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Macro-elasticity of granular materials composed of polyhedral particles

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Abstract

Particle shape variability is a key to understanding the rich behavior of granular materials. Polyhedra are among the most common particle shapes due to their ubiquitous origins in nature such as rock fragmentation and mineral crystallisation. Because of their faceted shape, polyhedral particles tend to assemble in jammed structures in which face-face and face-edge contacts between particles control the packing-level properties. In this paper, we use tri-periodic particle dynamics simulations to derive for the first time a generic analytical expression of the elastic moduli of polyhedral and spherical particle packings subjected to triaxial compression as a function of two contact network variables: (1) a “constraint number" that accounts for the face-face and edge-face contacts between polyhedra and is reduced to the coordination number in the case of spherical particles, and (2) the contact orientation anisotropy induced by compression. This expression accurately predicts the simulated evolution of elastic moduli during compression, revealing thereby the origins of the higher elastic moduli of polyhedral particle packings. We show that particle shape affects the elastic moduli through its impact on the contact network and the level of nonaffine particle displacements is the same for the simulated shapes. Its nearly constant value during compression underlies the constant values of our model parameters. By connecting the elastic moduli to the contact network through parameters that depend on particle shape, our model makes it possible to extract both the connectivity and anisotropy of granular materials from the knowledge of particle shape and measurements of elastic moduli.

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Acknowledgements

We warmly thank Carlos Santamarina for fruitful discussions. The authors acknowledge financial support by SIFCO project (CEA), EDF, and ORANO.

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Authors and Affiliations

  1. CEA, DES, IRESNE, DEC, SESC, LDOP, 13108, Saint Paul les Durance, France

    Duc Chung Vu & Lhassan Amarsid

  2. LMGC, CNRS, University of Montpellier, 34090, Montpellier, France

    Duc Chung Vu & Farhang Radjai

  3. IATE, INRAE, Institut Agro, University of Montpellier, 34000, Montpellier, France

    Jean-Yves Delenne

  4. 3SR, CNRS, University of Grenoble Alpes, 38400, Grenoble, France

    Vincent Richefeu

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  1. Duc Chung Vu
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Correspondence to Farhang Radjai.

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Vu, D.C., Amarsid, L., Delenne, JY. et al. Macro-elasticity of granular materials composed of polyhedral particles. Granular Matter 26, 6 (2024). https://doi.org/10.1007/s10035-023-01382-3

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