Breakdown of fiber bundles with stochastic load-redistribution

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.
Comment: 10 pages, 7 figures