Effective Material Properties in Effective Media and Mixtures
One way of dealing with effective media or mixtures of solids in electromagnetic models is to replace them with a homogenized medium. The electric and magnetic properties of this medium are computed from the properties of each phase by means of an averaging formula.
There are several possible approaches to compute an average material property starting from the material properties and the volume fraction of each material.
The following sections illustrate the different formulas available to compute the effective electrical conductivity, the effective relative permittivity, and the effective relative permeability of a homogenized medium. In the following, volume fractions of the materials are indicated with θi, where i is the material index, and they are assumed to be fractional (between 0 and 1). Up to five different materials can be specified as phases of the mixture. Typically, their volume fractions should add up to 1.