MICROMECHANICS AND EFFECTIVE MODULI OF ELASTIC COMPOSITES CONTAINING RANDOMLY DISPERSED ELLIPSOIDAL INHOMOGENEITIES

被引:252
作者
JU, JW
CHEN, TM
机构
[1] Department of Civil Engineering and Operations Research, Princeton University, Priceton, 08 544, NJ
关键词
D O I
10.1007/BF01180221
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
A micromechanical framework is proposed to investigate effective mechanical properties of elastic multiphase composites containing many randomly dispersed ellipsoidal inhomogeneities. Within the context of the representative volume element (RVE), four governing micromechanical ensemble-volume averaged field equations are presented to relate ensemble-volume averaged stresses, strains, volume fractions, eigenstrains, particle shapes and orientations, and elastic properties of constituent phases of a linear elastic particulate composite. A renormalization procedure is employed to render absolutely convergent integrals. Therefore, the micromechanical equations and effective elastic properties of a statistically homogeneous composite are independent of the shape of the RVE. Various micromechanical models can be developed based on the proposed ensemble-volume averaged constitutive equations. As a special class of models, inter-particle interactions are completely ignored. It is shown that the classical Hashin-Shtrikman bounds, Walpole's bounds, and Willi's bounds for isotropic or anisotropic elastic multiphase composites are related to the ''noninteracting'' solutions. Further, it is demonstrated that the Mori-Tanaka method coincides with the Hashin-Shtrikman bounds and the ''noninteracting'' micromechanical model in some cases. Specialization to unidirectionally aligned penny-shaped microcracks is also presented. An accurate, higher order (in particle concentration), probabilistic pairwise particle interaction formulation coupled with the proposed ensemble-volume averaged equations will be presented in a companion paper.
引用
收藏
页码:103 / 121
页数:19
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