Revisit on the fractal dimension in damage and fracture

Abstract

The catastrophic failure of materials is a complicated process, involving the nucleation, growth and coalescence of numerous cracks with a wide range of time and length scales. In this paper, the variation of fractal dimension and entropy during a damage evolution process, especially in the vicinity of a critical failure, is revisited. The results show that, as damage evolves, both the fractal dimension and entropy of the spatial distribution of microcracks decrease. A sudden drop of fractal dimension or entropy can be viewed as a likely precursor of fracture and its implications for the prediction of natural disasters such as mining-induced rock bursts and earthquakes are discussed.