BILATERAL CONTACT PROBLEM WITH FRICTION AND WEAR FOR AN ELECTRO ELASTIC-VISCOPLASTIC MATERIALS WITH DAMAGE

Abstract

We consider a mathematical problem for quasistatic contact between anelectro elastic-viscoplastic body and an obstacle. The contact is frictional and bilateral with a moving rigid foundation which results in the wear of the contacting surface. We employ the electro elastic-viscoplastic with damage constitutive law for the material. The evolution of the damage is described by an inclusion of parabolic type. The problem is formulated as a system of an elliptic variational inequality for the displacement, a parabolic variational inequality for the damage and a variational equality for the electric stress. We establish a variational formulation for the model and we give the wear conditions for the existence of a unique weak solution to the problem. The proofs are based on classical results for elliptic variational inequalities, parabolic inequalities and fixed point arguments.