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Conductivity Of A Periodic Particle Composite With Spheroidal Inclusions, Nicola Harfield

Nicola Bowler

The effective electrical conductivity of a two-phase material consisting of a lattice of identical spheroidal inclusions in a continuous matrix is determined analytically. The inclusions are located at the node points of a simple-cubic lattice and the axis of rotation of each spheroid coincides with one of the lattice vectors, such that the spheroids are aligned with each other and with the lattice. With an electric field applied in the direction of the rotation axes of the spheroids, the electric potential is found by solving Laplace's equation. The solution is found by analytically continuing the interstitial field into the particle …