Fractal dimension evolution of microcrack net in disordered materials

Fractal geometry is used to evaluate the degree of disorder of crack size distribution in brittle damaging materials. The fractal dimension of the 2D microcrack net turns out to increase from one to two during the loading process and microcrack propagation. This means that the material becomes more disordered with the damage evolution. The longer cracks, in fact, propagate more rapidly than the shorter and, at the same time, the crack size distribution increases its statistical dispersion. Some numerical examples, related to different initial microcrack densities and size distributions, are illustrated with the computer simulation of the system evolution.