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 language | English (US) |
|---|---|
| Pages (from-to) | 7945-7965 |
| Number of pages | 21 |
| Journal | International Journal of Solids and Structures |
| Volume | 38 |
| Issue number | 44-45 |
| DOIs | |
| State | Published - Oct 12 2001 |
Keywords
- Hashin-Shtrikman bounds
- Material anisotropy parameters
- Zeroth-order bounds
ASJC Scopus subject areas
- Mechanical Engineering
- Mechanics of Materials