An analytical model based on an equivalent capacitance circuit for expressing a static effective permittivity of a composite dielectric with complex-shaped inclusions is presented. The dielectric constant of 0-3 composites is investigated using this model. The geometry of the capacitor containing a composite dielectric is discretized into partial parallel-plate capacitor elements, and the effective permittivity of the composite is obtained from the equivalent capacitance of the structure. First, an individual cell diphasic dielectric (a high-permittivity spherical inclusion enclosed in a lower permittivity parallelepiped) is considered. The capacitance of this cell is modeled as a function of an inclusion radius/volume fraction. The proposed approach is extended over a periodic three-dimensional structure comprised of multiple individual cells. The results of modeling are compared with results obtained using different effective medium theories, including Maxwell Garnett, logarithmic, Bruggeman, series, and parallel mixing rules. It is found that the model predictions are in good agreement with the experimental data. The equivalent capacitance model may be applied to composites containing inclusions of any geometry and size. Although the method presented is at static electric field, it can be easily generalized for prediction of frequency-dependent effective permittivity.


Electrical and Computer Engineering

Second Department

Materials Science and Engineering


United States. Office of Naval Research

Keywords and Phrases

Cells (Electric); Permittivity; Capacitors; Composite materials

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2008 American Institute of Physics (AIP), All rights reserved.

Publication Date

01 Oct 2008