Variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance, friction and damage

We consider a model for quasistatic frictional contact between a viscoelastic body and a foundation. The material constitutive relation is assumed to be nonlinear. The mechanical damage of the material, caused by excessive stress or strain, is described by the damage function, the evolution of which is determined by a parabolic inclusion. The contact is modeled with the normal compliance condition and the associated version of Coulombʹs law of dry friction. We derive a variational formulation for the problem and prove the existence of its unique weak solution. We then study a fully discrete scheme for the numerical solutions of the problem and obtain error estimates on the approximate solutions.