A weakly curved inclusion in an elastic body with separation.

A problem with unknown boundary, which describes the equilibrium of a two-dimensional elastic body with a thin weakly curved inclusion, is studied. The inclusion can separate, thus producing a crack. Nonlinear boundary conditions are posed as inequalities on the crack shores so as to ensure the mutual nonpenetration of the shores. The unique solvability of the problem is proved. The problems of passing to the limit with respect to the thin inclusion rigidity are considered. In particular, a model is constructed by letting the rigidity parameter tend to infinity, and its properties are investigated. On the other hand, it is shown that the zero rigidity parameter of the inclusion exactly corresponds to the problem of equilibrium of an elastic body with a crack satisfying the boundary conditions of mutual nonpenetration of its shores. [ABSTRACT FROM AUTHOR]