A Minimum Problem Defining Effective Isotropic Elastic Properties

The paper discusses a special aspect of averages approximating the elastic properties of polycrystalline aggregates with a uniform orientation distribution. It is shown that the well known isotropic estimations by Voigt and Reuss and a recently suggested geometric mean of the local elasticity tensors minimize their distances to the single crystal elasticity tensors as well as to the corresponding volume averages. In this analysis, only the influence of the grain orientation distribution on the macroscopic response is considered.