Optimal control of rigidity parameters of thin inclusions in composite materials

In the paper, an equilibrium problem for an elastic body with a thin elastic and a volume rigid inclusion is analyzed.It is assumed that the thin inclusion conjugates with the rigid inclusion at a given point. Moreover, a delamination of the thininclusion is assumed. Inequality type boundary conditions are considered at the crack faces to prevent a mutual penetrationbetween the faces. A passage to the limit is justified as the rigidity parameter of the thin inclusion goes to infinity. Themain goal of the paper is to analyze an optimal control problem with a cost functional characterizing a deviation of thedisplacement field from a given function. A rigidity parameter of the thin inclusion serves as a control function. An existencetheorem to this problem is proved.