On the homogenization of orthotropic elastic composites by the strong-property-fluctuation theory

Andrew J. Duncan, Tom G. Mackay, Akhlesh Lakhtakia

Research output: Contribution to journalArticlepeer-review

Abstract

The strong-property-fluctuation theory (SPFT) provides a general framework for estimating the constitutive parameters of a homogenized composite material (HCM). We developed the elastodynamic SPFT for orthotropic HCMs in order to undertake numerical studies. A specific choice of two-point covariance function-which characterizes the distributional statistics of the generally ellipsoidal particles that constitute the component materials-was implemented. Representative numerical examples revealed that the lowest-order SPFT estimate of the HCM stiffness tensor is qualitatively similar to the estimate provided by the Mori-Tanaka mean-field formalism, but the differences between the two estimates vary as the orthotropic nature of the HCM is accentuated. The second-order SPFT provides a correction to the lowest-order estimate of the HCM stiffness tensor and density. The correction, indicating effective dissipation due to scattering loss, increases as the HCM becomes less orthotropic but decreases as the correlation length becomes smaller.

Original languageEnglish
Pages (from-to)507-532
Number of pages26
JournalIMA Journal of Applied Mathematics
Volume74
Issue number4
DOIs
Publication statusPublished - Aug 2009

Keywords

  • homogenization
  • strong-property-fluctuation theory
  • metamaterials
  • Mori-Tanaka mean-field formalism
  • SELF-CONSISTENT MODEL
  • WAVE-PROPAGATION
  • ELLIPSOIDAL INCLUSIONS
  • PARTICULATE COMPOSITES
  • ELECTROMAGNETIC-WAVES
  • MULTIPLE-SCATTERING
  • RANDOM-MEDIA
  • MORI-TANAKA
  • MODULI
  • METAMATERIALS

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