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.
Highlights
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
One of the overarching goals of solid state physics is to find a universal relationships between the lattice structure of matter in the solid state and its mechanical response
We showed that the mechanical response of solids is strongly affected by the degree of local orientational order of the lattice, whether fully enforced, low, or intermediate due to excluded-volume constraints in jammed packings)
Summary
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. 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. With the advent of computer simulations, it became clear that disordered solids, which are of paramount importance in many areas of technology and life sciences, cannot be described as perturbations about the crystalline order In this context, an unsolved problem is the striking difference in the elastic deformation behaviour of random networks and random packings. This means that packings have a comparatively larger bulk modulus, with respect to random networks, and remain well stable against compression near, at, and even below the critical coordination where shear rigidity vanishes This state of affairs has been revealed in simulation studies[2,4], at least since the 1970’s5. This leads to a significantly higher bulk modulus and a lower nonaffinity under compression
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