Existence for viscoplastic contact with Coulomb friction problems

Abstract

We present existence results in the study of nonlinear problem of frictional contact between an elastic‐viscoplastic body and a rigid obstacle. We model the frictional contact both by a Tresca′s friction law and a regularized Coulomb′s law. We assume, in a first part, that the contact is bilateral and that no separation takes place. In a second part, we consider the Signorini unilateral contact conditions. Proofs are based on a time‐discretization method, Banach and Schauder fixed point theorems.