Exact moduli of phase interchange invariant composites with coupled fields

A concise and general solution is derived for the exact effective moduli of a two-phase medium for multifield, coupled linear responses, in which the medium is insensitive to phase interchange. The constituents are isotropic and statistically symmetric. The solutions follow from a compatibility condition together with a phase interchange theorem recently discovered by Milgrom and Shtrikman [Phys. Rev. A 40, 1568 (1989)]. Due to the mathematical analogy, the obtained results are applicable to certain classes of two-dimensional polycrystals. The solution extends the corresponding results for two-coupled field media obtained by Benveniste [J. Mech. Phys. Solids 43, 553 (1995)].