Crossover behaviors in one and two dimensional heterogeneous load sharing fiber bundle models
Theoretical Condensed Matter Physics Division, Saha
Institute of Nuclear Physics, 1/AF,
Received in final form: 8 February 2013
Published online: 15 April 2013
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 follows the completely local load sharing mechanism and the other group follows 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 pc ∼ 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 pc 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.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2013