A Dynamic Electro-Elastic Viscoplastic Contact Problem with an Internal Variable

In this paper, we examine a dynamic contact problem involving an electro-elastic-viscoplastic body and a deformable base. The contact is characterized by an instantaneous normal response, and the behavior is described by an electro-elastic-viscoplastic law with an internal variable. We present both the mechanical and variational formulations of the problem, establishing the existence and uniqueness of the solution. Our proof relies on the theory of variational equations and fixed-point arguments.