Some fractal models of fracture

The paper deals with applications of fractal geometry methods to problems of fracture in brittle and quasibrittle materials. Possible ways to construct models, taking into account the fractal properties of the phenomenon, are discussed. It is shown that classical approaches do not work in fractal fracture and lead to the paradoxical conclusion that fractal cracking is impossible. Some new concepts appropriate for fractal fracture are introduced. In particular, the concept of specific energy-absorbing capacity for a unit of a fractal measure of a fractal set is considered. It is shown that fractal properties of a fractal pattern of microcracks can characterize the fracture energy of polyphase materials such as rock, concrete, ceramics, etc., and that fractal properties of the main crack surface can be inessential.