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Describing the properties of textured polycrystals in terms of their own elastic states

The basis of the space of symmetric second-rank tensors is presented. A concept of proper elastic states is introduced. The elastic and plastic behavior of volume-isotropic materials is described using spectral decompositions of second- and fourth-rank tensors. The energy of elastic deformation is decomposed into the energy of volume change and the energy of shape change for volume-isotropic materials. The elastic modulus tensor and the plasticity tensor are coaxed. They are written as decompositions over the same eigenstates. The coefficient of normal plastic anisotropy is calculated. It is regulated by the European standard EN 10130 "Cold rolled low carbon steel flat products for cold forming" along with the yield strength.