Penalty Method for an Unilateral Contact Problem with Coulomb's Friction for Locking Materials

Abstract.In this work, we study a unilateral contact problem with non local friction of Coulomb between a locking material and a rigid foundation. In the rst step, we present the mathematical model for a static process, we establish the variational formulation in the form of a variational inequality and we prove the existence and uniqueness of the solution. In the second step, using the penalty method we introduce the penalty numerical problem in the form of variational equality where we replace the law behavior and the law contact of Signorini. Then we show the convergence of the continuous penalty solution as the penalty parameter tends to innity. Then, the analysis of the nite element discretized penalty method is carried out.