Optimization of fracture time prediction for solids using the concept of deformation hierarchy and loading history analysis

The paper develops a statistical model for fracture of a condensed medium, which is based on concepts of deformation and fracture hierarchy and self-similarity. The material volume is represented as a system of interacting structural elements organized by the fractal tree principle. The model is peculiar in the use of a numerical analytical method for calculating the probability distribution function for fracture times of a structural element. This allows obtaining the analytical function for hierarchical systems with a large number of elements. To consider the influence of disperse damage accumulation on fracture time of a system we propose a universal scheme of using information on fracture of unit elements and their influence on the freacture probability distribution density of the system on the whole. The method is illustrated by the calculation of fracture time probability for rocks under quasistatic loading.