Аннотация:

The paper is devoted to the study of the equilibrium problem for an elastic body containing a delaminated thin rigid inclusion with a local defect. The problem is considered in a domain with a cut, on the faces of which boundary conditions of the inequality type are specified. The statement uses a positive parameter characterizing the degree of damage of the inclusion at a point. The problem is formulated in the form of a variational inequality, from which a complete system of equations and inequalities is obtained, fulfilled in the domain with a cut, as well as on the crack line. Limit transitions are substantiated for the damage parameter and it is shown that the limiting cases correspond to problems of a thin rigid inclusion with a break, as well as a problem with a solid rigid inclusion without defects.