A generalization of the particular A.A. Il'yushin's postulate is suggested for non-linear anisotropic materials, which allows obtaining asymptotically correct constitutive relations. In the case of elastic-plastic deformation of anisotropic materials, a reversible component of the deformations is taken, the direction vector of which in a six-dimensional space is a temperature strains vector. Variants of the yield theory and deformational theory of plasticity for anisotropic materials are proposed, in the frames of which induced anisotropy effects, rotation of the main axes of anisotropy, irreversible deformations under the applied hydrostatic pressure are described.
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