  Randomly textured polycrystalline materials of constituents with highly
anisotropic nature of grains can be considered globally isotropic. In order to
determine the isotropic properties, like elasticity or conductivity, we propose
a theory for averaging the coefficients of the corresponding tensors unifying
Voigt's, Reuss' or other self-consistent homogenization theories. We apply the
method to determine elastic moduli of untextured polycrystals with arbitrary
crystal structures, recovering experimental data with high precision for cubic
materials. We show that the average moduli can be used to predict analytically
stress and strain states inside individual grains as proven by the comparison
with neutron diffraction measurements. Finally, we discuss a few possible
generalizations for textured materials for further applications.
