The 4th-order isotropic tensor function of a symmetric 2nd-order tensor with applications to anisotropic elasto-plasticity

The effective elastic properties of polycrystals can vary significantly with their crystallographic texture [gamma]. Since a correlation of elastic and plastic properties has been proven (see [8] and references therein), a phenomenological modeling of the crystallographic texture induced elastic anisotropy is of importance in the context of both elasticity and plasticity. In the present paper an evolution equation for the effective elasticity tensors of aggregates of cubic crystals is specified by means of the theory of isotropic tenser functions. It is shown that constraints forced by the elastic symmetry on the micro scale simplify the phenomenological equations significantly.