A dynamic frictional contact problem for piezoelectric materials

We consider a mathematical model which describes the frictional contact between a piezoelectric body and an electrically conductive foundation. The process is dynamic, the materialʹs behavior is modeled with an electro-viscoelastic constitutive law and the contact is described by subdifferential boundary conditions. We derive the variational formulation of the problem which is in the form of a system involving a second order evolutionary hemivariational inequality for the displacement field coupled with a time-dependent hemivariational inequality for the electric potential field. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of abstract second order evolutionary inclusions with monotone operators.