Computational Modeling of Percolation Conduction and Diffusion of Heterogeneous Materials

Heterogeneous materials provide a unique combination of desirable mechanical, thermal or electrical properties. This dissertation presents several micro-structure modeling approaches to predict the effective properties of heterogeneous materials and demonstrates its certain application toward two highly heterogeneous, unconventional structural composite materials (carbon fiber reinforced composite materials and graphene nanoplatelets composite). By using the efficient computational algorithm based on the FEA, a randomly oriented disk-shaped particles system are generated. A new element partition scheme based on the vector operations and geometry of inclusion has been implemented to mesh the intersected disks. The computed equivalent conductivity is expressed as a power-law function form with the key parameters determined from curve fitting. Also, we proposed a novel random walk method to study the 2-D circular or elliptical and 3-D spherical or ellipsoidal non-overlapping system diffusion process. A Monte-Carlo scheme is applied to generate the particulate system for simulation. The effective diffusion coefficient has been predicted and compared to the finite element method and effective medium theory. The aspect ratio effect also investigated and compared to other numerical studies