Self-Organized Criticality in a Fibre-Bundle type model

TL;DR

This paper investigates a fibre-bundle model with load sharing, demonstrating that under certain conditions it self-organizes into a critical state characterized by power-law distributed avalanches, revealing insights into failure dynamics.

Contribution

It introduces a novel load transfer mechanism and shows how the system self-organizes into a critical state with a specific avalanche size distribution exponent.

Findings

Avalanche size distribution follows a power law with exponent ~1.5.

System reaches a self-organized critical state under certain conditions.

Internal transfer mechanism influences critical behavior.

Abstract

The dynamics of a fibre-bundle type model with equal load sharing rule is numerically studied. The system, formed by N elements, is driven by a slow increase of the load upon it which is removed in a novel way through internal transfers to the elements broken during avalanches. When an avalanche ends, failed elements are regenerated with strengths taken from a probability distribution. For a large enough N and certain restrictions on the distribution of individual strengths, the system reaches a self-organized critical state where the spectrum of avalanche sizes is a power law with an exponent $\tau\simeq 1.5$.