On a dynamic contact problem for elastic-visco-plastic materials

In this paper, we study a mathematical problem for dynamic contact between an elastic-visco-plastic body and an obstacle. The contact is frictionless, modelled with a normal compliance condition involving adhesion effect of contact surfaces. Evolution of the bonding field is described by a first order differential equation. We provide a weak formulation of the contact problem, in the form of an integro-differential system, and present an existence and uniqueness result for its solution. We then introduce and study a fully discrete scheme for solving the problem. While it is possible to show the convergence of the scheme without assuming additional solution regularities, we focus on the derivation of optimal order error estimates under certain solution regularity assumptions.