Thermally activated flow in models of amorphous solids

TL;DR

This paper investigates how thermal fluctuations influence the yielding transition in amorphous solids, providing analytical solutions and scaling laws that describe thermally activated flow across different models and simulations.

Contribution

It introduces a general scaling law for transition rounding due to thermal effects and validates it through analytical solutions and numerical simulations.

Findings

Analytical solution for thermally activated flow in HL model

Proposed a universal scaling law for transition rounding

Validated scaling law across multiple models and simulations

Abstract

Amorphous solids yield at a critical value $\Sigma_c$ of the imposed stress $\Sigma$ through a dynamical phase transition. While sharp in athermal systems, the presence of thermal fluctuations leads to the rounding of the transition and thermally activated flow even below $\Sigma_c$. Here, we study the steady state thermal flow of amorphous solids using a mesoscopic elasto-plastic model. In the Hebraud-Lequex (HL) model we provide an analytical solution of the thermally activated flow at low temperature. We then propose a general scaling law that also describes the transition rounding. Finally, we find that the scaling law holds in numerical simulations of the HL model, a 2D elasto-plastic model, and in previously published molecular dynamics simulations of 2D Lennard-Jones glass.