A Dynamic Contact Problem Between Elasto-Viscoplastic Piezoelectric Bodies with Adhesion

Abstract

We consider a dynamic frictionless contact problem between two elasto-viscoplastic piezoelectric 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 field whose evolution is described by a first order differential equation. We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of nonlinear evolution equations with monotone operators, a classical existence and uniqueness result on parabolic inequalities, differential equations and fixed-point arguments.