Optimal Percolation Thresholds of Two- and Three-Dimensional Engineering Composites

Theoretical prediction of percolation thresholds universally applicable for various composites remains a major theoretical challenge. In the work done by Xu (2011, “Ellipsoidal Bounds and Percolation Thresholds of Transport Properties of Composites,” Acta Mech., 223, pp. 765–774), a variational method is developed to predict optimal percolation thresholds for transport properties of three dimensional composites subjected to full dispersion of fillers. In this paper, simplified formulae are provided for engineering applications of 3D composites. New formulae are derived for optimal percolation thresholds of 2D composites, i.e., laminates and thin films, and for composites containing a combination of fillers with different aspect ratios. The effects of dimensionality and waviness are especially discussed.