On the dynamic behaviour of a thermoviscoelastic body in frictional contact with a rigid obstacle

Abstract

We consider the dynamic behaviour of a thermoviscoelastic body which may come into frictional contact with a rigid obstacle. The frictional contact is modelled by general contact and friction laws which include as special cases the power law normal compliance condition and the corresponding generalization of Coulomb's law of dry friction. The stress-strain constitutive relation is assumed to be of Kelvin-Voigt type and the frictional heat generation on the contact surface is taken into account. In this setting we establish the existence of a solution to a weak version of the energy-elasticity system which consists of a parabolic equation coupled with a variational inequality.