Micromechanics-based nonlocal modeling of elastic matrices containing aligned spheroidal inclusions

A micromechanics-based nonlocal constitutive equation relating the ensemble averages of stress and strain for a matrix containing a random distribution of non-spherical hard inclusions having macroscopic transversely-isotropic behavior is derived. The model of impenetrable particles considered consists of identical spheroids having aligned orientations. The analysis builds on and generalises previous papers where elastic composites containing spherical and randomly oriented spheroid-shaped inclusions were analysed. In particular, it is shown how the task of the statistical description of the microstructure can be make reasonable by performing a simple scale transformation. The new constitutive equation is then used to explore nonlocal effects of shape and spatial distribution of inclusions on the anisotropic response of the composite.