Computational Prediction of Conductivities of Disk-Shaped Particulate Composites

The effective conductivities are determined for randomly oriented disk-shaped particles using an efficient computational algorithm based on the finite element method. The pairwise intersection criteria of disks are developed using a set of vector operations. An element partition scheme has been implemented to connect the elements on different disks across the lines of intersection. The computed conductivity is expressed as a function of the density and the size of the circular disks or elliptical plates. It is further expressed in a power-law form with the key parameters determined from curve fittings. The particle number and the trial number of simulations vary with the disk size to minimize the computational effort in search of the percolation paths. The estimated percolation threshold agrees well with the result reported in the literature. It has been confirmed that the statistical invariant for percolation is a cubic function of the characteristic size, and that the definition of percolation threshold is consistent with that of the equivalent system containing spherical particles. The effect of aspect ratio to the percolation threshold has been studied in this article. High aspect ratio will decrease the percolation threshold. Binary dispersions of disks of different radii have also been investigated to study the effect of the size distribution. The approximate solutions in the power-law function have potential applications in advanced composites with embedded graphene nanoplatelets