A dynamic contact problem for elastic–viscoplastic materials with normal damped response and damage

Abstract

We consider a mathematical model which describes the frictional contact between a deformable body and a foundation. The process is assumed to be dynamic and the material behavior is described by a elastic–viscoplastic constitutive law with damage. The frictional contact is modeled with subdifferential boundary conditions. We derive the variational formulation of the problem which is a coupled system of a hemivariational inequality for the displacement and a parabolic variational inequality for the damage field. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of hyperbolic hemivariational inequality, a classical existence, and uniqueness result on parabolic inequalities and a fixed point argument.