  We consider an anisotropic homogenized composite medium (HCM) arising from
isotropic particulate component phases based on ellipsoidal geometries. For
cubically nonlinear component phases, the corresponding zeroth-order
strong-permittivity-fluctuation theory (SPFT) (which is equivalent to the
Bruggeman homogenization formalism) and second-order SPFT are established and
used to estimate the constitutive properties of the HCM. The relationship
between the component phase particulate geometry and the HCM constitutive
properties is explored. Significant differences are highlighted between the
estimates of the Bruggeman homogenization formalism and the second-order SPFT
estimates. The prospects for nonlinearity enhancement are investigated.
