ABSTRACT
In this chapter we consider two quasistatic frictionless contact problems for a body made of an elastic-viscoplastic material. The mechanical damage of the material, caused by excessive stress or strain, is taken into account. In the first problem the contact is modeled with the Signorini condition and in the second one it is modelled with normal compliance. We provide variational formulations for the mechanical problems and sketch the proof of the existence of a unique weak solution to each one of the models. We also introduce and study a fully discrete scheme for the numerical solutions of the problems and, under suitable assumption on the regularity of the solution, we derive optimal order error estimates. Moreover, we prove that the solution of the Signorini problem can be obtained as the limit of the solutions of the problem with normal compliance when the stiffness coeficient of the foundation tends to infinity.
