Critical behaviour of mixed random fibers, fibers on a chain and random graph

TL;DR

This paper investigates the critical failure behavior of various random fiber bundle models with different threshold distributions and load sharing rules, including mixed, Weibull, and fibers on a random graph, revealing how these factors influence critical stress.

Contribution

It introduces a mixed RFBM with a discontinuous threshold distribution and analyzes its critical behavior under global load sharing, also studying fibers on a random graph with local load sharing.

Findings

Critical stress depends on the distribution discontinuity measure.

Exact variation of critical stress with fiber number for uniform distribution.

Mean field critical behavior established for fibers on a random graph.

Abstract

We study random fiber bundle model (RFBM) with different threshold strength distributions and load sharing rules. A mixed RFBM within global load sharing scheme is introduced which consists of weak and strong fibers with uniform distribution of threshold strength of fibers having a discontinuity. The dependence of the critical stress of the above model on the measure of the discontinuity of the distribution is extensively studied. A similar RFBM with two types of fibers belonging to two different Weibull distribution of threshold strength is also studied. The variation of the critical stress of a one dimensional RFBM with the number of fibers is obtained for strictly uniform distribution and local load sharing using an exact method which assumes one-sided load transfer. The critical behaviour of RFBM with fibers placed on a random graph having co-ordination number 3 is investigated numerically for uniformly distributed threshold strength of fibers subjected to local load sharing rule, and mean field critical behaviour is established.