Criticality in the approach to failure in amorphous solids

TL;DR

This paper proposes that amorphous solids are critical throughout the entire stress range below failure, with system-spanning plastic events whose size diverges at failure, challenging the idea that criticality only occurs at the failure point.

Contribution

It introduces a new perspective that amorphous solids exhibit critical behavior across all stress levels below failure, supported by elastoplastic model validation.

Findings

Plastic rearrangements are system-spanning and diverge at failure.

The stability exponent $ heta$ varies continuously with stress.

Predictions are confirmed in elastoplastic models.

Abstract

Failure of amorphous solids is fundamental to various phenomena, including landslides and earthquakes. Recent experiments indicate that highly plastic regions form elongated structures that are especially apparent near the maximal shear stress $\Sigma_{\max}$ where failure occurs. This observation suggested that $\Sigma_{\max}$ acts as a critical point where the length scale of those structures diverges, possibly causing macroscopic transient shear bands. Here we argue instead that the entire solid phase ($\Sigma<\Sigma_{\max}$) is critical, that plasticity always involves system-spanning events, and that their magnitude diverges at $\Sigma_{\max}$ independently of the presence of shear bands. We relate the statistics and fractal properties of these rearrangements to an exponent $\theta$ that captures the stability of the material, which is observed to vary continuously with stress, and we confirm our predictions in elastoplastic models.