Elasticity in Amorphous Solids: Nonlinear or Piece-Wise Linear?

TL;DR

This paper argues that the elastic response of amorphous solids under strain is better described as piece-wise linear rather than nonlinear, emphasizing the importance of quenched versus annealed averages and a stress-dependent shear modulus.

Contribution

It challenges the common nonlinear expansion approach, proposing a piece-wise linear elastic model with a theoretical framework based on stress-dependent shear modulus.

Findings

Elastic response is piece-wise linear, not nonlinear.

Significant difference between quenched and annealed averages.

A stress-dependent shear modulus provides a useful description.

Abstract

Quasi-static strain-controlled measurements of stress vs strain curves in macroscopic amorphous solids result in a nonlinear looking curve that ends up either in mechanical collapse or in a steady-state with fluctuations around a mean stress that remains constant with increasing strain. It is therefore very tempting to fit a nonlinear expansion of the stress in powers of the strain. We argue here that at low temperatures the meaning of such an expansion needs to be reconsidered. We point out the enormous difference between quenched and annealed averages of the stress vs. strain curves, and propose that a useful description of the mechanical response is given by a stress (or strain) dependent shear modulus for which a theoretical evaluation exists. The elastic response is piece-wise linear rather than nonlinear.