Contact problems with friction for hemitropic solids: boundary variational inequality approach

TL;DR

This paper develops a boundary variational inequality framework for contact problems with friction in hemitropic elastic solids, proving existence, uniqueness, and continuous dependence of solutions.

Contribution

It introduces a novel boundary variational inequality approach for frictional contact problems in hemitropic solids, establishing key theoretical results.

Findings

Existence and uniqueness of weak solutions are proven.

Solutions depend continuously on problem data and friction coefficient.

Necessary and sufficient conditions for solvability are established for interior problems.

Abstract

We study the interior and exterior contact problems for hemitropic elastic solids. We treat the cases when the friction effects, described by Tresca friction (given friction model), are taken into consideration either on some part of the boundary of the body or on the whole boundary. We equivalently reduce these problems to a boundary variational inequality with the help of the Steklov-Poincar'e type operator. Based on our boundary variational inequality approach we prove existence and uniqueness theorems for weak solutions. We prove that the solutions continuously depend on the data of the original problem and on the friction coefficient. For the interior problem necessary and sufficient conditions of solvability are established when friction is taken into consideration on the whole boundary.