Percolation and localization in the random fuse model

We analyse 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 behaviour, quantifying the deviations from percolation and discussing alternative scaling laws for damage. The analysis of damage profiles confirms that localization occurs abruptly, starting from a uniform damage landscape. Finally, we show that the cumulative damage distribution follows the normal distribution, suggesting that damage is uncorrelated on large length scales.