Problem of equilibrium for hyperelastic body with rigid inclusion and non-penetrating crack

The paper deals with a solid body containing a rigid inclusion with a crack on its boundary. This body is assumed to be hyperelastic; therefore, we describe it within the framework of finite-strain theory. Moreover, we implement a non-interpenetration condition, which does not allow the opposite crack faces to penetrate each other. The main object of our research is energy minimization corresponding to the problem of equilibrium for the described body. By the use of variational methods, it is shown that this problem has a solution. Then we discuss a boundary value problem that is satisfied by the equilibrium solution.