Quasi-static effective permittivity of periodic composites containing complex shaped dielectric particles

TLDR: In this article, a methodology for computing the quasi-static effective permittivity of a two-dimensional or three-dimensional (3-D) lattice of dielectric particles is described.

Abstract: A methodology is described for computing the quasi-static effective permittivity of a two-dimensional (2-D) or three-dimensional (3-D) lattice of dielectric particles. The particles in this composite material may have complicated shapes. This methodology uses a moment method based technique to determine the electric dipole moments of the particles immersed in a uniform electric field. The effective permittivity is then obtained using an appropriate macroscopic model. With this methodology, the mutual interaction between particles can be accounted for accurately. The computed effective permittivity for round cylinders and spheres suspended in a host are compared with our previous T-matrix method results as well as the Maxwell Garnett (MG) formula predictions. Three additional examples involving square (2-D), rounded square (2-D), and spherical (3-D) dielectric inclusions are also given, illustrating the shape effects on the computation of the quasi-static effective permittivity. While the square- and cubic-shaped particles can possess great mutual interaction, surprisingly their effective permittivity is well predicted for all volume fractions by the simple MG formula in both 2-D and 3-D problems.