RVE size estimates for elastic matrices with spherically multi-layer inclusions

A micromechanics-based nonlocal constitutive equation for a matrix containing a random distribution of homogeneous solid spheres is employed to analyze the case of spherically multi-layer inhomogeneous inclusions. The analysis builds on and generalizes previous papers focused on two-phase composites. In particular, it is shown how the task of the derivation of elastic properties for the inclusion phase can be make reasonable by replacing inhomogeneous inclusions with homogeneous spheres having equivalent elastic moduli. The constitutive equation is then used to explore nonlocal effects of layer distribution in the inclusions on the response of the composite material and derive quantitative estimates of the minimum RVE size over which a nonlocal correction to the standard local model is needed to provide a sensible description of the constitutive response of the material