A dynamic problem with wear involving electro-elastic-viscoplastic materials with damage

Abstract

A dynamic contact problem is
considered in the paper. The material behavior is described by
electro-elastic-viscoplastic law with piezoelectric effects. The body is in
contact with damage and an obstacle. The contact is frictional and bilateral
with a moving rigid foundation which results in the wear of the contacting
surface. The damage of the material caused by elastic deformations. The
evolution of the damage is described by an inclusion of parabolic type. The
problem is formulated as a coupled system of an elliptic variational
inequality for the displacement, variational equation for the electric
potential and a parabolic variational inequality for the damage. We establish
a variational formulation for the model and we prove the existence of a unique
weak solution to the problem. The proof is based on a classical existence and
uniqueness result on parabolic inequalities, differential equations and fixed
point arguments.