Abstract
The analytic properties of the bulk effective dielectric coefficient εe of a composite medium, viewed as a function of the component coefficients ε1,ε2,…, are reviewed in Section I, and are then used to discuss rigorous bounds for (real and complex) εe when various types of partial information are available about the medium. General methods are described in Section II for constructing optimal and rigorous bounds for both real and complex εe in two-component composites. A method for constructing rigorous bounds for εe in composites made of more than two components is described in Section III. Optimum bounds are found for real εe. For complex εe the optimization problem has not been fully resolved. Nevertheless, bounds for complex εe are obtained that are better than some other bounds that have recently been derived in Refs. 6 and 7.
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Bergman, D.J. (1986). The Effective Dielectric Coefficient of a Composite Medium: Rigorous Bounds from Analytic Properties. In: Ericksen, J.L., Kinderlehrer, D., Kohn, R., Lions, JL. (eds) Homogenization and Effective Moduli of Materials and Media. The IMA Volumes in Mathematics and its Applications, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8646-9_2
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