Analysis and numerical treatment of a thermo-electro-visoplastic frictional contact problem with adhesion and internal states variable

Abstract

We consider a frictional contact problem between a thermo-electro-viscoplastic body and a conductive foundation. The contact is frictional; it is modeled with normal compliance, and the adhesion of the contact surfaces is taken into account. The material has internal state variables. We derive a variational formulation for the model and prove the existence of a unique weak solution to the problem. The proof is based on results for elliptic variational inequalities, differential equations, and fixed-point theory. Finally, we present a finite element algorithm to approximate solutions to our problem and provide an error estimate for these approximations.