On limitations of conventional approaches to homogenization applied to uniaxial dielectric composite materials

摘要

Under certain conditions, the Bruggeman formalism yields estimates of the effective constitutive parameters of homogenized composite materials (HCMs) which are physically implausible. Furthermore, under these conditions, the generalized Hashin-Shtrikman bounds (which are equivalent to the estimates of the effective constitutive parameters of the HCMs provided by the Maxwell Garnett formalism) exhibit strong resonances. The conditions are that (ⅰ) the real parts of the constitutive parameters of the constituent materials have opposite signs; and (ⅱ) the constituent materials are weakly dissipative. These limitations - which we had previously established for isotropic dielectric HCMs - are shown to afflict uniaxial dielectric HCMs.