The effective conductivities of composites with cubic arrays of spheroids and cubes

A boundary element method is developed for computing the effective conductivity of a composite material containing periodic arrays of particles of arbitrary shape. Utilizing the periodic nature of the problem, steady conduction through a unit cell is analyzed by solving the integral representation of the Laplace equation. The accuracy of the method is validated by comparing the numerical results with analytic solutions for periodic arrays of spherical and spheroidal particles, in particular at high particle volume fractions. The utility of the boundary element method is demonstrated by determining the effective conductivities of simple-cubic, body-centered-cubic, and face-centered-cubic arrays of spheroids and cubes over the entire range of the particle volume fraction.