Universal non-Debye low-frequency vibrations in sheared amorphous solids

TL;DR

This paper investigates low-frequency vibrational modes in sheared amorphous solids, revealing stress-dependent regimes and universal power-law behaviors near plastic events, advancing understanding of amorphous material mechanics.

Contribution

It uncovers stress-sensitive low-frequency vibrational regimes and universal scaling laws in amorphous solids near plasticity, which were not previously characterized.

Findings

Shear-stabilized ensembles show a $D(9) \u2208 9^5$ regime.

Near plastic events, the eigenvalue distribution scales with 9_P - 9, exhibiting a 9^6 power-law.

Universal properties of the Hessian eigenvalues are characterized near plasticity.

Abstract

We study energy minimized configurations of amorphous solids with a simple shear degree of freedom. We show that the low-frequency regime of the vibrational density of states of structural glass formers is crucially sensitive to the stress-ensemble from which the configurations are sampled. In both two and three dimensions, a shear-stabilized ensemble displays a $D(\omega_{\min}) \sim \omega^{5}_{\min}$ regime, as opposed to the $\omega^{4}_{\min}$ regime observed under unstrained conditions. We also study an ensemble of two dimensional, strained amorphous solids near a plastic event. We show that the minimum eigenvalue distribution at a strain $\gamma$ near the plastic event occurring at $\gamma_{P}$, displays a collapse when scaled by $\sqrt{\gamma_P - \gamma}$, and with the number of particles as $N^{-0.22}$. Notably, at low-frequencies, this scaled distribution displays a robust $D(\omega_{\min}) \sim \omega^{6}_{\min}$ power-law regime, which survives in the large $N$ limit. Finally, we probe the universal properties of this ensemble through a characterization of the second and third eigenvalues of the Hessian matrix near a plastic event.