Incremental Maxwell Garnett formalism for homogenizing particulate composite media

Incremental and differential Maxwell Garnett formalisms for bi-anisotropic composites

“…Both codes produced identical results in all cases tested. The number of iteration steps for the IMG formalism is finite, because N is finite, and therefore no convergence problems can arise so long as an adequately large value of N is used [4]. For implementing the DMG formalism, one can rely on well-tested algorithms in numerical libraries so that no numerical problems are to be expected either.…”

On extended homogenization formalisms for nanocomposites

“…Like the Bruggeman formalism, the Maxwell Garnett formalism is based on depolarization dyadics [24], but with one of the constituent phases playing the role of the ambient medium. Therefore, the Maxwell Garnett formalism -including its incremental [37] and differential [38] variants -may be extended by implementing the appropriate η-dependent depolarization dyadic D(η).…”

A limitation of the Bruggeman formalism for homogenization

“…As a direct consequence, the Maxwell Garnett homogenization formalism, like the Bruggeman homogenization formalism, is inapplicable to the scenarios of (i) with (ii). This limitation also extends to the recently developed incremental [31] and differential [32] variants of the Maxwell Garnett formalism.…”