Crack roughness and avalanche precursors in the random fuse model

TL;DR

This study uses large-scale simulations of the two-dimensional random fuse model to analyze crack roughness and avalanche precursors, revealing universal scaling behaviors and deviations from mean-field predictions.

Contribution

It demonstrates anomalous crack roughness scaling and universal avalanche size distributions, highlighting differences from mean-field models and lattice geometry effects.

Findings

Crack roughness exhibits anomalous scaling consistent with experiments.

Avalanche size distribution follows a power law with a universal cutoff.

Distribution exponent $ au$ exceeds mean-field value, with slight lattice dependence.

Abstract

We analyze the scaling of the crack roughness and of avalanche precursors in the two dimensional random fuse model by numerical simulations, employing large system sizes and extensive sample averaging. We find that the crack roughness exhibits anomalous scaling, as recently observed in experiments. The roughness exponents ($\zeta$, $\zeta_{loc}$) and the global width distributions are found to be universal with respect to the lattice geometry. Failure is preceded by avalanche precursors whose distribution follows a power law up to a cutoff size. While the characteristic avalanche size scales as $s_0 \sim L^D$, with a universal fractal dimension $D$, the distribution exponent $\tau$ differs slightly for triangular and diamond lattices and, in both cases, it is larger than the mean-field (fiber bundle) value $\tau=5/2$.