Dynamic frictional thermoviscoelastic contact problem with normal compliance and damage

Abstract

We study a dynamic problem describing the frictional contact between a thermoviscoelastic body and a foundation. The thermoviscoelastic constitutive law includes a damage effect described by the parabolic inclusion with the homogeneous Neumann boundary condition and a temperature effect described by the first order evolution equation. The contact is modeled with normal compliance condition with friction. We present a variational formulation of the problem and establish an existence and uniqueness of the weak solution. The proof is based on parabolic variational inequalities of first and second kind, first order evolutionary variational equations and fixed point arguments.