Statistical properties of fracture in a random spring model

TL;DR

This paper compares the fracture properties of a 2D random spring model with the scalar random fuse model through large-scale simulations, finding similar damage localization and scaling laws, thus validating scalar models for disordered fracture analysis.

Contribution

It demonstrates that scalar models like the random fuse model accurately capture the fracture behavior of more complex spring models in disordered systems.

Findings

Damage initially uniform and localizes at peak load

Scaling laws for damage density and fracture strength are similar in both models

Scalar models faithfully represent fracture properties of disordered systems

Abstract

Using large scale numerical simulations we analyze the statistical properties of fracture in the two dimensional random spring model and compare it with its scalar counterpart: the random fuse model. We first consider the process of crack localization measuring the evolution of damage as the external load is raised. We find that, as in the fuse model, damage is initially uniform and localizes at peak load. Scaling laws for the damage density, fracture strength and avalanche distributions follow with slight variations the behavior observed in the random fuse model. We thus conclude that scalar models provide a faithful representation of the fracture properties of disordered systems.