Relaxation dynamics in strained fiber bundles

TL;DR

This paper investigates the relaxation process of fiber bundles under load, analyzing how the number of failure steps depends on stress levels and identifying a universal critical divergence exponent.

Contribution

It provides a combined simulation and theoretical analysis of relaxation dynamics in fiber bundles, revealing a universal critical exponent for failure behavior.

Findings

Number of failure steps depends on applied stress and initial load

Critical divergence characterized by an exponent of -1/2

Universal behavior independent of fiber threshold distribution

Abstract

Under an applied external load the global load-sharing fiber bundle model, with individual fiber strength thresholds sampled randomly from a probability distribution, will relax to an equilibrium state, or to complete bundle breakdown. The relaxation can be viewed as taking place in a sequence of steps. In the first step all fibers weaker than the applied stress fail. As the total load is redistributed on the surviving fibers, a group of secondary fiber failures occur, etc. For a bundle with a finite number of fibers the process stops after a finite number of steps, $t$. By simulation and theoretical estimates, it is determined how $t$ depends upon the stress, the initial load per fiber, both for subcritical and supercritical stress. The two-sided critical divergence is characterized by an exponent -1/2, independent of the probability distribution of the fiber thresholds.