Crossover behavior in a mixed-mode fiber bundle model

Abstract

We introduce a mixed-mode load sharing scheme in a fiber bundle model. This model reduces exactly to equal-load-sharing (ELS) and local-load-sharing (LLS) models at the two extreme limits of a single-load-sharing parameter. We identify two distinct regimes: (a) the mean-field regime where the ELS mode dominates and (b) the short-range regime dominated by the LLS mode. The crossover behavior is explored through a numerical study of the 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, the fiber bundle model shows crossover behavior from mean-field to short-range interactions.