Cooperative dynamics in the Fiber Bundle Model

TL;DR

This paper reviews the cooperative failure dynamics in the Fiber Bundle Model, focusing on equal-load-sharing mechanisms and their analytical and simulation insights.

Contribution

It provides a concise review of analytical developments and simulation comparisons in the Fiber Bundle Model with equal-load-sharing failure dynamics.

Findings

Mean-field load-sharing simplifies analysis

Analytical results match simulation data

Insights into failure progression in fiber bundles

Abstract

We discuss the cooperative failure dynamics in the Fiber Bundle Model where the individual elements or fibers are Hookean springs, having identical spring constant but different breaking strengths. When the bundle is stressed or strained, especially in the equal-load-sharing scheme, the load supported by the failed fiber gets shared equally by the rest of the surviving fibers. This mean-field type statistical feature (absence of fluctuations) in the load-sharing mechanism helped major analytical developments in the study of breaking dynamics in the model and precise comparisons with simulation results. We intend to present a brief review on these developments.