Analysis of a Contact Problem Modeled by Hemivariational Inequalities in Thermo-Piezoelectricity

Abstract

We study a quasistatic contact problem from both variational and numerical perspectives, focusing on a thermo-piezoelectric body interacting with an electrically and thermally rigid foundation. The contact is modeled with a normal damped response and unilateral constraint for the velocity field, associated with a total slip-dependent version of Coulomb’s law of dry friction. The electrical and thermal conditions on the contact surface are described by Clarke’s subdifferential boundary conditions. We formulate the problem’s weak form as a system combining a variational-hemivariational inequality with two hemivariational inequalities. Utilizing recent results in the theory of hemivariational inequalities, along with the fixed point method, we demonstrate the existence and uniqueness of the weak solution. Furthermore, we examine a fully discrete scheme for the problem employing the finite element method, and we establish error estimates for the approximate solutions.