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