Soumyajyoti Biswas, Bikas K. Chakrabarti
We study the effect of heterogeneous load sharing in the fiber bundle models of fracture. We divide the system into two groups of fibers (fraction p and 1-p) in which one group follow the completely local load sharing mechanism and the other follow global load sharing mechanism. We argue that patches of local disorders in the loading plate can cause such a situation. We find that in 2d a finite crossover point comes up near p_c~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). This crossover can occur due to geometrical percolation of disorders in the system and the critical point can get modified by occasional long range load transfer process. We also show how the critical point depends on the loading history, which is identified as a special property of local load sharing.
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http://arxiv.org/abs/1209.2569
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