Analysis of electro-visco-elastic contact problem with friction

Abstract

A quasistatic frictional contact problem is studied. The material behavior is modeled with a nonlinear electro-visco-elastic constitutive law, allowing piezoelectric effects. The body may come into contact with a rigid obstacle. Contact is described with the Signorini condition, a version of Coulomb's law of dry friction, and a regularized electrical conductivity condition. We derive a variational formulation of the problem, then, under a smallness assumption on the coefficient of friction, we prove an existence and uniqueness result of a weak solution for the model. The proof is based on arguments of elliptic variational inequalities and fixed points of operators.