A statistical model for ubiquitiformal crack extension in quasi-brittle materials

Considering the heterogeneity of real materials, a simple statistical model is proposed to describe a ubiquitiformal crack extension in quasi-brittle materials. The complexity of the ubiquitiformal crack is obtained by using the box-counting dimension. In the model, it is assumed that the crack propagates in the direction of the minimum energy dissipation and the heterogeneity of material properties is characterized by the Weibull distribution. The calculated numerical results of the complexity are found to be in good agreement with previous experimental data. Moreover, it is also verified that the complexity is uniquely determined by the Weibull distribution parameters, though the styles of crack extension in each computation are a little bit different from each other, due to the randomness of the spatial distribution of the material properties.