Analysis of results for a quasistatic frictional contact problem with normal damped response in thermo-viscoelasticity

Abstract

In this manuscript, we explore a mathematical model that describes the quasistatic contact process with friction between a body governed by a nonlinear thermo-viscoelastic constitutive law and an obstacle. The contact is represented using a general condition for a normal damped response. We then develop a variational formulation for the mechanical problem and prove the existence of a weak solution. The proof is based on techniques involving variational inequalities, parabolic variational equality, and fixed-point methods. Finally, a perturbation of the data is introduced, and a convergence result is established as the perturbation parameter approaches zero.