A boundary variational inequality approach to unilateral contact problems with friction for micropolar hemitropic solids

We investigate unilateral contact problems for micropolar hemitropic elastic solids. Our study includes Tresca friction (given friction model) along some parts of the boundary of the body. We equivalently reduce these problems to boundary variational inequalities 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. We treat also the case, when the body is not fixed, but only submitted to force and couple stress vectors along some parts of the boundary and is in unilateral frictional contact with a rigid foundation. In this situation we present necessary and sufficient conditions of solvability. Copyright © 2010 John Wiley & Sons, Ltd.