Avalanches in Breakdown and Fracture Processes

TL;DR

This paper studies how disordered materials break down under increasing forces, revealing avalanche phenomena and scaling laws that resemble spinodal nucleation, with implications for understanding fracture and electrical breakdown.

Contribution

It combines mean-field analysis with 2D simulations to characterize avalanche behavior and scaling laws in breakdown processes, linking them to spinodal nucleation.

Findings

Avalanche events precede breakdown in models.

Scaling laws describe avalanche size distributions.

Breakdown exhibits a first order transition.

Abstract

We investigate the breakdown of disordered networks under the action of an increasing external---mechanical or electrical---force. We perform a mean-field analysis and estimate scaling exponents for the approach to the instability. By simulating two-dimensional models of electric breakdown and fracture we observe that the breakdown is preceded by avalanche events. The avalanches can be described by scaling laws, and the estimated values of the exponents are consistent with those found in mean-field theory. The breakdown point is characterized by a discontinuity in the macroscopic properties of the material, such as conductivity or elasticity, indicative of a first order transition. The scaling laws suggest an analogy with the behavior expected in spinodal nucleation.