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