Simulation numérique des problèmes de contact avec frottement

Numerical simulation of contact and friction problems

Laboratoire de Mécanique et de Génie Civil, Université Montpellier II, CNRS, Montpellier

Abstract

The purpose of this paper is to discuss three questions related to numerical simulation of dynamical or quasi-static problems in presence of unilateral contact and dry friction.

- Choosing contact and friction laws: among several possible choices, Signorini's conditions and Coulomb's law are presented and commented.

- The dynamical equations together with contact and friction relations are written down. For numerical purpose these equations have to be discretized. An explicit and an implicit typical numerical scheme, together with an explicit and implicit scheme for contact and friction relations are proposed, allowing to exhibit four classes of methods using local or general variables.

- These methods of resolution will be illustrated in the particular case of a one dimentional dynamical frictional problem.