Non-Affine Displacements and the Non-Linear Response of a Strained Amorphous Solid

TL;DR

This paper shows that amorphous solids can exhibit yield behavior through reversible strains without irreversible reorganization, and that large strains can cause stress relaxation driven by non-affine motions.

Contribution

It reveals that yield in amorphous solids can occur reversibly and links non-affine motions to stress relaxation, challenging traditional views on irreversible structural changes.

Findings

Reversible strains can cause yield without irreversible reorganization.

Large strains lead to complete stress relaxation.

Rigidity depends on configurational space size, not sampling method.

Abstract

We demonstrate that irreversible structural reorganization is not necessary for the observation of yield behaviour in an amorphous solid. While the majority of solids strained to their yield point do indeed undergo an irreversible reorganization, we find a significant fraction of solids exhibit yield via a reversible strain. We also demonstrate that large instantaneous strains in excess of the yield stress can result in complete stress relaxation, a result of the large non-affine motions driven by the applied strain. The empirical similarity of the dependence of the ratio of stress over strain on the non-affine mean squared displacement with that for the shear modulus obtained from quiescent liquid at non-zero temperature supports the proposition that rigidity depends on the size of the sampled configurational space only, and is insensitive as to how this space is sampled.