A model for composites containing three-dimensional ellipsoidal inclusions

A model is developed for the mechanical properties of composites containing complex inclusions with no axes of symmetry, e.g. three dimensional ellipsoids (a(1) > a(2) > a(3)) characterized by two aspect ratios, alpha =a(1)/a(3) and beta = a(1)/a(2), by using the Eshelby's equivalent tensor with a Mori-Tanaka type model. The influences of the primary and secondary aspect ratios on the effective elastic moduli of nanocomposites containing aligned isotropic inclusions are examined. The model is limited to unidirectionally aligned inclusions where both the matrix and the inclusions have linearly elastic, homogeneous properties. The longitudinal moduli (E-11, E-22 and E-33) and the shear moduli (mu(12), mu(13) and mu(23)) are calculated. The longitudinal Young's modulus E-11 increases, as the primary and secondary aspect ratios increase. However, the transverse Young's modulus E-22 and shear modulus mu(12) decrease, as the secondary aspect ratio increases. (c) 2005 Elsevier Ltd. All rights reserved.