VARIATIONAL AND NUMERICAL ANALYSIS OF THE SIGNORINI’S CONTACT PROBLEM IN VISCOPLASTICITY WITH DAMAGE

We consider the quasistatic Signorini’s contact problem with damage for elastic-viscoplastic bodies. The mechanical damage of the material, caused by excessive stress or strain, is described by a damage function whose evolution is modeled by an inclusion of parabolic type. We pro-vide a variational formulation for the mechanical problem and sketch a proof of the existence of a uniqueweak solution of themodel.We then in-troduce and study a fully discrete scheme for the numerical solutions of the problem. An optimal order error estimate is derived for the approx-imate solutions under suitable solution regularity. Numerical examples are presented to show the performance of the method. 1