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.
KeywordsPercolation Threshold Effective Conductivity Spherical Inclusion Ellipsoidal Inclusion Effective Shear Modulus
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