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

5 Scopus citations

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

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Keywords

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

Fingerprint Dive into the research topics of 'On the quasistatic effective elastic moduli for elastic waves in three-dimensional phononic crystals'. Together they form a unique fingerprint.

  • Cite this