Evolution of Viscoelastic Contact Problems for Piezoelectric Materials with Adhesion

In this paper we consider a second order evolution inclusion with a coercive viscosity operator and a multivalued term of subdifferential form. The study is motivated by the dynamic problem of frictional contact between a viscoelastic piezoelectric deformable body and a foundation. The interaction between the body and the foundation is described, due to the skin effects, by a nonmonotone possibly multivalued law between the bonding forces and the corresponding displacements. This law is expressed by the Clarke subdifferential of a locally Lipschitz nonconvex nonsmooth superpotential and leads to a hemivariational inequality of hyperbolic type. Such inequality results from the d’Alembert principle for a dynamic mechanical system (1; 6).