Variational and Numerical Approaches to Contact Problems With Coulomb Friction in Thermoviscoelasticity

ABSTRACT In this work, we present a mathematical model that describes the quasistatic frictional contact between a thermoviscoelastic body and a conductive foundation. The contact is modeled using Signorini's conditions, and the friction is described by Coulomb's law. The existence and uniqueness of a weak solution are proven using the theory of first‐order evolution variational inequalities and the Banach fixed point theorem. Finally, we present numerical results for a two‐dimensional test problem to demonstrate the efficiency of the proposed algorithm.