Variability of mesoscopic mechanical disorder in disordered solids

TL;DR

This paper investigates the variability of mesoscopic mechanical disorder in disordered solids, introducing a quantifier $hi$ related to shear modulus fluctuations, revealing bounds and divergence near critical points.

Contribution

It defines and analyzes a universal measure of mechanical disorder in disordered solids, establishing bounds and behavior near unjamming transitions.

Findings

$hi$ has a lower bound in glassy solids.

$hi$ can diverge near the unjamming point.

Disorder quantification relates to elastic and plastic properties.

Abstract

Quantifying mechanical disorder in solids, either disordered crystals or glassy solids, and understanding its range of variability are of prime importance, e.g.~for discovering structure-properties relations. The bounds on the degree of mechanical fluctuations in disordered solids and how those depend on solids formation history remain unknown. Here, we study a broadly applicable quantifier of mesoscopic mechanical disorder $\chi$, defined via the dimensionless fluctuations of the shear modulus, over a wide variety of disordered computer solids and upon varying different control parameters. $\chi$ is intimately related to basic properties of disordered solids, such as elastic constants and plastic deformability, and can be experimentally extracted by wave-attenuation measurements. We find that a large variety of self-organized glassy solids, where disorder is an emergent property, appear to satisfy a generic lower bound on $\chi$. On the other hand, we show that $\chi$ is unbounded from above, and may diverge in systems driven towards the critical unjamming point. These results highlight basic properties of disordered solids and set the ground for systematically quantifying mechanical disorder across different systems.