In this paper we consider an elastic medium weakened by a doubly periodic system of circular holes filled with absolutely rigid inclusions. The medium (binder) is weakened by two doubly periodic systems of rectilinear cracks with connections between the shores in the end zones. General concepts are constructed that describe a class of problems with a doubly periodic distribution of stresses outside circular holes and cracks under transverse shear. An analysis of the ultimate equilibrium of cracks in the framework of the model of the end zone is performed on the basis of a nonlocal fracture criterion with a force condition for the advance of the crack tip and a deformation condition for determining the advance of the edge of the end zone of the crack.
