PENALTY METHOD FOR UNILATERAL CONTACT PROBLEM WITH COULOMB’S FRICTION FOR LOCKING MATERIAL

Abstract

In this work, we study a unilateral contact problem with non local friction of Coulomb<br />between a locking material and a rigid foundation. In the first step , we present the mathematical<br />model for a static process, we establish the variational formulation in the form of a variational<br />inequality and we prove the existence and uniqueness of the solution. In the second step, using<br />the penalty method we introduce the penalized problem numerical in the form of variational<br />equality where we replace the law behavior and the law contact of Sigorini . The we show the<br />convergence of the continuous penalty solution as the penalty parameter n tends towards infinity.<br />Then, the analysis of the finite element discretized penalty method is carried out.