Ellipsoidal Bounds of Elastic Composites

Abstract

The formulation of rigorous bounds for the physical properties of composites constitutes one of the most fundamental parts of applied mechanics. In this work, the so-called ellipsoidal bounds, as a generalization of the Hashin-Shtrikman spherical bounds, are formulated for elastic moduli of multiphase composites. Explicit formulas are derived to estimate the bounds for the elastic moduli of isotropic composites. Asymptotic analyses are conducted for composites containing needlelike and disklike fillers with aspect ratios approaching infinity and zero, respectively. The new bounds and estimates are expected to be useful for polycrystals and composites containing fillers, especially with large or small aspect ratios, such as nanowires, nanotubes, and nanoplatelets.