Mixed variational formulation for frictional contact problem in electro-elasticity

Abstract

We consider a mathematical model that describes the frictional contact of a piezoelectric body with an electrically conductive foundation. The material’s behavior is described by means of an electroelastic constitutive law, the contact is bilateral and associated with Trescas law of dry friction. We derive a mixed variational formulation of the problem, which is in the form of a coupled system for the displacement field, the electric potential, and a Lagrange multiplier. Then we prove the existence of a unique weak solution to the model by combining saddle-point theory and the fixed-point technique. Moreover, we present an efficient algorithm for approximating the weak solution for the contact problem, including friction and electrical contact conditions. We conclude by a numerical example that illustrates the applicability of the model.