Finite element modelling of the permittivity of lossy composite materials

An ab initio numerical simulation model has been used to compute the complex effective dielectric constant of a two-component lossy composite material, in the quasistatic limit. A computational algorithm with a conventional finite element formulation solves Laplace's equation for a spatially heterogeneous medium, using the field calculation package FLUX3D. In this way, different three-dimensional topological arrangements of the components were considered. The composite material consists of dense spheres of uniform size that are arranged in simple, body-centered and face centered cubic lattices. A comparison with McLachlan's generalized effective medium equation is further provided over a wide range of conditions.