Local structure controls shear and bulk moduli in disordered solids

TL;DR

This paper develops a theoretical framework linking local orientational order to the shear and bulk moduli in disordered solids, explaining differences in elasticity between packings and networks, and matching experimental data.

Contribution

It provides a quantitative analytical connection between local microstructure and macroscopic elasticity in amorphous solids, addressing a key gap in understanding.

Findings

Local orientational order affects elasticity in packings and networks.

Packings exhibit less nonaffinity under compression, leading to lower G/K ratios.

The theory accurately describes experimental data on compressed emulsions.

Abstract

Paradigmatic model systems, which are used to study the mechanical response of matter, are random networks of point-atoms, random sphere packings, or simple crystal lattices, all of these models assume central-force interactions between particles/atoms. Each of these models differs in the spatial arrangement and the correlations among particles. In turn, this is reflected in the widely different behaviours of the shear (G) and compression (K) elastic moduli. The relation between the macroscopic elasticity as encoded in G, K and their ratio, and the microscopic lattice structure/order, is not understood. We provide a quantitative analytical connection between the local orientational order and the elasticity in model amorphous solids with different internal microstructure, focusing on the two opposite limits of packings (strong excluded-volume) and networks (no excluded-volume). The theory predicts that, in packings, the local orientational order due to excluded-volume causes less nonaffinity (less softness or larger stiffness) under compression than under shear. This leads to lower values of G/K, a well-documented phenomenon which was lacking a microscopic explanation. The theory also provides an excellent one-parameter description of the elasticity of compressed emulsions in comparison with experimental data over a broad range of packing fractions.