On discrete models in fracture mechanics

In two papers published in 1969, where the foundations of the theory of brittle fracture were laid, Valentin Valentinovich Novozhilov introduced a necessary and sufficient criterion for estimating the strength of an elastic body weakened by a cut and formulated the concept of brittle fracture. The criterion is based on taking account of the body discrete structure, and the fracture process is treated as loss of stability of elastic equilibrium. These two facts, fracture discreteness and loss of stability in the deformation of the breaking bond, underlie numerous phenomena, which could not be discovered in the framework of continuum mechanics. In the present paper, the following effects of taking these facts into account are briefly discussed: an unstable leg of the stress-strain diagram and the capture of part of the fracture energy by the lattice, the role of the lattice dimension, radiation in quasi-static and dynamic crack propagation including the radiation structure, the role of the dynamic factor, irregularities in the crack growth, crack propagation under the action of high-frequency waves including steady-state modes with periodically varying speed, and cracks in continuum discrete models.