Effect of discontinuity in threshold distribution on the critical behaviour of a random fiber bundle

Abstract

The critical behaviour of a Random Fiber Bundle Model with mixed uniform distribution of threshold strengths and global load sharing rule is studied with a special emphasis on the nature of distribution of avalanches for different parameters of the distribution. The discontinuity in the threshold strength distribution of fibers non-trivially modifies the critical stress as well as puts a restriction on the allowed values of parameters for which the recursive dynamics approach holds good. The discontinuity leads to a non-universal behaviour in the avalanche size distribution for smaller values of avalanche size. We observe that apart from the mean field behaviour for larger avalanches, a new behaviour for smaller avalanche size is observed as a critical threshold distribution is approached. The phenomenological understanding of the above result is provided using the exact analytical result for the avalanche size distribution. Most interestingly,the prominence of non-universal behaviour in avalanche size distribution depends on the system parameters.

arXiv comment6 pages, 4 figures, text and figures modified

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Cited by in corpus (5)

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• Universality class of fiber bundles with strong heterogeneities
• Continuous Damage Fiber Bundle Model for Strongly Disordered Materials
• A random fiber bundle with many discontinuities in the threshold distribution
• Damage process of a fiber bundle with a strain gradient