R. Gachechiladze, J. Gwinner, D. Natroshvili

A Boundary Variational Inequality Approach to Unilateral Contact with Hemitropic Materials

abstract:
We study unilateral frictionless contact problems with hemitropic materials in the theory of linear elasticity. We model these problems as unilateral (Signorini type) boundary value problems, give their variational formulation as spatial variational inequalities, and transform them to boundary variational inequalities with the help of the potential method for hemitropic materials. Using the self-adjointness of the Steklov-Poincaré operator, we obtain the equivalence of the boundary variational inequality formulation and the corresponding minimization problem. Based on our variational inequality approach we derive existence and uniqueness theorems. Our investigation includes the special particular case of only traction-contact boundary conditions without prescribing the displacement and microrotation vectors along some part of the boundary of the hemitropic elastic body.

Mathematics Subject Classification: 35J85, 74A35, 49J40

Key words and phrases: Elasticity theory, hemitropic material, boundary variational inequalities, potential method, unilateral problems.