The fractal behaviour of crack propagation in brittle materials

In this paper we try to show how a reasonable equation for crack propagation in brittle materials naturally leads to self-affine or statistically self-similar failure structures. We argue that the fractal behaviours of crack propagation in brittle materials are in essence determined by the scale-invariance of the Fokker-Planck equation. This approach provides a good illustration for understanding the microscopic origin of fractal behaviour in real materials.