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

A methodology is described in this paper for computing the quasi-static eff ective permittivity of a two-dimensional (2-D) or three-dimensional (3-D) l attice of dielectric particles. The particles in this composite material ma y have complicated shapes. This methodology uses a moment method based tech nique to determine the electric dipole moments of the particles immersed in a uniform electric field. The effective permittivity is then obtained usin g an appropriate macroscopic model. With this methodology, the mutual inter action between particles can be accounted for accurately. The computed effe ctive permittivity for round cylinders and spheres suspended in a host are compared with our previous T-matrix method results as well as the Maxwell G arnett (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 particle s can possess great mutual interaction, surprisingly their effective permit tivity is well predicted for all volume fractions by the simple MG formula in both 2-D and 3-D problems.