Mean field description of aging linear response in athermal amorphous solids

TL;DR

This paper develops an analytical mean field model to describe aging linear response in athermal amorphous solids, revealing universal scaling laws and validating them with computer simulations.

Contribution

It introduces a universal mean field framework for aging response in amorphous solids, including new scaling laws for stress relaxation.

Findings

Stress relaxes to an age-dependent plateau with a timescale growing with age.

Universal scaling exponents are independent of the noise spectrum exponent.

Simulation results agree well with theoretical predictions.

Abstract

We study the linear response to strain in a mean field elastoplastic model for athermal amorphous solids, incorporating the power-law mechanical noise spectrum arising from plastic events. In the "jammed" regime of the model, where the plastic activity exhibits a non-trivial slow relaxation referred to as aging, we find that the stress relaxes incompletely to an age-dependent plateau, on a timescale which grows with material age. We determine the scaling behaviour of this aging linear response analytically, finding that key scaling exponents are universal and independent of the noise exponent $\mu$. For $\mu>1$, we find simple aging, where the stress relaxation timescale scales linearly with the age $t_{\rm w}$ of the material. At $\mu=1$, which corresponds to interactions mediated by the physical elastic propagator, we find instead a $t_{\rm w}^{1/2}$ scaling arising from the stretched exponential decay of the plastic activity. We compare these predictions with measurements of the linear response in computer simulations of a model jammed system of repulsive soft athermal particles, during its slow dissipative relaxation towards mechanical equilibrium, and find good agreement with the theory.