Effective constitutive properties of a disordered elastic solid medium via the strong-fluctuation approach

Nickolay P. Zhuck, Akhlesh Lakhtakia

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

1 Unique Systems, Inc., 181 Don Park Road, Markham, Ontario, Canada L3R 1C2. A general scheme is developed for estimating the effective constitutive properties of a randomly disordered elastic solid medium. The presented methodology, already known in electromagnetics and acoustics, is based on renormalizing the conventional equations of motion. The resulting equations lend themselves to an approximate averaging procedure, which holds for strong fluctuations in the constitutive properties of the disordered medium provided the renormalization constants are chosen appropriately and the length-scales of the random perturbations are small. As an example, the homogenization of anisotropic spherical inclusions randomly dispersed in an isotropic host medium is considered, and the effective Lamé constants of the homogenized disordered medium evaluated and discussed.

Original languageEnglish (US)
Pages (from-to)543-566
Number of pages24
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume455
Issue number1982
DOIs
StatePublished - Jan 1 1999

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Disordered Media
Equations of motion
Acoustics
Fluctuations
Random Perturbation
Homogenization
Renormalization
Length Scale
Averaging
Ontario
Equations of Motion
Inclusion
isotropic media
homogenizing
Canada
roads
Methodology
equations of motion
estimating
inclusions

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

Cite this

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N2 - 1 Unique Systems, Inc., 181 Don Park Road, Markham, Ontario, Canada L3R 1C2. A general scheme is developed for estimating the effective constitutive properties of a randomly disordered elastic solid medium. The presented methodology, already known in electromagnetics and acoustics, is based on renormalizing the conventional equations of motion. The resulting equations lend themselves to an approximate averaging procedure, which holds for strong fluctuations in the constitutive properties of the disordered medium provided the renormalization constants are chosen appropriately and the length-scales of the random perturbations are small. As an example, the homogenization of anisotropic spherical inclusions randomly dispersed in an isotropic host medium is considered, and the effective Lamé constants of the homogenized disordered medium evaluated and discussed.

AB - 1 Unique Systems, Inc., 181 Don Park Road, Markham, Ontario, Canada L3R 1C2. A general scheme is developed for estimating the effective constitutive properties of a randomly disordered elastic solid medium. The presented methodology, already known in electromagnetics and acoustics, is based on renormalizing the conventional equations of motion. The resulting equations lend themselves to an approximate averaging procedure, which holds for strong fluctuations in the constitutive properties of the disordered medium provided the renormalization constants are chosen appropriately and the length-scales of the random perturbations are small. As an example, the homogenization of anisotropic spherical inclusions randomly dispersed in an isotropic host medium is considered, and the effective Lamé constants of the homogenized disordered medium evaluated and discussed.

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