Scenarios for the quasistatic growth of a slightly curved and kinked crack

A variational-asymptotic model of the Griffith criterion for the development of a crack is constructed for a complex stress-strain state. It is assumed that the shear loads are much smaller than the breaking loads but the longitudinal loading of the crack is taken into account. Using asymptotic analysis, the problem of finding the minimum of the total energy of a body with a crack reduces to a sequence of algebraic equations, the solutions of which determine the form of the branch of the crack and its length as a function of a time-like dimensionless parameter. The absence of solutions is treated as a conversion of the fracture process to a dynamic stage and the impossibility of a quasistatic formulation of the problem. In particular, the application of shear and longitudinal loads just leads to an avalanche-type growth of the crack.