Percolation thresholds in the homogenization of spheroidal particles oriented in two directions

We consider percolation thresholds which arise in the homogenization of composite mediums based on three different types of component particles. An extension of the standard Bruggeman homogenization formalism is implemented in order to take account of the sizes, shapes, and orientations of the component particles. The relationships between the geometric attributes of the component particles and the constitutive parameters of the homogenized composite mediums are investigated. In particular, percolation thresholds arising in the homogenization of conducting component particles oriented in two directions and nonconducting component particles are explored via representative numerical examples. Anisotropies in these percolation thresholds are highlighted.