Abstract
The effective conductivities (σ <sub>eff</sub> ) of rectangular arrays of aligned spheroids are accurately determined. The array structure is governed by the array aspect ratio (r <sub>a</sub> ), inclusion aspect ratio (r <sub>i</sub> ), and inclusion volume fraction (f). By varying these three parameters, a wide range of array structure can be generated and the effects of the three parameters on the effective conductivities of the array are investigated. The present array is found to be a more efficient structure in utilizing the enhancing or reducing effect of the inclusion, as compared to the simple cubic array of spheres. For cases of equal r <sub>a</sub> and r <sub>i</sub> , the effective parallel conductivity (σ <sub>eff</sub> <sup>=</sup> ) increases, while the effective perpendicular conductivity (σ <sub>eff</sub> <sup>+</sup> ) decreases with increasing aspect ratio, but both are only a weak function of the aspect ratio if the reduced conductivity of the inclusion (σ) is within the range of 0.1-10. At a fixed r <sub>i</sub> , σ <sub>eff</sub> <sup>=</sup> decreases while σ <sub>eff</sub> <sup>+</sup> increases with increasing r <sub>a</sub> . If r <sub>a</sub> is fixed, σ <sub>eff</sub> <sup>=</sup> increases while σ <sub>eff</sub> <sup>+</sup> decreases with increasing r <sub>i</sub> . For prolate systems (r <sub>i</sub> >1), σ <sub>eff</sub> <sup>=</sup> is greater than σ <sub>eff</sub> <sup>+</sup> for all permissible f if r <sub>i</sub> ≥r <sub>a</sub> , but the magnitude order switches at higher f when r <sub>i</sub> <r <sub>a</sub> . As to oblate systems (r <sub>i</sub> <1), σ <sub>eff</sub> <sup>=</sup> is less than σ <sub>eff</sub> <sup>+</sup> for all permissible f if r <sub>i</sub> ≤r <sub>a</sub> , but the magnitude order switches at higher f when r <sub>i</sub> >r <sub>a</sub> . © 1999 American Institute of Physics.