A random fiber bundle with many discontinuities in the threshold distribution

Abstract

We study the breakdown of a random fiber bundle model (RFBM) with $n$-discontinuities in the threshold distribution using the global load sharing scheme. In other words, $n+1$ different classes of fibers identified on the basis of their threshold strengths are mixed such that the strengths of the fibers in the $i-th$ class are uniformly distributed between the values ${\sigma }_{2i-2}$ and ${\sigma }_{2i-1}$ where $1\le i\le n+1$. Moreover, there is a gap in the threshold distribution between $i-th$ and $i+1-th$ class. We show that although the critical stress depends on the parameter values of the system, the critical exponents are identical to that obtained in the recursive dynamics of a RFBM with a uniform distribution and global load sharing. The avalanche size distribution (ASD), on the other hand, shows a non-universal, non-power law behavior for smaller values of avalanche sizes which becomes prominent only when a critical distribution is approached. We establish that the behavior of the avalanche size distribution for an arbitrary $n$ is qualitatively similar to a RFBM with a single discontinuity in the threshold distribution ($n=1$), especially when the density and the range of threshold values of fibers belonging to strongest ($n+1$)-th class is kept identical in all the cases.

6 pages, 4 figures, Accepted in Phys. Rev. E

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Cited by in corpus (2)

• Failure Processes in Elastic Fiber Bundles
• Brittle to quasibrittle transition in a compound fiber bundle