Phase-Interchange Relations

  • Salvatore Torquato
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 16)


We refer to expressions that link the effective properties of a two-phase heterogeneous material to the effective properties of the same microstructure but with the phases interchanged as phase-interchange relations. When such rigorous relations apply to a wide class of heterogeneous materials, they can provide useful tests of analytical and numerical estimates of the effective properties. We focus here on the effective conductivity and elastic moduli of two-phase composites and, to a lesser extent, of polycrystals. The two-dimensional relations are shown to have interesting implications for percolation behavior. Finally, we remark on phase-interchange relations for the trapping constant and fluid permeability.


Effective Property Shear Modulo Effective Conductivity Duality Relation Conductivity Tensor 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Salvatore Torquato
    • 1
  1. 1.Department of Chemistry and Princeton Materials InstitutePrinceton UniversityPrincetonUSA

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