Scaling, localization and anisotropy in fracturing central-force spring lattices with strong disorder

We analyze scaling and localization phenomena in the fracture of a random central-force spring lattice model with strong disorder by means of computer simulation. We investigate the statistical and topological properties of the developing damage pattern and the scaling behaviour of the threshold. Our observations show that from the beginning and up to the point of maximum stress, damage develops in a uniform manner, qualitatively like in a percolating lattice, but numerically different from random percolation. Beyond the maximum-stress point localization and anisotropy come into play, resulting in final crack formation. The fraction of broken bonds at which the lattice fails, as well as the strain corresponding to failure, scale with the lattice size via power laws. The roughness of the final crack scales as a power law of the crack length over three decades of lengthscale.