A SIMPLIFIED FOURIER-SERIES EXPANSION METHOD FOR COMPUTING THE EFFECTIVE DIELECTRIC-CONSTANT OF A 2-COMPONENT, 3-DIMENSIONAL COMPOSITE-MATERIAL WITH GEOMETRIC SYMMETRY

The mixing theory for predicting electric behaviors of composite mater ials is essential to the interpretation of electromagnetic remote sens ing and material sciences. Developing an accurate and versatile comput ation method to evaluate the effective dielectric constant of a compos ite material has been an interesting topic. Since the effective dielec tric constant of the composite material is a function of both the diel ectric constant of each component and the microgeometry of the materia l, a mixing theory has to consider the role of the geometric structure of the material. We present a method to compute the effective dielect ric constant of a two-component three-dimensional mixture with geometr ic symmetry using a simplified Fourier series expansion. The developed method can be applied to materials with arbitrary porosity. Three mod els 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 com posite 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 el ectric field distribution in the material is also presented. We calcul ated 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 sec ond order compared to the formulation without considering geometry sym metry.