On optimal zeroth-order bounds with application to Hashin-Shtrikman bounds and anisotropy parameters

J. C. Nadeau, M. Ferrari

Research output: Contribution to journalArticle

23 Scopus citations

Abstract

A new result presented in this paper is the evaluation of the Hashin-Shtrikman bounds for composites composed of arbitrarily anisotropic constituents. To date, evaluation of the Hashin-Shtrikman bounds are limited to composites with isotropic constituents or to polycrystalline composites with specific crystal symmetries. The generality of the exact result presented herein is achieved through a reinterpretation of Kröner's (J. Mech. Phys. Solids 25 (1977) 137) recursive relations for nth-order bounds and the optimal zeroth-order (n = 0) bound. The definitions of optimal zeroth-order bounds are extended to all even-ordered tensors and procedures are presented to evaluate these bounds for all second-and fourth-order tensors. While optimal zeroth-order bounds are not new, the ability to calculate them for fourth-order tensors of arbitrary symmetry is new. Utilizing the zeroth-order bounds, material anisotropy parameters are defined which quantity the extent of anisotropy for even-ordered tensors.

Original languageEnglish (US)
Pages (from-to)7945-7965
Number of pages21
JournalInternational Journal of Solids and Structures
Volume38
Issue number44-45
DOIs
StatePublished - Oct 12 2001

Keywords

  • Hashin-Shtrikman bounds
  • Material anisotropy parameters
  • Zeroth-order bounds

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials

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