Correlation between avalanches and emitted energies during fracture with variable stress release range

TL;DR

This study investigates how the correlation between avalanche sizes and emitted energies during fracture varies with stress release range in fiber bundle models, revealing different behaviors in 1D and 2D systems.

Contribution

It introduces a variable stress release range parameter in fiber bundle models and analyzes its impact on avalanche-energy correlation and distribution patterns.

Findings

In the mean-field limit, avalanche size and energy are highly correlated with a universal power-law distribution.

In 1D, correlation decreases with stress release range, leading to different distribution types for energy and size.

In 2D, high correlation persists, resulting in exponential distributions regardless of stress release range.

Abstract

We observe the failure process of a fiber bundle model with a variable stress release range, $\gamma$, higher the value of $\gamma$ lower the stress release range. By tuning $\gamma$ from low to high, it is possible to go from the mean-field (MF) limit of the model to local load sharing (LLS) where local stress concentration plays a crucial role. In the MF limit, the avalanche size $s$ and energy $E$ emitted during the avalanche are highly correlated producing the same distribution for both $P(s)$ and $Q(E)$: a scale-free distribution with a universal exponent -5/2. With increasing $\gamma$, the model enters the LLS limit. In this limit, due to the presence of local stress concentration such correlation $C(\gamma)$ between $s$ and $E$ decreases where the nature of the decreases depends highly on the dimension of the bundle. In 1d, the $C(\gamma)$ stars from a high value for low $\gamma$ and decreases towards zero when $\gamma$ is increased. As a result, $Q(E)$ and $P(s)$ are similar at low $\gamma$, an exponential one, and then $Q(E)$ becomes power-law for high-stress release range though $P(s)$ remains exponential. On the other hand, in 2d, the $C(\gamma)$ decreases slightly with $\gamma$ but remains at a high value. Due to such a high correlation, the distribution of both $s$ and $E$ is exponential in the LLS limit independent of how large $\gamma$ is.