Configuration of a ubiquitiformal crack and its complexity

Based on the heterogeneity of real materials, a simple statistical model for the ubiquitiformal cracks extension was proposed to describe the configuration of aubiquitiformal crack (or the fracture surface) in brittle materials, and then the complexity of the ubiquitiformal crack was obtained by the box counting dimension. In the present model, it is assumed that the crack propagates always in the direction of the minimum dissipation of energy (successively estimated by the minimum strength, the minimum distance andthe minimum angle) and that the material properties obey the Weibull distribution. The numerical results of the complexity of the ubiquitiformal crack are found to be in good agreement with previous experimental data. Furthermore, it is also found that the complexity can be determined by the Weibull distribution parameters and be independent of the randomness or fluctuation of the ubiquitiformal crack configuration.