Variational study of a frictionless contact problem with electrical effects

Abstract

In this memoir, we study a contact problem for a viscoelastic material with electrical effects in a quasistatic process. The contact is modeled by a normal compliance and a frictionless contact condition. We present a variational formulation of the model and prove the existence and uniqueness of a weak solution. The proofs are based on the nonlinear equations involving monotone operators, as well as on fixed-point arguments. Finally, we prove the convergence of the problem's solution when we introduce a perturbation of certain data.