Abstract
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 +/- 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 +/- 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. DOI:
10.1103/PhysRevLett.109.255701
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