A simplified Fourier series expansion method for computing the effective dielectric constant of a two-component, three-dimensional composite material with geometric symmetry

Abstract

The mixing theory for predicting electric behaviors of composite materials is essential to the interpretation of electromagnetic remote sensing and material sciences. Developing an accurate and versatile computation method to evaluate the effective dielectric constant of a composite material has been an interesting topic. Since the effective dielectric constant of the composite material is a function of both the dielectric constant of each component and the microgeometry of the material, a mixing theory has to consider the role of the geometric structure of the material. We present a method to compute the effective dielectric constant of a two-component three-dimensional mixture with geometric symmetry using a simplified Fourier series expansion. The developed method can be applied to materials with arbitrary porosity. Three models have been studied: simple, body-centered, and face-centered cubic lattices. The Fourier series expansion method avoids the difficulty of boundary-condition matching and has no limit on the porosities of composite materials. To simplify the Fourier series expansion technique, geometric symmetry of the composite material is assumed. The computed numerical results have verified the success of the formulation. The electric field distribution in the material is also presented. We calculated the effective dielectric constant with a CPU time reduction of 1.2 - 6 times for the first-order approximation and 5 - 26 times for the second order compared to the formulation without considering geometry symmetry.