Protocol-dependent shear modulus of amorphous solids

TL;DR

This paper explores the shear response of amorphous solids, revealing two distinct shear moduli linked to different deformation protocols, and connects these findings to theoretical predictions in high-dimensional models.

Contribution

It identifies and measures two shear moduli in amorphous solids, linking their ratio to pressure near the jamming transition, supported by theoretical insights from infinite-dimensional models.

Findings

Two shear moduli, μ_ZFC and μ_FC, characterize amorphous solids.

The ratio μ_FC/μ_ZFC vanishes as the square root of pressure at jamming.

Results align with theoretical predictions from infinite-dimensional solutions.

Abstract

We investigate the linear elastic response of amorphous solids to a shear strain at zero temperature. We find that the response is characterized by at least two distinct shear moduli. The first one, $\mu_{\rm ZFC}$, is associated with the linear response of a single energy minimum. The second, $\mu_{\rm FC}$, is related to sampling, through plastic events, an ensemble of distinct energy minima. We provide examples of protocols that allow one to measure both shear moduli. In agreement with a theoretical prediction based on the exact solution in infinite spatial dimensions, the ratio $\mu_{\rm FC}/\mu_{\rm ZFC}$ is found to vanish proportionally to the square root of pressure at the jamming transition. Our results establish that amorphous solids are characterized by a rugged energy landscape, on which the infinite-dimensional solution can give useful insight.