Percolation and localization in the random fuse model

Abstract

We analyze damage nucleation and localization in the random fuse model with strong disorder using numerical simulations. In the initial stages of the fracture process, damage evolves in an uncorrelated manner, resembling percolation. Subsequently, as the damage starts to accumulate, current enhancement at the tips of the microcracks leads eventually to catastrophic failure. We study this behavior quantifying the deviations from percolation and discussing alternative scaling laws for damage. The analysis of damage profiles confirms that localization occurs abruptly starting from an uniform damage landscape. Finally, we show that the cumulative damage distribution follows the normal distribution, suggesting that damage is uncorrelated on large length scales.

Extended and revised version, including a new section, 21 pages and 19 figures. To appear in JSTAT

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• From Brittle to Ductile Fracture in Disordered Materials
• Rigidity percolation control of the brittle-ductile transition in disordered networks
• Fiber networks below the isostatic point: fracture without stress concentration
• Brittle to Ductile Transition in a Fiber Bundle with Strong Heterogeneity
• Crackling noise in paper peeling
• Size scaling of failure strength with fat-tailed disorder in a fiber bundle model
• Damage Growth in Random Fuse Networks
• Statistical Physics of Fracture Surfaces Morphology
• Usage leading to an abrupt collapse of connectivity
• Blending stiffness and strength disorder can stabilize fracture
• Stability in fiber bundle model : Existence of strong links and the effect of disorder