Optimal control of a rigidity parameter of thin inclusions in elastic bodies with curvilinear cracks

The paper concerns an optimal control problem for a 2D elastic body with a thin rigid inclusion and a crack. Inequality type boundary conditions are imposed at the crack faces to provide a mutual non-penetration between the crack faces. The cost functional characterizes a derivative of the energy functional with respect to the crack length. A rigidity of the inclusion is considered as a control function. The main result consists in a proof of the solution existence to the optimal control problem.