Percolation and localization in the random fuse model

TL;DR

This paper investigates damage evolution and localization in the random fuse model with strong disorder, revealing a transition from uncorrelated damage resembling percolation to abrupt localization leading to failure.

Contribution

It provides a detailed numerical analysis of damage nucleation, localization, and scaling laws in the random fuse model, highlighting the transition from percolation-like damage to catastrophic failure.

Findings

Damage initially evolves uncorrelated, similar to percolation.

Localization occurs abruptly from a uniform damage landscape.

Damage distribution follows a normal distribution on large scales.

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.