On the relevance of disorder in athermal amorphous materials under shear

TL;DR

This paper investigates how structural disorder influences the behavior of sheared amorphous materials, revealing that its effects differ significantly between thermal and athermal systems at a mean-field level.

Contribution

It demonstrates that structural disorder impacts athermal and thermal amorphous systems differently, with disorder affecting the emergence of yield stress only in thermal models.

Findings

Disorder has no qualitative effect in the HL athermal model.

Disorder leads to a finite yield stress in thermal models like SGR.

Thermal and athermal systems exhibit different statistical mechanisms for yield stress emergence.

Abstract

We show that, at least at a mean-field level, the effect of structural disorder in sheared amorphous media is very dissimilar depending on the thermal or athermal nature of their underlying dynamics. We first introduce a toy model, including explicitly two types of noise (thermal versus athermal). Within this interpretation framework, we argue that mean-field athermal dynamics can be accounted for by the so-called H{\'e}braud-Lequeux (HL) model, in which the mechanical noise stems explicitly from the plastic activity in the sheared medium. Then, we show that the inclusion of structural disorder, by means of a distribution of yield energy barriers, has no qualitative effect in the HL model, while such a disorder is known to be one of the key ingredients leading kinematically to a finite macroscopic yield stress in other mean-field descriptions, such as the Soft-Glassy-Rheology model. We conclude that the statistical mechanisms at play in the emergence of a macroscopic yield stress, and a complex stationary dynamics at low shear rate, are different in thermal and athermal amorphous systems.