To the Theory of Formation of Large Cracks in Brittle Solids

Abstract

Model of formation of large cracks in brittle solids taking into account various space-time scales of crack accumulation during deformation is constructed. In the framework of the phase field method, a system of two coupled nonlinear parabolic equations which describes the deformation of a loaded medium during crack initiation is obtained on two spatial and time scales. The conditions at which a homogeneous distribution of cracks becomes instable are found. The development of the instability is accompanied by the formation of large cracks.