TY - JOUR

T1 - Effective conductivity of anisotropic two-phase composite media

AU - Sen, Asok K.

AU - Torquato, S.

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1989

Y1 - 1989

N2 - We derive a new perturbation expansion for the effective conductivity tensor e of a macroscopically anisotropic d-dimensional two-phase composite of arbitrary microstructure. The nth-order tensor coefficients ssAn(i) of the expansion (termed n-point microstructural parameters) are given explicitly in terms of integrals over the set of n-point probability functions (associated with the ith phase) which statistically characterize the microstructure. Macroscopic anisotropy arises out of some asymmetry in the microstructure, i.e., due to statistical anisotropy (e.g., a distribution of oriented, nonspherical inclusions in a matrix, layered media, such as sandstones and laminates, etc.). General and useful properties of the n-point microstructural parameters are established, and contact is made with the formal results of Milton. We then derive rigorous nth-order bounds on e (from our perturbation expansion) that depend upon the n-point parameters ssAn(i) for n=1, 2, 3, and 4. This is the first time that such bounds (for n>1) have been explicitly given in terms of the ssAn(i).

AB - We derive a new perturbation expansion for the effective conductivity tensor e of a macroscopically anisotropic d-dimensional two-phase composite of arbitrary microstructure. The nth-order tensor coefficients ssAn(i) of the expansion (termed n-point microstructural parameters) are given explicitly in terms of integrals over the set of n-point probability functions (associated with the ith phase) which statistically characterize the microstructure. Macroscopic anisotropy arises out of some asymmetry in the microstructure, i.e., due to statistical anisotropy (e.g., a distribution of oriented, nonspherical inclusions in a matrix, layered media, such as sandstones and laminates, etc.). General and useful properties of the n-point microstructural parameters are established, and contact is made with the formal results of Milton. We then derive rigorous nth-order bounds on e (from our perturbation expansion) that depend upon the n-point parameters ssAn(i) for n=1, 2, 3, and 4. This is the first time that such bounds (for n>1) have been explicitly given in terms of the ssAn(i).

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U2 - 10.1103/PhysRevB.39.4504

DO - 10.1103/PhysRevB.39.4504

M3 - Article

AN - SCOPUS:35949014049

VL - 39

SP - 4504

EP - 4515

JO - Physical Review B

JF - Physical Review B

SN - 0163-1829

IS - 7

ER -