Crossover behavior in a mixed mode fiber bundle model

Abstract

We introduce a mixed-mode load sharing scheme in fiber bundle model. This model reduces exactly to equal load sharing (ELS) and local load sharing (LLS) models at the two extreme conditions of the load sharing rule. We identify two distinct regimes: a) Mean-field regime where ELS mode dominates and b) short range regime dominated by LLS mode. The crossover behavior is explored through the numerical study of strength variation, the avalanche statistics, susceptibility and relaxation time variations, the correlations among the broken fibers and their cluster analysis. Analyzing the moments of the cluster size distributions we locate the crossover point of these regimes. We thus conclude that even in one dimension, fiber bundle model shows crossover behavior from mean-field to short range interactions.