The general mathematical theory of plasticity and the Ilyushin postulates of macroscopic definahility and isotropy

The physical laws of the connection between stresses and strains of the general modern theory of the processes of elastoplastic deformation and its postulates of macroscopic definiteness and isotropy of initially isotropic continuous media are considered and analyzed. The foundations of this theory in continuum mechanics were developed in the middle of 20th century by the outstanding Russian mechanicist, corresponding member of the Russian Academy of Sciences, academician of Russian academy of rocket and artillery sciences, head of the department of the theory of elasticity of Moscow university of M. V. Lomonosov, by A. A. Ilyushin. His theory of small elastoplastic deformations under simple loading became a generalization of Genky's deformation theory of flow, and his theory of elastoplastic processes which are close to simple loading became a generalization of flow theory of Saint-Venant–Mises for reinforcing medium. In these works, the concepts of simple and complex loading processes, the concepts of directing deviation tensors of form change were introduced. The Bridgman's law of elastic variation of the volume and the universal laws of the single curve of hardening of Roche and Eichinger under simple loading, and the universal law of hardening of Odquist for plastic deformations generalized to strengthening elastic-plastic media for processes close to simple loading, but without taking into account the specific history of deformation for trajectories of small and medium curvature were adopted. The question of the possibility of applying the postulate of isotropy to the evaluation of the influence of parameters of the form of the stress-strain state arising due to deformation anisotropy when the internal structure of materials changes is discussed. Also, the question of the legitimacy of representing symmetric tensors of the second rank of stresses and deformations in the form of vectors of the coordinate linear Euclidean six-dimensional space is discussed. The corresponding principle of the identity of tensors and vectors is proposed.