In the talk, we discuss the recent results related to the equilibrium
problems for elastic bodies with cracks and rigid inclusions. Cracks are
located on the boundaries of rigid inclusions. To prevent a mutual
penetration between crack faces, the inequality type boundary conditions
are considered at the crack faces. Solution existence for optimal control
problems is proved with a cost functional related to the rupture Griffith
criterion. We analyze also overlapping domain problems with cracks and
rigid inclusions.