A generalized self-consistent method for the effective conductivity of composites with ellipsoidal inclusions and cracked bodies

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Abstract
This paper is concerned with the determination of the effective thermal conductivity of particulate composites with ellipsoidal-type inclusions at nondilute concentrations with special emphasis given to the case of cracked bodies with elliptical cracks. The inclusions or cracks are randomly oriented so that the solid is effectively isotropic. The adopted micromechanics model is the ‘‘generalized self-consistent’’ scheme which is based on the concept that a particle surrounded by some matrix material ‘‘sees’’ an effective medium. The method, whose reliability has already been proved in the literature, is applied for the first time in the present paper to composites containing inclusions of ellipsoidal shape. The generality of the presented analysis allows the treatment of cracked bodies with randomly oriented elliptical cracks. New results are given for particulate composites and cracked bodies.