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

Journal Article (Journal Article)

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. © 2001 Elsevier Science Ltd. All rights reserved.

Full Text

Duke Authors

Cited Authors

  • Nadeau, JC; Ferrari, M

Published Date

  • October 12, 2001

Published In

Volume / Issue

  • 38 / 44-45

Start / End Page

  • 7945 - 7965

International Standard Serial Number (ISSN)

  • 0020-7683

Digital Object Identifier (DOI)

  • 10.1016/S0020-7683(00)00393-0

Citation Source

  • Scopus