Statistical Physics of Elasto-Plastic Steady States in Amorphous Solids: Finite Temperatures and Strain Rates

TL;DR

This paper investigates how finite temperature and strain rate influence the statistical physics of plastic deformation in amorphous solids, identifying three regimes with distinct behaviors and proposing a scaling theory for data collapse.

Contribution

It introduces a comprehensive scaling theory that unifies the effects of temperature and strain rate on plastic deformation statistics in amorphous solids.

Findings

Identification of three temperature regimes with distinct plastic event statistics

Development of a scaling theory that collapses data across different temperatures and strain rates

Demonstration of the different physical mechanisms governing cross-over behaviors

Abstract

The effect of finite temperature $T$ and finite strain rate $\dot\gamma$ on the statistical physics of plastic deformations in amorphous solids made of $N$ particles is investigated. We recognize three regimes of temperature where the statistics are qualitatively different. In the first regime the temperature is very low, $T<T_{\rm cross}(N)$, and the strain is quasi-static. In this regime the elasto-plastic steady state exhibits highly correlated plastic events whose statistics are characterized by anomalous exponents. In the second regime $T_{\rm cross}(N)<T<T_{\rm max}(\dot\gamma)$ the system-size dependence of the stress fluctuations becomes normal, but the variance depends on the strain rate. The physical mechanism of the cross-over is different for increasing temperature and increasing strain rate, since the plastic events are still dominated by the mechanical instabilities (seen as an eigenvalue of the Hessian matrix going to zero), and the effect of temperature is only to facilitate the transition. A third regime occurs above the second cross-over temperature $T_{\rm max}(\dot\gamma)$ where stress fluctuations become dominated by thermal noise. Throughout the paper we demonstrate that scaling concepts are highly relevant for the problem at hand, and finally we present a scaling theory that is able to collapse the data for all the values of temperatures and strain rates, providing us with a high degree of predictability.