Microstructurally-based homogenization of electromagnetic properties of periodic media

Abstract

A general method for homogenization of the electromagnetic properties of a heterogeneous periodic medium is developed, based on its microstructure. This method is inspired by micromechanics (Nemat-Nasser and Hori, 1999). Contrary to other conventional techniques, commonly used in electromagnetism to calculate the overall properties of composites, this microstructurally-based method does not require an explicit numerical solution of the Maxwell equations. We define the macroscopic field quantities as volume averages of the spatially variable fields, taken over a representative volume element (RVE), consisting of a unit cell of the periodic medium (Hill, 1963; Willis, 1981; Hashin, 1983; Nemat-Nasser, 1986). The boundary conditions are based on the Bloch representation of wave propagation in the heterogeneous media. Instead of explicitly solving the Maxwell equations, these equations are directly used in the averaging scheme. This distinguishes our method from others, where usually a known point-wise solution is used to obtain the average field quantities. The resulting constitutive relations therefore may be used to directly estimate the response of any heterogeneous periodic assembly of material constituents of given geometry and properties. To cite this article: A.V. Amirkhizi, S. Nemat-Nasser, C. R. Mecanique 336 (2008).