Study of two quasistatic viscoplastic contact problems with adhesion

Abstract

We consider two quasistatic contact problems for viscoplastic materials. The contact is modeled with Signorini's condition in the first problem, and with normal compliance in the second one. In both problems the adhesion of the contact surfaces, caused by glue, is taken into account and the evolution of the bonding field is described by a first order differential equation. For each model, we provide the variational formulation, state a result on the existence of a unique weak solution, and indicate that the solution of the Signorini problem can be obtained as the limit of the solutions of the problem with normal compliance as the stiffness coefficient of the foundation tends to infinity. We also introduce and discuss a fully discrete scheme for solving the Signorini problem; under certain solution regularity assumptions, an optimal order error estimate holds. © Springer 2006.