Universality class of fiber bundles with strong heterogeneities
arXiv:0802.2695 · doi:10.1209/0295-5075/81/54005
Abstract
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<α<1 of fibers is unbreakable, while the remaining 1-αfraction is characterized by a distribution of breaking thresholds. Assuming global load sharing, we show analytically that there exists a critical fraction of the components α_c which separates two qualitatively different regimes of the system: below α_c the burst size distribution is a power law with the usual exponent τ=5/2, while above α_c the exponent switches to a lower value τ=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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