Abstract
While several micromechanical models have been developed today in the literature for two-phase media, the extent of their applicability to multiphase materials need yet to be investigated. The present paper studies the effective thermal conductivity of multicomponent composites, and concentrates on two methods: (a) the Mori-Tanaka model, (b) The “generalized self-consistent scheme”. The Mori-Tanaka method of “back-stress” previously developed in the context of elasticity of composites is applied here to the conduction problem. The “generalized self-consistent scheme”, based on a particle-matrix embedding in the effective medium, is studied in this paper in the context of multicomponent media and two variations of this method distinctly different in their imbedding procedure are proposed.
Numerical results are given for three-phase composites illustrating and comparing the proposed methods.
Resumé
Plusieurs modéles de micromécanique existent aujoud'hui dans la litérature des matériaux á deux phases. L'applicabilité de ces modéles aux matériaux á multi-phases nécessite d'autre part d'être examinée. Ce travail étudie la conductivité thermale des matériaux á multi-phases et se concentre sur deux méthodes: a) le modéle de Mori-Tanaka b) la méthode “auto-consistante” généralisée. La méthode de Mori-Tanaka, développée auparavant dans le cadre des propriétés mécaniques des composites est appliquée ici au probléme de conduction. La méthode “autoconsistante” généralisée est étudiée dans le cadre des matériaux á multi-phases et deux alternatives de cette méthode distinctement différentes dans leur formalisme sont proposées. Pour des matériaux á trois phases on donne des resultats numériques qui illustrent et comparent les méthodes proposées.
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Benveniste, Y. On the effective thermal conductivity of multiphase composites. Z. angew. Math. Phys. 37, 696–713 (1986). https://doi.org/10.1007/BF00947917
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DOI: https://doi.org/10.1007/BF00947917