On Existence and Uniqueness of the Solution of a Two-Surfaces Contact Problem Using a Fixed Point Approach

Abstract

In this work, we give the proof of the existence and uniqueness of the solution to the weak form of a two-surfaces contact problem using fixed point approach. We begin by modeling the evolution of a two deformable surfaces contact problem with a general viscoplastic law, the contact is considered frictionless and governed by the Signorini-type condition with an initial gap. Then, we derive the variational formulation of the classical problem. Finally, we conclude our work by establishing an existence and uniqueness theorem for the weak form.