Effective conductivity of anisotropic two-phase composite media

Asok K. Sen, S. Torquato

Research output: Contribution to journalArticlepeer-review

110 Scopus citations


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).

Original languageEnglish (US)
Pages (from-to)4504-4515
Number of pages12
JournalPhysical Review B
Issue number7
StatePublished - 1989
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics


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