Effective-Medium Approximations

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

Abstract

In this chapter we will show that single-inclusion solutions obtained in Chapter 17 can also be utilized to derive popular effective-medium approximations, which investigators have employed to estimate effective properties for a wide range of volume fractions, as well as phase properties (when appropriate). However, these approximations necessarily can account only for simple microstructural information, such as volume fraction and inclusion shape. Thus, although effective-medium approximations can provide qualitative trends on the behavior of the effective properties of dispersions, they cannot be quantitatively predictive for general situations. In applying the variety of different effective-medium approximations that have been proposed, it is important to understand the class of microstructures and conditions under which they are valid. Moreover, any reasonable approximation should satisfy existing property bounds.

Keywords

Percolation Threshold Effective Conductivity Spherical Inclusion Ellipsoidal Inclusion Effective Shear Modulus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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