Avtandil Gachechiladze, Roland Gachechiladze

Unilateral Contact Problems for Homogeneous Hemitropic Elastic Solids with a Friction

In the present paper, we study a one-sided contact problem for a micropolar homogeneous elastic hemitropic medium with a friction. Here, on a part of the elastic medium surface with a friction, instead of a normal component of force stress there is prescribed the normal component of the displacement vector. We consider two cases, the so-called coercive case (when the elastic medium is fixed along some part of the boundary) and noncoercive case (without fixed parts). By using the Steklov-Poincaré operator, we reduce this problem to an equivalent boundary variational inequality. Based on our variational inequality approach, we prove the existence and uniqueness theorems for the weak solution. In the coercive case, the problem is unconditionally solvable, and the solution depends continuously on the data of the original problem. In the noncoercive case, we present in a closed-form the necessary condition for the existence of a solution of the contact problem. Under additional assumptions, this condition is also sufficient for the existence of a solution.

Mathematics Subject Classification: 35J86, 49J40, 74M10, 74M15

Key words and phrases: Elasticity theory, hemitropic solids, contact problem with a friction, boundary variational inequality