Exact Contrast Expansions

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


For two-phase media in which variations in the phase properties are small, formally exact perturbation series for both the effective conductivity (Beran 1968, Phan-Thien and Milton 1982) and effective elastic moduli (Beran 1968, Dederichs and Zeller 1973, Willis 1981) have been developed. Such weak-contrast expansions are found by first obtaining corresponding expansions of either the local electric field E(x) or the local strain field ε(x) via integral equations. For specificity, it is useful to state the weak-contrast form of the effective conductivity σe of a macroscopically isotropic medium, keeping in mind that analogous results exist for anisotropic media and for the effective elastic tensor.


Effective Conductivity Conductivity Tensor Stiffness Tensor Effective Shear Modulus Effective Bulk Modulus 
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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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