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Micromechanics and Nanomechanics of Composite Solids pp 371–389Cite as

Effects of Local Spin on Overall Properties of Granule Materials

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Abstract

This paper proposes continuumnization of a set of rigid body spherical particles which are regularly arranged and connected by springs. Continuumnization converts translation and spin of all particles to spatially varying functions, together with derivation of material properties from spring constants. It is shown that a function of particles’ spin tends to vanish in the limit as the radius of the particles goes to zero. The governing equations of the functions of translation and spin are studied for a symmetric assembly of rigid body particles. The characteristic equation of the governing equations shows the presence of high-frequency modes of spin, as well as waves which correspond to P- and S-waves of ordinary continuum.

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Notes

  1. 1.

    Note that while the ordinary definition of the gradient is \((\boldsymbol{\nabla }\mathbf{u})_{ij} = \frac{\partial u_{i}} {\partial x_{j}}\), we define the gradient component in this way in order to make the expression of \(\boldsymbol{\nabla }\cdot \mathbf{n}\) consistent.

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Acknowledgements

This work was supported by JSPS KAKENHI Grant Number 25220908. Part of the results was obtained by using the K computer at the RIKEN Advanced Institute for Computational Science.

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Authors and Affiliations

  1. Earthquake Research Institute, The University of Tokyo, 1-1-1 Yayoi, Bunkyo, Tokyo, 113-0031, Japan

    Muneo Hori, Supprasert Sument, Lalith Wijerathne & Tsuyoshi Ichimura

  2. RIKEN Advanced Institute of Computational Science, 7-1-26 Minatoshima-Minami, Chuo, Kobe, Hyogo, 650-0047, Japan

    Jian Chen

Authors
  1. Muneo Hori
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  2. Jian Chen
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  3. Supprasert Sument
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  4. Lalith Wijerathne
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  5. Tsuyoshi Ichimura
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Correspondence to Muneo Hori .

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Editors and Affiliations

  1. Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada

    Shaker A. Meguid

  2. Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, New Jersey, USA

    George J Weng

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Hori, M., Chen, J., Sument, S., Wijerathne, L., Ichimura, T. (2018). Effects of Local Spin on Overall Properties of Granule Materials. In: Meguid, S., Weng, G. (eds) Micromechanics and Nanomechanics of Composite Solids. Springer, Cham. https://doi.org/10.1007/978-3-319-52794-9_13

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  • DOI: https://doi.org/10.1007/978-3-319-52794-9_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-52793-2

  • Online ISBN: 978-3-319-52794-9

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