Micromechanical modeling of the multi-coated ellipsoidal inclusion: application to effective thermal conductivity of composite materials

In this work, a new multi-coated inclusion model to determine the effective thermal conductivity of reinforced composite materials is developed. The methodology is based on Green’s functions technique and integral equation which gives the local thermal fields through concentration equations in each phase of the composite-inclusion. The solution is presented within the general framework of anisotropic thermal behavior of the phases and ellipsoidal inclusions. The effective behavior of multi-coated inclusion-reinforced material is determined within a ‘(N+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(N+1)$$\end{document}-phase’ Generalized Self-Consistent Scheme. To assess the present model’s reliability, some comparisons with other micromechanical models and exact solutions are presented for different inclusions’ morphologies. The model is applied to two-phase materials, and the results are compared to bounds established for ellipsoidal shape. Some results for three-phase materials are given regarding the influence of the thermal contrast between phases and the shape of inclusions.