Discrete Fracture Model with Anisotropic Load Sharing

TL;DR

This paper introduces a 2D discrete fracture model with anisotropic load sharing, analyzing how anisotropy influences macroscopic properties, critical stress, and failure avalanches, and finds that anisotropy does not alter the crossover point between load sharing regimes.

Contribution

It presents a novel anisotropic stress-transfer function in a 2D fracture model and investigates its effects on macroscopic behavior and failure statistics, extending understanding of load sharing.

Findings

Anisotropy does not change the crossover point γ_c=2 in 2D.

Global load sharing behavior approaches the ideal slowly for finite systems when γ ≤ 2.

The crossover value γ_c=2 remains the same as in the isotropic case.

Abstract

A two-dimensional fracture model where 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 2D. 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 $\gamma\le2$, the global load sharing behavior is approached very slowly.