with the simulation of a glass/rubber experiment.; De très nombreux problèmes rencontrés dans l'industrie sont liés aux évolutions que subissent les interfaces. Le contact, le frottement et l'adhésion y jouent un rôle fondamental. Ce travail est une contribution au développement d'un modèle qui couple adhésion et frottement et qui autorise la cicatrisation des liens adhésifs lorsque les corps sont remis en contact après avoir été séparés. Ce modèle est appelé modèle d'adhésion cicatrisante. Dans le cadre de ce mémoire, les applications concernent plus particulièrement l'étude du contact verre/élastomère. La formation du col d'adhésion, les phénomènes « jump-on » et « jump-off » et la formation et la propagation des ondes de Schallamach sont abordés. Le travail propose une modélisation à l'échelle des surfaces, issue de considérations thermodynamiques et qui simule les effets des interactions de type van der Waals. Outre la possible cicatrisation des liens lors de l'approche des corps, l'originalité du modèle est que les processus d'endommagement et de cicatrisation des liens adhésifs sont tous deux liés à la vitesse de sollicitation au niveau de l'interface. Selon les applications envisagées, l'approche permet ainsi de considérer deux sources possibles de dissipations. L'une est surfacique et liée au comportement de l'interface. La seconde est volumique et liée au comportement des corps. La formulation dynamique est donnée dans le cadre de la mécanique non régulière. Les méthodes numériques correspondantes sont mises en œuvre dans la plateforme LMGC90 (Montpellier - Marseille). Le modèle est testé sur des Benchmarks et validé sur la simulation d'une expérience de tribologie de contact verre/élastomère.