Interaction of cracks with bonds between their faces in an isotropic medium reinforced by a regular system of stringers

A problem of an elastic isotropic medium with a system of foreign (transverse with respect to crack alignment) rectilinear inclusions is considered. The medium is assumed to be attenuated by a periodic system of rectilinear cracks with zones where the crack faces interact with each other. These zones are assumed to be adjacent to the crack tips, and their sizes can be commensurable with the crack size. Interaction between the crack faces in the tip zone is modeled by introducing bonds (adhesion forces) between the cracks with a specified strain diagram. The boundary-value problem of the equilibrium of a periodic system of cracks with bonds between their faces under the action of external tensile loads and forces in the bonds is reduced to a nonlinear singular integrodifferential equation with a kernel of the Cauchy kernel type. The condition of critical equilibrium of the cracks with the tip zones is formulated with allowance for the criterion of critical tension of the bonds. A case of a stress state of the medium containing zones where the crack faces interact with each other is considered.