PROBABILISTIC MODELING OF MULTISCALE FRACTURE

Classical mechanics of fracture has accumulated extensive experimental data indicating the multiscale nature of fracture processes in materials. This has been reflected in the development of unified models of accumulation of damage and fracture. The process of formation of microdefects and subsequent fracture have a clearly expressed stochastic nature. For this reason a considerable interest in the problem of the construction of probabilistic hierarchical models of fracture has developed in recent time. In the present paper, we describe a hierarchical model of the fracture process in a discrete medium the elements of which possess stochastic strength properties. Time is eliminated from this model, which makes it possible to a certain extent to relate the model to "stochastic quasistatics." The relative simplicity of the "mechanical" component of this model is compensated for by the possibility of a rigorous analysis of it within the framework of probability-theoretical approaches. We obtained equations defining the microstrength of the system in questions in probabilistic terms. When investigating these equations, we use nonconventional methods, in particular, the renormalization group method. As a result of an asymptotic analysis, we identified a new class of scale-invariant (probabilistic) distributions of strength. In the present paper, we give a brief review of related models. Also, we describe the basic principles of the construction of models of stochastic fracture for discrete media. These principles have much in common with those of the theory of reliability of multielement systems with dependent failures.