Polarization approximations for the macroscopic elastic constants of transversely isotropic multicomponent unidirectional fiber composites

The multicomponent transversely isotropic fiber composites, with unidirectional cylindrical fibers made from different component materials and embedded in a continuous binding matrix, are considered. Hashin-Shtrikman-type polarization trial fields developed earlier by us to bound effective moduli of composites are used to construct polarization approximations for four from the five effective elastic constants of the multicomponent composites, except the longitudinal Young's modulus, for which the classical volume-weighted-average approximation appears sufficiently accurate and general. The approximations contain certain free parameters. Those parameters can be determined from dilute solutions for circular inclusions, which yield results coincided with Maxwell and Mori-Tanaka approximations in the case, or from the reference effective moduli at some finite volume proportions of the components numerically or experimentally. The simple polarization approximations obey Hashin-Shtrikman bounds over all volume proportions of the components and agree well with numerical results on benchmark models.