A dynamic viscoelastic contact problem with normal compliance and damage

We consider a model for dynamic frictionless contact between a viscoelastic body and a foundation. The material constitutive relation is assumed to be nonlinear and the contact is modelled with the normal compliance condition. 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. 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. Finally, we report some numerical results in the simulation of two-dimensional test problems.