A Thermo-Electro-Viscoelastic Contact Problem with Adhesion and Damage

Abstract. This paper is devoted to the study of the mathematical model involving a frictionless contact between an electro-elasto-viscoplastic body with thermal effects and a conductive adhesive foundation. The process is mechanically dynamic and electrically static. The contact is modeled with a normal compliance where the adhesion is taken into account and a regularized electrical conductivity condition. We derive a variational formulation of the problem and prove its unique weak solution. The proof is based on nonlinear evolution equations with monotone operators, differential equations and fixed point arguments.