First-Order Transition in the Breakdown of Disordered Media

TL;DR

This paper investigates the failure process in disordered media under increasing force, revealing it as a first-order phase transition through mean-field theory and numerical simulations, with implications for understanding material breakdown.

Contribution

It introduces a mean-field theoretical framework for the breakdown in disordered media and confirms predictions with numerical simulations, highlighting the role of elastic interactions.

Findings

Failure process resembles a first-order phase transition.

Numerical simulations confirm mean-field predictions.

Elastic interactions lead to avalanche scaling.

Abstract

We study the approach to global breakdown in disordered media driven by increasing external forces. We first analyze the problem by mean-field theory, showing that the failure process can be described as a first-order phase transition, similarly to the case of thermally activated fracture in homogeneous media. Then we quantitatively confirm the predictions of the mean-field theory using numerical simulations of discrete models. Widely distributed avalanches and the corresponding mean-field scaling are explained by the long-range nature of elastic interactions. We discuss the analogy of our results to driven disordered first-order transitions and spinodal nucleation in magnetic systems.