Thin rigid inclusions with delaminations in elastic plates

In the paper, we propose an elastic plate model with delaminated thin rigid inclusions and provide mathematical analysis of the model. Both vertical and horizontal displacements of the plate are taken into account. It is assumed that the inclusion is delaminated which leads to an appearance of a crack. To provide a mutual non-penetration between crack faces we impose non-linear boundary conditions at the crack faces with unknown set of a contact. A correct problem formulation is proposed, and an existence of solutions is proved for different locations of the rigid inclusion inside of the elastic body.