Effective moduli of composites based on confocal ellipsoid model

A confocal ellipsoid model is proposed to predict the effective moduli of the composites with three-dimensional randomly oriented inclusions. The change of inclusion's distribution due to the increase of the inclusion's volume fraction is taken into account. The analytical expressions of the effective shear and bulk moduli are given, and they are compared with those predicted by the Mori-Tanaka (MT) method, the Ponte-Castaneda-Willis (PCW) method and Hashin-Shtrikman (HS) bounds. The results show that the prediction value of the present method is between the results of the MT method and the PCW method. In addition, the influence of different orientational averaging methods on the effective moduli of the composites is also discussed.