Mathematica file for article "Analytical modelling of the electrical conductivity of CNT-filled polymer nanocomposites"

Developed by Eshelby, the equivalent inclusion method (EIM) shows that the elastic fields inside an ellipsoidal inhomogeneity can be assumed to be uniform if the ellipsoidal particle is perfectly bonded to an infinitely extended matrix with a uniform load applied at infinity. This idea is extended to evaluate the  overall electrical conductivity of inclusion-matrix materials.
First, the method is applied to a matrix with a single ellipsoidal particle and then extended to a matrix with numerous ellipsoidal particles, considering the interactions between them. This model presents a rigorous analytical formulation for computing effective electrical conductivity of polymer nanocomposites based on Equivalent Inclusion Method. Two main mechanisms are considered: Electron hopping and Conductive networks of inclusions.