Inclusion interaction and effective material properties in a particle-filled composite material system

This work presents a methodology implementing random packing of spheres combined with commercial finite element method (FEM) software to optimize the material properties, such as Young’s modulus, Poisson’s ratio, and coefficient of thermal expansion (CTE) of two-phase materials used in electronic packaging. The methodology includes an implementation of a numerical algorithm of random packing of spheres and a technique for creating conformal FEM mesh of a large aggregate of particles embedded in a medium. We explored the random packing of spheres with different diameters using particle generation algorithms coded in MATLAB. The FEM meshes were generated using software MATLAB and TETGEN. After importing the databases of the nodes and elements into commercial FEM software ANSYS, the composite materials with spherical fillers and the polymer matrix were modeled using ANSYS. The effective Young’s modulus, Poisson’s ratio, and CTE along different axes were calculated using ANSYS by applying proper loading and boundary conditions. It was found that the composite material was virtually isotropic. The Young’s modulus and Poisson’s ratio calculated by FEM models were compared to a number of analytical solutions in the literature. For low volume fraction of filler content, the FEM results and analytical solutions agree well. However, for high volume fraction of filler content, there is some discrepancy between FEM and analytical models and also among the analytical models themselves. The discrepancy is attributed to the multi-body interaction effect of the filler particles when they are getting close.