Analysis of quasistatic viscoelastic viscoplastic piezoelectric contact problem with friction and adhesion

Abstract

In this paper we study the process of bilateral contact with adhesion and friction between a piezoelectric body and an insulator obstacle, the so-called foundation. The material’s behavior is assumed to be electro-viscoelastic-viscoplastic; the process is quasistatic, the contact is modeled by a general nonlocal friction law with adhesion. The adhesion process is modeled by a bonding field on the contact surface. We derive a variational formulation for the problem and then, under a smallness assumption on the coefficient of friction, we prove the existence of a unique weak solution to the model.The proofs are based on a general results on elliptic variational inequalities and fixed point arguments.