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Fracturing highly disordered materials

We investigate the role of disorder on the fracturing process of heterogeneous materials by means of a two-dimensional fuse network model. Our results in the extreme disorder limit reveal that the backbone of the fracture at collapse, namely the subset of the largest fracture that effectively halts the global current, has a fractal dimension of $1.22 \pm 0.01$. This exponent value is compatible with the universality class of several other physical models, including optimal paths under strong disorder, disordered polymers, watersheds and optimal path cracks on uncorrelated substrates, hulls of explosive percolation clusters, and strands of invasion percolation fronts. Moreover, we find that the fractal dimension of the largest fracture under extreme disorder, $d_f=1.86 \pm 0.01$, is outside the statistical error bar of standard percolation. This discrepancy is due to the appearance of trapped regions or cavities of all sizes that remain intact till the entire collapse of the fuse network, but are always accessible in the case of standard percolation. Finally, we quantify the role of disorder on the structure of the largest cluster, as well as on the backbone of the fracture, in terms of a distinctive transition from weak to strong disorder characterized by a new crossover exponent.