A convergence result in elastic-viscoplastic contact problems with damage

This work deals with the approximation of the contact problem for a viscoplastic material with the Signorini contact conditions by the problem with normal compliance, when the surface deformability coefficient converges to zero, i.e., when the surface stiffness tends to infinity, which represents a perfectly rigid obstacle. The possible damage of the material caused by compression or tension is taken into account. The approximate problem is formulated as a variational inequality and its convergence to the Signorin problem is proved. Then, the fully discrete scheme for the two problems is described and its convergence established. Results of numerical simulations, based on these schemes, are presented in one and two dimensions which show the convergence.