A quasistatic viscoplastic contact problem with normal compliance and friction

Abstract

We consider a quasistatic contact problem between a viscoplastic body and an obstacle, the so‐called foundation. The contact is modelled with normal compliance and the associated version of Coulomb's law of dry friction. We derive a variational formulation of the problem and, under a smallness assumption on the normal compliance functions, we establish the existence of a weak solution to the model. The proof is carried out in several steps. It is based on a time‐discretization method, arguments of monotonicity and compactness, Banach fixed point theorem and Schauder fixed point theorem.