Fiber Bundle model with Highly Disordered Breaking Thresholds

We present a study of the fiber bundle model using equal load sharing dynamics where the breaking thresholds of the fibers are drawn randomly from a power law distribution of the form \(p(b)\sim b^{-1}\) in the range \(10^{-\beta}\) to \(10^{\beta}\). Tuning the value of \(\beta\) continuously over...

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Bibliographic Details
Published in:arXiv.org 2015-02
Main Authors: Chandreyee Roy, Kundu, Sumanta, Manna, S S
Format: Article
Language:English
Subjects:
Avalanches
Breakdown
Breaking
Brittle materials
Bundling
Catastrophic failure analysis
Crossovers
Load sharing
Loads (forces)
Mathematical models
Power law
Thresholds
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Summary:We present a study of the fiber bundle model using equal load sharing dynamics where the breaking thresholds of the fibers are drawn randomly from a power law distribution of the form \(p(b)\sim b^{-1}\) in the range \(10^{-\beta}\) to \(10^{\beta}\). Tuning the value of \(\beta\) continuously over a wide range, the critical behavior of the fiber bundle has been studied both analytically as well as numerically. Our results are: (i) The critical load \(\sigma_c(\beta,N)\) for the bundle of size \(N\) approaches its asymptotic value \(\sigma_c(\beta)\) as \(\sigma_c(\beta,N) = \sigma_c(\beta)+AN^{-1/\nu(\beta)}\) where \(\sigma_c(\beta)\) has been obtained analytically as \(\sigma_c(\beta) = 10^\beta/(2\beta e\ln10)\) for \(\beta \geq \beta_u = 1/(2\ln10)\), and for \(\beta
ISSN:2331-8422
DOI:10.48550/arxiv.1502.05143