Effective conductivity and average polarizability of random polycrystals

Marco Avellaneda, Oscar Bruno

Research output: Contribution to journalArticlepeer-review


A third-order expansion for the effective thermal conductivity tensor K * of anisotropic polycrystalline cell materials is derived. The coefficients of the expansion are given in terms of the average polarizability tensor, a nondimensional quantity determined from the grain shape and crystallographic orientation distributions independent of other details of the microgeometry such as two (or more) particle correlation functions. Explicit numerical results for a wide variety of microgeometries made of ellipsoidal cells are obtained. This calculation uses a new method that exploits the symmetry properties of the effective conductivity tensor of a cell material as a function of the single-crystal conductivities.

Original languageEnglish (US)
Pages (from-to)2047-2056
Number of pages10
JournalJournal of Mathematical Physics
Issue number8
StatePublished - 1990

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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