Micromechanical modeling of the anisotropic thermal conductivity of ellipsoidal inclusion-reinforced composite materials with weakly conducting interfaces

•Micromechanical model for the thermal conductivity of heterogeneous material containing ellipsoidal inclusions.•Anisotropic thermal conduction per phase.•Weakly conducting interface.•Green function technique and the interior and exterior-point Eshelby’s tensors.•Exact analytical expressions of local thermal intensity fields.•Effective anisotropic thermal conductivity of the equivalent material. The present paper deals with the micromechanical modeling of the effective thermal conductivity of composite materials containing ellipsoidal inclusions with interfaces thermal resistance. At these interfaces between inclusions and the surrounding medium, the heat flux is assumed continuous while the temperature field undergoes to a discontinuity. The solution of this problem of heterogeneous thermal conductivity is obtained thanks to a micromechanical approach based on the generalized Eshelby's thermal conductivity tensor and the Kapitza’s interface thermal resistance model. Moreover, the present study is conducted in the general case of an anisotropic thermal conductivity of each phase and the inclusions are assumed to have an ellipsoidal shape. Results in terms of the thermal intensity field localization inside each phase are presented and then analyzed in light of the effects of some model parameters. The effective thermal conductivity of the equivalent material has been predicted through classical homogenization schemes such as the Mori-Tanaka, the Self-consistent, the Generalized self-consistent and the Differential scheme. The model predictions have been also compared with results provided by previous investigations.