Universality class of fiber bundles with strong heterogeneities

Details Universality class of fiber bundles with strong heterogeneities Universality class of fiber bundles with strong heterogeneities

2008-02-19

arxiv.org/abs/0802.2695v1

EPL, 81 (2008) 54005

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1209/0295-5075/81/54005

We study the effect of strong heterogeneities on the fracture of disordered materials using a fiber bundle model. The bundle is composed of two subsets of fibers, i.e. a fraction 0<\alpha<1 of fibers is unbreakable, while the remaining 1-\alpha fraction is characterized by a distribution of breaking thresholds. Assuming global load sharing, we show analytically that there exists a critical fraction of the components \alpha_c which separates two qualitatively different regimes of the system: below \alpha_c the burst size distribution is a power law with the usual exponent \tau=5/2, while above \alpha_c the exponent switches to a lower value \tau=9/4 and a cutoff function occurs with a diverging characteristic size. Analyzing the macroscopic response of the system we demonstrate that the transition is conditioned to disorder distributions where the constitutive curve has a single maximum and an inflexion point defining a novel universality class of breakdown phenomena.

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