Exact moduli and bounds of two-phase composites with coupled multifield linear responses

This work is concerned with the effective moduli of a two-phase medium consisting of isotropic phases with a linear response phenomenon involving n coupled driving fields. Examples of physical phenomena of this kind are the magnetoelectric effect, the thermoelectric effect and coupled, multispecies diffusion, etc. We show that the effective moduli of the composite can be exactly expressed in a finite series form, involving only the moduli of the components, with at most n independent coefficients to be specified. For a composite medium insensitive to phase interchange we derive explicit solutions for the exact moduli of the composite. In addition, bounds are constructed from the existing results in single-field effects. The basic formulation starts from the formalism established by Straley [(1981) Thermoelectric properties of inhomogeneous materials. J. Phys. D. Appl. Phys. 14, 2101-2105]. The main tool in the analysis is a simple matrix decomposition scheme, which provides a simple mathematical bridge to link the existing results in singlefield effects with those in coupled multifields.