  Starting from a Cauchy elastic composite with a dilute suspension of randomly
distributed inclusions and characterized at first-order by a certain
discrepancy tensor (see part I of the present article), it is shown that the
equivalent second-gradient Mindlin elastic solid: (i.) is positive definite
only when the discrepancy tensor is negative defined; (ii.) the non-local
material symmetries are the same of the discrepancy tensor, and (iii.) the
nonlocal effective behaviour is affected by the shape of the RVE, which does
not influence the first-order homogenized response. Furthermore, explicit
derivations of non-local parameters from heterogeneous Cauchy elastic
composites are obtained in the particular cases of: (a) circular cylindrical
and spherical isotropic inclusions embedded in an isotropic matrix, (b)
n-polygonal cylindrical voids in an isotropic matrix, and (c) circular
cylindrical voids in an orthortropic matrix.
