Self-organized dynamics in local load sharing fiber bundle models

TL;DR

This paper investigates a 2D local load sharing fiber bundle model under slow external loading, revealing self-organized criticality with scale-free avalanche distributions and analytical insights into the mean-field limit.

Contribution

It introduces a detailed analysis of self-organized criticality in a local load sharing fiber bundle model, including analytical and numerical results for different load redistribution schemes.

Findings

Scale-free avalanche size distribution observed

Analytical estimates match numerical simulations in mean-field limit

Model exhibits self-organized criticality with stationary load per fiber

Abstract

We study the dynamics of a local load sharing fiber bundle model in two dimensions, under an external load (which increases with time at a fixed slow rate) applied at a single point. Due to the local load sharing nature, the redistributed load remains localized along the boundary of the broken patch. The system then goes to a self-organized state with a stationary average value of load per fiber along the (increasing) boundary of the broken patch (damaged region) and a scale free distribution of avalanche sizes and other related quantities are observed. In particular, when the load redistribution is only among nearest surviving fiber(s), the numerical estimates of the exponent values are comparable with those of the Manna model. When the load redistribution is uniform along the patch boundary, the model shows a simple mean-field limit of this self-organizing critical behaviour, for which we give analytical estimates of the saturation load per fiber values and avalanche size distribution exponent. These are in good agreement with numerical simulation results.