Computational measurement of void percolation thresholds of oblate particles and thin plate composites

The void percolation thresholds of random oblate particles and thin plate composites are measured computationally using the lattice mapping technique and the Monte Carlo simulation scheme. Two types of spatially uncorrelated inclusions have been investigated: oblate ellipsoids and elliptical thin plates, with which the site and bond percolation systems are developed separately. The results are obtained from the finite-size lattices followed by a mathematical extrapolation to the infinite domains. The computational results are validated by a comparison with the numerical solutions of the limiting cases found in the literature. It is concluded that the void percolation thresholds of oblate inclusions have a much stronger dependence on the geometric aspect ratio of the inclusions compared to those of the prolate counterparts. In the limit, the percolation threshold g is measured to be 22.86 for circular thin disks. Approximate solutions are presented in the form of polynomial functions and Pade approximants. The results have potential applications in composite material designs and molecular diffusion problems. VC 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4730333]