EFFECTIVE CONDUCTIVITY IN A CHECKERBOARD GEOMETRY AT HIGH CONDUCTANCE RATIO AND HIGH-CONCENTRATION

We calculate the effective electrical conductivity in a two-dimensional two-phase composite with checkerboard geometry, solving numerically the truncated set of linear equations for (n + 1) coefficients determining the electric potential [Bao Ke-da, Axell, and Grimvall, Phys. Rev. B 41, 4330 (1990)]. Accurate values for this geometry are given at high concentrations 0.1 < c1 < 0.5 and high conductance ratios 10(2) < S2 less-than-or-equal-to 10(6). Even near the percolation threshold, our analytic expression for the potential can give convergent solutions. In order to study the role of the geometric form of fiber cross sections we compare our results with the transverse conductivity of fibers with other cross sections, thus illustrating that in some cases the geometry of the cross section becomes important.