Effective conductivity in isotropic heterogeneous media using a strong-contrast statistical continuum theory

A. Mikdam, A. Makradi, Said Ahzi, H. Garmestani, D. S. Li, Y. Remond

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37 Citations (Scopus)


The strong-contrast formulation is used to predict the effective conductivity of a porous material. The distribution, shape and orientation of the two phases are taken into account using two- and three-point probability distribution functions. A new approximation for the three-point probability function appropriate for two-phase media is proposed and discussed. Computed results for the effective conductivity using the strong-contrast formulation are compared to the Voigt and the Hashin-Shtrikman upper-bound estimates. These results show that the predicted effective conductivity is lower than both Voigt and Hashin-Shtrikman bounds. Compared to previous results using the weak-contrast formulation, the strong-contrast formulation seems to provide a better estimate for the effect of the microstructure on the conductivity.

Original languageEnglish
Pages (from-to)76-86
Number of pages11
JournalJournal of the Mechanics and Physics of Solids
Issue number1
Publication statusPublished - Jan 2009
Externally publishedYes



  • Effective conductivity
  • Heterogeneous media
  • Probability functions
  • Statistical continuum
  • Strong contrast

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

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