ANALYSIS OF A ELECTRO-ELASTIC CONTACT PROBLEM WITH FRICTION AND ADHESION

We consider a mathematical model which describes the quasistatic frictional contact between a piezoelectric body and an obstacle, the so-called foundation. A nonlinear electro-elastic constitutive law is used to model the piezoelectric material. The contact is modelled with Signorini's conditions and the associated with a regularized Coulomb's law of dry friction in witch the adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation. We derive a variational formulation for the model, in the form of a coupled system for the displacements, the electric potential and the adhesion. Under a smallness assumption on the coefficient of friction, we prove the existence of a unique weak solution of the model. The proof is based on arguments of time-dependent quasi-variational inequalities, differential equations and Banach's fixed point theorem.