“…The principal elastic compliance of a polycrystalline material is determined by taking a spatial average of the elastic constants of all the crystals using a uniform probability density function (Nanthikesan and Sunder, 1994). Eskandarian (2005) obtained the upper and lower boundaries, as well as the average values of polycrystalline elastic constants. He obtained the upper limit of the elastic constants by assuming that all the grains undergo the same uniform strain (Voigt, 1910), and the lower limits of the elastic constants by assuming the uniform stress field for all the grains (Reuss, 1929).…”