Discrete fracture model with anisotropic load sharing

A two-dimensional fracture model in which the interaction among elements is modeled by an anisotropic stress-transfer function is presented. The influence of anisotropy on the macroscopic properties of the samples is clarified, by interpolating between several limiting cases of load sharing. Furthermore, the critical stress and the distribution of failure avalanches are obtained numerically for different values of the anisotropy parameter alpha and as a function of the interaction exponent gamma. From numerical results, one can certainly conclude that the anisotropy does not change the crossover point gamma(c) = 2 in two dimensions. Hence, in the limit of infinite system size, the crossover value gamma(c) = 2 between local and global load sharing is the same as the one obtained in the isotropic case. In the case of finite systems, however, for gamma <= 2, the global load sharing behavior is approached very slowly.