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 (a1>a2>a3) characterized by two aspect ratios, α=a1/a3 and β=a1/a2, 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 (E11, E22 and E33) and the shear moduli (μ12, μ13 and μ23) are calculated. The longitudinal Young's modulus E11 increases, as the primary and secondary aspect ratios increase. However, the transverse Young's modulus E22 and shear modulus μ12 decrease, as the secondary aspect ratio increases.