Do Athermal Amorphous Solids Exist?

TL;DR

This paper investigates the elastic properties of amorphous solids, revealing that nonlinear elastic coefficients diverge in the thermodynamic limit, which questions the fundamental existence of elasticity in such materials.

Contribution

It demonstrates that nonlinear elastic coefficients in amorphous solids exhibit anomalous fluctuations and divergence, challenging the traditional concept of solidity at finite strains.

Findings

Shear modulus remains finite.

Higher-order nonlinear coefficients diverge in the thermodynamic limit.

Elasticity in amorphous solids is fundamentally linked to plasticity.

Abstract

We study the elastic theory of amorphous solids made of particles with finite range interactions in the thermodynamic limit. For the elastic theory to exist one requires all the elastic coefficients, linear and nonlinear, to attain a finite thermodynamic limit. We show that for such systems the existence of non-affine mechanical responses results in anomalous fluctuations of all the nonlinear coefficients of the elastic theory. While the shear modulus exists, the first nonlinear coefficient B_2 has anomalous fluctuations and the second nonlinear coefficient B_3 and all the higher order coefficients (which are non-zero by symmetry) diverge in the thermodynamic limit. These results put a question mark on the existence of elasticity (or solidity) of amorphous solids at finite strains, even at zero temperature. We discuss the physical meaning of these results and propose that in these systems elasticity can never be decoupled from plasticity: the nonlinear response must be very substantially plastic.