The development of composite materials with fine fibers necessitates modeling of equilibrium problems of elastic bodies containing fine inclusions. It is known that inclusions can delaminate and form a crack on the inclusion boundary. In this case, in simulations it is important to choose boundary conditions on the crack faces. In this paper, the inequalities that prevent mutual penetration of the crack faces are used as boundary conditions. In order to explore similar models, one can refer to monograph [1], where the corresponding bibliography is given. Note that the classical approach to the description of cracks in elastic bodies is characterized by linear boundary conditions of equalities on the crack faces [2, 3].
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