To the theory of formation of large cracks in brittle solids

A model of the large cracks formation in brittle solids is formulated taking into account different space-time scales of crack accumulation during deformation. Within the framework of the phase field method, a system of two coupled nonlinear parabolic equations is obtained that describe the deformation of a loaded medium during crack initiation on two spatial and temporal scales. The conditions are found under which the uniform distribution of cracks becomes unstable. The development of instability is accompanied by the formation of large cracks.