A new mixing rule for predicting of frequency-dependent material parameters of composites

A number of mixing rules are proposed in the literature to predict the dependence of effective material parameters of composites, the permittivity and permeability, on frequency and concentration. Alternatively to the mixing rules, properties of composites can be considered in terms of the Bergman-Milton theory (BMT), which employs the concept of the spectral function. All known mixing rules are particular cases of the BMT. Particularly, the Ghosh-Fuchs theory (GFT) has been proposed based on the BMT. The GFT is shown to agree well with measured material parameters of composites filled with ferromagnetic metal powders. However, the GFT is not convenient for use because of its complicated mathematical form. Herein, a simple analytic formulation of the GFT is proposed. The new mixing rule is based on the shape of the spectral function typical for the Bruggeman effective medium theory with the averaged depolarization factor of inclusions and the percolation thresholds introduced as fitting parameters. Since the permittivity and permeability of a composite are governed by the same mixing rule, these fitting parameters are found from the concentration dependence of permittivity of the composite for further use in the analysis of the frequency dependence of permeability. The proposed mixing law is valid for the case of nearly spherical shape of inclusions in the composite, e. g., stone-like inclusions.