A simple model to predict effective conductivity of multicomponent matrix-based composite materials with high volume concentration of particles

For high-contrast-component-property composites, most popular effective medium approximations that are based on the dilute analytical solution for an ellipsoidal inclusion embedded in an infinite matrix diverge significantly from each other and from experimental and numerical data. This paper discusses the challenges in this research area and proposes some homogenization strategies to solve the problems. In this work, a simple effective medium approximation is constructed to predict the effective conductivity of multicomponent matrix-based composites containing high concentrations of particles in d-dimensional space (d=2,3). The maximum volume fraction that depends on particle size distribution and the geometric approximation are accounted for in the micromechanical model to obtain new closed-form solutions. A flexible version of the model containing a free parameter is proposed to make the predictions more accurate at very high-volume fraction of inclusions. Applications are illustrated by comparing the theoretical predictions with the available experimental data or finite element simulations for various types of material to show the agreeable results close to the maximal packing points of the interactions.