A dynamic contact problem between elasto-viscoplastic piezoelectric bodies with normal compliance adhesion and damage

Abstract

We consider a dynamic frictionless contact problem between two elasto-viscoplastic piezo- electric bodies with damage. The evolution of the damage is described by an inclusion of parabolic type. The contact is modelled with normal compliance condition. The adhesion of the contact surfaces is considered and is modelled with a surface variable, the bonding eld whose evolution is described by a rst order di erential equation: .......................... We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on argu- ments of nonlinear evolution equations with monotone operators, a classical existence and uniqueness result on parabolic inequalities, di erential equations and xed-point arguments.