The physical laws characterizing the relation between stresses and strains are considered and analyzed in the general modern theory of elastoplastic deformations and in its postulates of macroscopic definability and isotropy for initially isotropic continuous media. The fundamentals of this theory in continuum mechanics were developed by A.A. Il’yushin in the mid-twentieth century. His theory of small elastoplastic deformations under simple loading became a generalization of Hencky’s deformation theory of flow, whereas his theory of elastoplastic processes which are close to simple loading became a generalization of the Saint-Venant–Mises flow theory to the case of hardening media. In these theories, the concepts of simple arid complex loading processes arid the concept of directing form change tensors are introduced; the Bridgman law of volume elastic change and the universal Roche–Eichinger laws of a single hardening curve under simple loading are adopted; and the Odquist hardening for plastic deformations is generalized to the case of elastoplastic hardening media for the processes of almost simple loading without consideration of a specific history of deformations for the trajectories with small arid mean curvatures. In this paper we discuss the possibility of using the isotropy postulate to estimate the effect of forming parameters in the stress-strain state appeared due to the strain-induced anisotropy during the change of the internal structures of materials. We also discuss the possibility of representing the second-rank symmetric stress and strain tensors in the form of vectors in the linear coordinate six-dimensional Euclidean space. An identity principle is proposed for tensors and vectors.

中文翻译：

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可塑性的一般数学理论和宏观可定义性和各向同性的伊洛申假设

在一般的现代弹塑性变形理论中，并考虑了表征应力与应变之间关系的物理定律，并针对宏观各向同性的连续介质假定了宏观可分辨性和各向同性。AA Il'yushin在20世纪中叶提出了该理论在连续力学中的基础。他的简单载荷作用下的小弹塑性变形理论成为Hencky流动变形理论的概括，而他的近似于简单载荷作用的弹塑性过程理论成为Saint-Venant-Mises流动理论对硬化介质的推广。在这些理论中，引入了简单和复杂的加载过程的概念以及引导形式变化张量的概念。采用体积弹性变化的布里奇曼定律和简单荷载作用下单一硬化曲线的通用罗氏-艾辛格定律。塑性变形的Odquist硬化一般适用于弹塑性硬化介质的情况，用于几乎简单的加载过程，而没有考虑平均曲率较小的轨迹的特定变形历史。在本文中，我们讨论了使用各向同性假设来估计在材料内部结构变化期间由于应变引起的各向异性而在应力-应变状态下出现的成形参数的影响的可能性。我们还讨论了在线性坐标六维欧几里得空间中以矢量形式表示第二对称应力和应变张量的可能性。