On the quasistatic effective elastic moduli for elastic waves in three-dimensional phononic crystals

A. A. Kutsenko, A. L. Shuvalov, A. N. Norris

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Effective elastic moduli for 3D solid-solid phononic crystals of arbitrary anisotropy and oblique lattice structure are formulated analytically using the plane-wave expansion (PWE) method and the recently proposed monodromy-matrix (MM) method. The latter approach employs Fourier series in two dimensions with direct numerical integration along the third direction. As a result, the MM method converges much quicker to the exact moduli in comparison with the PWE as the number of Fourier coefficients increases. The MM method yields a more explicit formula than previous results, enabling a closed-form upper bound on the effective Christoffel tensor. The MM approach significantly improves the efficiency and accuracy of evaluating effective wave speeds for high-contrast composites and for configurations of closely spaced inclusions, as demonstrated by three-dimensional examples.

Original languageEnglish (US)
Pages (from-to)2260-2272
Number of pages13
JournalJournal of the Mechanics and Physics of Solids
Volume61
Issue number11
DOIs
StatePublished - Nov 1 2013

Fingerprint

Elastic waves
elastic waves
matrix methods
modulus of elasticity
Elastic moduli
Crystals
plane waves
crystals
expansion
Fourier series
numerical integration
Crystal lattices
inclusions
tensors
Tensors
anisotropy
Anisotropy
composite materials
coefficients
matrices

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Keywords

  • Effective moduli
  • Homogenization
  • Monodromy matrix
  • Plane-wave expansion

Cite this

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abstract = "Effective elastic moduli for 3D solid-solid phononic crystals of arbitrary anisotropy and oblique lattice structure are formulated analytically using the plane-wave expansion (PWE) method and the recently proposed monodromy-matrix (MM) method. The latter approach employs Fourier series in two dimensions with direct numerical integration along the third direction. As a result, the MM method converges much quicker to the exact moduli in comparison with the PWE as the number of Fourier coefficients increases. The MM method yields a more explicit formula than previous results, enabling a closed-form upper bound on the effective Christoffel tensor. The MM approach significantly improves the efficiency and accuracy of evaluating effective wave speeds for high-contrast composites and for configurations of closely spaced inclusions, as demonstrated by three-dimensional examples.",
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On the quasistatic effective elastic moduli for elastic waves in three-dimensional phononic crystals. / Kutsenko, A. A.; Shuvalov, A. L.; Norris, A. N.

In: Journal of the Mechanics and Physics of Solids, Vol. 61, No. 11, 01.11.2013, p. 2260-2272.

Research output: Contribution to journalArticle

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AU - Kutsenko, A. A.

AU - Shuvalov, A. L.

AU - Norris, A. N.

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