Optimal control of inclusions in an elastic body crossing the external boundary

The paper addresses optimal control of the elastic thin inclusions located in an elastic body and crossing the external boundary. The inclusions are assumed to delaminate, thus forming a crack between the inclusions and the matrix. We impose some nonlinear boundary conditions at the crack faces that do not allow the crack faces to penetrate into each other. We prove the solvability of optimal control problems in which the quality functional characterizes the displacement of the points of the elastic inclusions located outside the elastic body, and the length of the inclusions located inside the elastic body is the control function. The case is doscussed of the zero angle between the inclusions and the external boundary.