  The full elasticity tensor for nano-crystalline copper is derived in
molecular simulations by performing numerical tests for a set of generated
samples of the polycrystalline material. The results are analysed with respect
to the anisotropy degree of the overall stiffness tensor resulting from the
limited number of grain orientations and their spatial distribution. The
dependence of the overall bulk and shear moduli of an isotropized polycrystal
on the average grain diameter is analysed. It is found that while the shear
modulus decreases with grain size, the bulk modulus shows negligible dependence
on the grain diameter and is close to the bulk modulus of a single crystal. A
closed-form mean-field model of effective elastic properties for a bulk
nano-grained polycrystal with cubic grains, i.e. made of a material with cubic
symmetry, is formulated. In the model all parameters are based on the data for
a single crystal and on the averaged grain size without any need for additional
fitting. It is shown that the proposed model provides predictions of
satisfactory qualitative and quantitative agreement with atomistic simulations.
