Transverse shear of an isotropic elastic medium in the case when the binder and inclusions are weakened by crack initiation

An elastic medium is considered, weakened by a doubly periodic system of round holes, filled with absolutely rigid inclusions, soldered along the bypass and has a crack initiation. The medium (binder) is weakened by two periodic systems of rectilinear crack initiation directed collinear to the abscissa and ordinate axes, and their sizes are not the same. General representations are constructed that describe a class of problems with a doubly periodic stress distribution outside circular holes and cracks under transverse shear. The analysis of the limiting equilibrium of cracks in the framework of the end zone model is carried out on the basis of a nonlocal fracture criterion with a force condition for the propagation of the crack tip and a deformation condition for determining the advancement of the edge of the end zone of the crack. Basic resolving equations are obtained in the form of infinite algebraic systems and three nonlinear singular integro-differential equations. The equations in each approximation were solved by the Gaussian method with the choice of the principal element for different values of the order of M, depending on the radius of the holes. Calculations were carried out to determine the forces in the connections of the end zones and the ultimate loads causing the growth of cracks.