Crossover behaviors in one and two dimensional heterogeneous load sharing fiber bundle models

TL;DR

This study investigates how heterogeneous load sharing affects fracture behavior in fiber bundle models, revealing a finite crossover point between local and global load sharing in 1D and 2D systems influenced by disorder percolation.

Contribution

It introduces a model combining local and global load sharing mechanisms and identifies a finite disorder threshold for crossover in 2D fiber bundle models.

Findings

Finite crossover point near p_c~0.53 in 2D systems

Critical behavior below p_c matches mean field predictions

Crossover driven by geometrical percolation of disorders

Abstract

We study the effect of heterogeneous load sharing in the fiber bundle models of fracture. The system is divided into two groups of fibers (fraction $p$ and $1-p$) in which one group follow the completely local load sharing mechanism and the other group follow global load sharing mechanism. Patches of local disorders (weakness) in the loading plate can cause such a situation in the system. We find that in 2d a finite crossover (between global and local load sharing behaviours) point comes up at a finite value of the disorder concentration (near $p_c\sim 0.53$), which is slightly below the site percolation threshold. We numerically determine the phase diagrams (in 1d and 2d) and identify the critical behavior below $p_c$ with the mean field behavior (completely global load sharing) for both dimensions. This crossover can occur due to geometrical percolation of disorders in the loading plate. We also show how the critical point depends on the loading history, which is identified as a special property of local load sharing.