Induced anisotropic magneto-resistance in a composite medium with a periodic microstructure: numerical results and exact relations

Generic three-dimensional (3D) exact relations are found between macroscopic or bulk-effective moduli of composite systems with related microstructures. These relations can be established between effective values of material coefficients of the same type (e.g. conductivities of two different composites) as well as between different types of material coefficients (e.g. conductivity and permittivity or conductivity and magnetic permeability). As an example of possible application of these relations, a set of Keller-like quasi-3D relations are derived for the case of columnar-shaped parallel inclusions and general orientations of the applied magnetic field.