Mean field fracture in disordered solids: statistics of fluctuations

TL;DR

This paper uses a mean-field model to analyze the transition between brittle and ductile failure in disordered solids, revealing how disorder variance and rigidity influence avalanche statistics and critical behavior.

Contribution

It introduces a mean-field framework to predict the brittle-ductile transition and explains the emergence of power law versus Gaussian avalanche distributions.

Findings

Brittle response shows power law avalanche distributions.

Ductile response exhibits Gaussian avalanche statistics.

Transition depends on disorder variance and elastic moduli.

Abstract

Power law distributed fluctuations are known to accompany \emph{terminal} failure in disordered brittle solids. The associated intermittent scale-free behavior is of interest from the fundamental point of view as it emerges universally from an intricate interplay of threshold-type nonlinearity, quenched disorder, and long-range interactions. We use the simplest mean-field description of such systems to show that they can be expected to undergo a transition between brittle and quasi-brittle (ductile) responses. While the former is characterized by a power law distribution of avalanches, in the latter, the statistics of avalanches is predominantly Gaussian. The realization of a particular regime depends on the variance of disorder and the effective rigidity represented by a combination of elastic moduli. We argue that the robust criticality, as in the cases of earthquakes and collapsing porous materials, indicates the self-tuning of the system towards the boundary separating brittle and ductile regimes.