Variational–hemivariational approach to quasistatic viscoplastic contact problem with normal compliance, unilateral constraint, memory term, friction and damage

Abstract

The aim of this paper is to study a mathematical model which describes the quasistatic frictional contact between a viscoplastic body and a foundation. The material’s behavior is modeled with a rate-type constitutive law with internal state variable. The contact is modeled with normal compliance, unilateral constraint and memory term, friction and damage. We present the classical formulation of the problem and we derive its variational–hemivariational formulation. Finally, we prove its unique weak solvability. The proof is based on abstract results for a class of history-dependent variational–hemivariational inequalities.