A Quasistatic unilateral contact problem with slip-dependent coefficient of friction for nonlinear elastic materials

Abstract

Existence of a weak solution under a smallness assumption of the coefficient of friction for the problem of quasistatic frictional contact between a nonlinear elastic body and a rigid foundation is established. Contact is modelled with the Signorini condition. Friction is described by a slip dependent friction coefficient and a nonlocal and regularized contact pressure. The proofs employ a time-discretization method, compactness and lower semicontinuity arguments.

Keywords

• Existence
• quasistatic
• nonlinear elastic
• slip-dependent friction
• incremental
• variational inequality.