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

TL;DR

This paper proves the existence and uniqueness of solutions for a two-surfaces contact problem modeled with viscoplastic law, using a fixed point approach and variational formulation.

Contribution

It introduces a novel fixed point method to establish existence and uniqueness for a complex contact problem with viscoplastic behavior.

Findings

Proved existence of solutions for the contact problem.

Established uniqueness of the solution.

Formulated the problem using variational methods.

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.