A FRICTIONAL CONTACT PROBLEM WITH NORMAL COMPLIANCE FOR VISCOELASTIC MATERIALS WITH LONG MEMORY

Abstract

This paper is devoted to study a quasistatic contact problem be-tween a viscoelastic material with long memory and a foundation. Thecontact is modelled with a version of Coulomb’s law of dry friction anda general normal compliance condition. We derive a variational formu-lation of the model and, under a smallness assumption, we establishthe existence of a weak solution to the problem. The proof is based onthe time-discretization method, the Banach fixed point theorem andarguments of compactness, lower semicontinuity and monotonicity