Abstract
An averaging method, Mori and Tanaka's theory, predicts the upper and lower bounds by Hashin and Shtrikman by exchanging material properties of the matrix and inclusion. However experimental results of porous media are very close to the upper bounds, and are also consistent with a numerical result of a body with periodic micro-structures. Here we propose a new approach using Mori and Tanaka's theory in which two materials are included into the matrix but the volume fraction of the matrix material is taken to be zero as a limit. Results show that either upper or lower bound by Hashin and Shtrikman is a probable estimate when the volume fraction of one material is very small.
