Breakdown of fiber bundles with stochastic load-redistribution

TL;DR

This paper investigates the fracture behavior of fiber bundles with stochastic load redistribution, using integral equations to analyze different load-sharing rules and threshold distributions, bridging global and local load transfer mechanisms.

Contribution

It introduces a stochastic fiber-bundle model with random load redistribution after fiber failure, providing a Markov approximation and integral equation framework for analysis.

Findings

Breakdown properties depend on load redistribution rules and threshold distributions.

Model interpolates between global and local load sharing.

Comparison with existing models highlights differences in failure behavior.

Abstract

We study fracture processes within a stochastic fiber-bundle model where it is assumed that after the failure of a fiber, each intact fiber obtains a random fraction of the failing load. Within a Markov approximation, the breakdown properties of this model can be reduced to the solution of an integral equation. As examples we consider two different versions of this model that both can interpolate between global and local load redistribution. For the strength thresholds of the individual fibers, we consider a Weibull distribution and a uniform distribution, both truncated below a given initial stress. The breakdown behavior of our models is compared with corresponding results of other fiber-bundle models.