A General Theory of Coupled Linear-Response of Inhomogeneous Media

A generally exact theory for predicting the effective behavior of coupled linear-response for inhomogeneous media is developed. The theory can not only give the general results of the effective principal and coupled moduli for the coupled multifield problems, but also provide the interrelationships between these effective moduli. It can be directly employed to describe the coupled two-field or three-field response of any inhomogeneous media.