A quasistatic bilateral contact problem with friction for nonlinear elastic materials

Abstract

We consider a mathematical model describing the bilateral contact between a deformable body and a foundation. We use a nonlinear elastic constitutive law. The contact takes into account the effects of friction, which are modelled with the regularized friction law. We derive a variational formulation of the problem and establish the existence of a weak solution under a smallness assumption of the friction coefficient. The proof is based on arguments of compactness, lower semicontinuity and time discretization.

Keywords

• Nonlinear elasticity
• bilateral contact
• friction
• variational inequality
• weak solution.