### 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.

Original language | English (US) |
---|---|

Article number | 18724 |

Journal | Scientific Reports |

Volume | 6 |

DOIs | |

State | Published - Jan 6 2016 |

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### ASJC Scopus subject areas

- General

### Cite this

*Scientific Reports*,

*6*, [18724]. https://doi.org/10.1038/srep18724

**Local structure controls the nonaffine shear and bulk moduli of disordered solids.** / Schlegel, M.; Brujic, J.; Terentjev, E. M.; Zaccone, A.

Research output: Contribution to journal › Article

*Scientific Reports*, vol. 6, 18724. https://doi.org/10.1038/srep18724

}

TY - JOUR

T1 - Local structure controls the nonaffine shear and bulk moduli of disordered solids

AU - Schlegel, M.

AU - Brujic, J.

AU - Terentjev, E. M.

AU - Zaccone, A.

PY - 2016/1/6

Y1 - 2016/1/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84953242940&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84953242940&partnerID=8YFLogxK

U2 - 10.1038/srep18724

DO - 10.1038/srep18724

M3 - Article

VL - 6

JO - Scientific Reports

JF - Scientific Reports

SN - 2045-2322

M1 - 18724

ER -