Numerical analysis and simulations of a dynamic frictionless contact problem with damage

The process of dynamic frictionless contact between a viscoelastic body and a reactive foundation, which includes material damage, is modelled, numerically analyzed, and simulated. Contact is modelled with the normal compliance condition. The damage of the material, resulting from tension or compression, is described by the damage field which measures the pointwise fractional decrease in the load carrying capacity of the material. The evolution of the damage is governed by a parabolic differential inclusion. A fully discrete scheme for the problem is proposed, and error estimates on the numerical solutions derived. The scheme has been implemented and numerical simulations of the evolution of the mechanical state of the system and its material damage are presented.