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A random fiber bundle with many discontinuities in the threshold distribution
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A random fiber bundle with many discontinuities in the threshold distribution
Uma Divakaran? and Amit Dutta?
Department of Physics, Indian Institute of Technology Kanpur - 208016, India
(Dated: July 31, 2008)
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 σ2i?2 and σ2i?1 where
1 ≤ i ≤ 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.
-
PACS numbers: 46.50. +a, 62.20.Mk, 64.60.Ht, 81.05.Ni
I. INTRODUCTION
What causes fracture of materials in nature? Are
there any precursor that signals the imminence of a com-
plete breakdown so that we can avoid them taking place?
These are few of the many questions that physicists and
engineers are looking at now a days to explore the frac-
ture dynamics of heterogeneous materials[1, 2]. A prior
knowledge of fail
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