Anisotropic thermal conductivity of composites with ellipsoidal inclusions and highly conducting interfaces

•Micromechanical model of the thermal conductivity of composite.•Ellipsoidal inclusions and anisotropic thermal conduction per phase.•Highly conducting interface.•Green function technique.•Analytical expressions of local thermal intensity fields. The present paper deals with the micromechanical modeling of the effective thermal conductivity of composite materials containing ellipsoidal inclusions with highly conducting interfaces. At these interfaces between inclusions and the surrounding medium, the temperature field is assumed continuous while the heat flux undergoes to a discontinuity. The proposed model is based on the solution of the Eshelby's inclusion problem with highly conducting interfaces. Moreover, the present study is conducted in the general case of an anisotropic thermal conductivity per phase and ellipsoidal inclusions. Results in terms of the thermal intensity field inside each phase are proposed and then analyzed in light of the effects of some model parameters. The effective thermal conductivity of the composite has been predicted through classical homogenization schemes such as the Dilute medium, the Mori-Tanaka and the Differential schemes. The model predictions have been also compared with some results provided by previous investigations.