Hello Everyone!

I am relatively new to the Mori–Tanaka homogenization method and would appreciate some conceptual guidance.

Most of the literature I have read explains the Mori–Tanaka theory for composites, where an isotropic matrix contains inclusions of a particular shape (e.g., spherical, prolate, or oblate ellipsoids). The effective properties are then expressed using the Eshelby tensor, which accounts for the shape of the inclusion.

What I would like to understand better is the following:

• Suppose we have an isotropic matrix (for example, a metal hydride powder bed).
• Into this matrix, we introduce inhomogeneous inclusions, i.e., inclusions that may themselves have anisotropic properties (such as graphite flakes or expanded natural graphite, which have very different in-plane vs through-plane conductivities).

My specific questions are:

Any intuitive explanation, along with the mathematical expressions, would be very helpful. References to good learning resources (textbooks or review papers) would also be greatly appreciated