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2021 | OriginalPaper | Chapter

3. A Two-Dimensional Lattice with Non-dense Packing of Particles

Authors : Vladimir I. Erofeev, Prof. Dr. Igor S. Pavlov

Published in: Structural Modeling of Metamaterials

Publisher: Springer International Publishing

Abstract

In this chapter, we consider a model of a granular medium as a rectangular lattice of rigid ellipse-shaped particles. Each particle of such a lattice possesses two translational and one rotational degrees of freedom. The space between the particles is a massless medium through which the force and coupled interactions are transmitted. In limiting cases, this model degenerates either into a chain of ellipse-shaped particles or into a square lattice of round particles. The main objectives of this chapter are to derive dynamic equations of a granular medium consisting of anisotropic particles and to identify the relationships between the physicomechanical properties of a granular material and the parameters of its microstructure. Using the results obtained in the chapter, it is possible to determine the elastic properties of an anisotropic nanocrystalline (granular) material with non-dense packing of particles by measuring the velocities of elastic waves propagating along different crystallographic directions [1].

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previous chapter A 2D Lattice with Dense Packing of the Particles

next chapter Application of the 2D Models of Media with Dense and Non-dense Packing of the Particles for Solving the Parametric Identification Problems

Magnon is a quasiparticle corresponding to a quantum of spin waves in magnetically ordered systems [20]. Magnon plays the same role with respect to spin vibrations as phonon plays with respect to crystal lattice vibrations.

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Title: A Two-Dimensional Lattice with Non-dense Packing of Particles
Authors: Vladimir I. Erofeev
Prof. Dr. Igor S. Pavlov
Publisher: Springer International Publishing
Book: Structural Modeling of Metamaterials
Print ISBN: 978-3-030-60329-8

Electronic ISBN: 978-3-030-60330-4

Copyright Year: 2021
DOI: https://doi.org/10.1007/978-3-030-60330-4_3