Local structure controls the nonaffine shear and bulk moduli of disordered solids
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Schlegel, M., Brujic, J., Terentjev, E., & Zaccone, A. (2016). Local structure controls the nonaffine shear and bulk moduli of disordered solids. Scientific Reports https://doi.org/10.1038/srep18724
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.
This work was supported by the Theoretical Condensed Matter programme grant from EPSRC. M.S. thanks the Konrad-Adenauer-Stiftung for their financial support.
External DOI: https://doi.org/10.1038/srep18724
This record's URL: https://www.repository.cam.ac.uk/handle/1810/252766
Attribution 2.0 UK: England & Wales
Licence URL: http://creativecommons.org/licenses/by/2.0/uk/