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

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–Poincaré 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.

Keywords:

• elasticity theory
• hemitropic solid
• contact problem with given friction
• Tresca friction
• boundary variational inequality

AMS Subject Classifications::

• 35J86
• 47A50
• 74A35
• 74M10
• 74M15

Acknowledgements

This research was supported by the Georgian National Science Foundation (GNSF) grant No. GNSF/ST07/3-170.