Variational analysis of an electro viscoelastic contact problem with friction

A mathematical model which describes the quasistatic frictional contact between a piezoelectric body and a deformable foundation is studied in this paper. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. The contact is described with the normal compliance condition and a version of Coulomb’s law of friction. A variational formulation of the model, in the form of a coupled system for the displacements and the electric potential, is derived. The existence of a unique weak solution of the model is established under a smallness assumption of the friction coefficient. The proof is based on arguments of evolutionary variational inequalities and fixed points of operators.