Surface perturbation of an elastodynamic contact problem with friction

Abstract

International audienceWe consider the dynamical process of an elastic body in unilateral fricitonal contact with a rigid foundation. Friction is modelled with the Coulomb law with a coefficient that depends on the slip velocity. To allow for velocity discontinuities we use the elastodynamic (hyperbolic) framework. Nevertheless, this does not lead to a well-posed problem. To remedy this, we perturb the solution of the elastodynamical problem in a thin layer next to the contact boundary. This is a generalization of an approach previously studied in a one-dimensional case. We establish existence and uniqueness results for the perturbed and regularized problem and provide an interpretation of this perturbation

Mass redistribution method for finite element contact problems in elastodynamics

“…Concerning the continuous purely elastodynamic contact problems (hyperbolic problems), as far as we know, an existence result has been proved in a scalar two dimensional case by Lebeau-Schatzman [15], Kim [12], in the vector case with a modified contact law by Renard-Paumier [24], but no uniqueness result is known. This ill-posedness leads to numerical instabilities of time integration schemes.…”

Comparison of two approaches for the discretization of elastodynamic contact problems

“…For purely contact elastodynamic problems (hyperbolic problems), as far as we know, the existence result has been proved in a scalar two dimensional case by Lebeau and Schatzman [4,3] and in the vector case, with a modified contact law, by Renard and Paumier [8]. It seems that no energy conserving result has been proved in the continuous framework.…”

Existence of a solution to a dynamic unilateral contact problem for a cracked viscoelastic body

“…Pratt and Ricaud [11] have studied dynamic contact problems with friction by using discretization techniques, in a particular case of a normal compliance law. Paumier and Renard [9] have solved an elastodynamic contact problem with surface perturbation. In this paper, we extend the existence result obtained in [3], for a dynamic unilateral contact problem with nonlocal friction, without any additional assumption on velocity or acceleration, to a cracked viscoelastic body.…”

“…Plus récemment, pour un matériau de Kelvin-Voigt, d'autres résultats d'existence ont été obtenus pour des problèmes dynamiques de contact avec frottement par Cocou, Ricaud et Pratt [2,3,11]. Paumier et Renard [9] ont résolu un problème de contact en élastodynamique avec perturbation de surface. Tous ces résultats ont été obtenus dans des domaines réguliers.…”