Time Scales in the Theory of Elasto-Plasticity of Amorphous Solids

TL;DR

This paper investigates the different time scales involved in elasto-plasticity of amorphous solids, revealing that stress and configurational variables often relax on distinct time scales, challenging current assumptions.

Contribution

It demonstrates through simulations that stress and configurational degrees of freedom in amorphous solids relax on different time scales, providing new insights into macroscopic elasto-plasticity theories.

Findings

Configurational variables can reach steady state on different time scales from stress.

Numerical simulations in 2D and 3D support the distinct relaxation times.

Current theories assuming same time scale for stress and configurational variables are incomplete.

Abstract

Developing a macroscopic theory of elasto-plasticity in amorphous solids calls for (i) identifying the relevant macro state-variables and (ii) discriminating the different time-scales which characterize these variables. In current theories it is assumed that the stress reaches its elasto-plastic steady state value on the same time-scale as the configurational variables (be they the configurational energy, configurational entropy or the effective temperature). By examining numerical simulations in two and three dimensions we show that this is generally not the case, the configurational degrees of freedom may reach the elasto-plastic steady state on the time scales which can be very different from the time scale of the stress. We provide a physical discussion to rationalize these findings.