К вопросу об определяющих законах связи общей математической теории пластичности

Abstract

The paper discusses the question of the reliability and applicability of the general laws of the mathematical theory of plasticity. In a new direction of the theory of plasticity (the theory of elastic-plastic deformation processes) the isotropy postulate is given, which establishes the invariance of the connection between stresses and strains. However, this invariance during orthogonal transformations of the image of the process and its vectors in the linear coordinate space can be violated due to a change in the invariants of the form of the stress-strain state. However, numerous experiments show that the influence of these invariants is weak and can be neglected. In the theory of flow, the main hypothesis is the assumption of the decomposition of total deformations into elastic and plastic parts. Such decomposition under complex loading is impossible and contradicts the concept of the complete and incomplete plastic states of the material. This article shows that the flow theory is a special case of the theory of processes. An extended version of the theory of flow is obtained, which can be used for medium-curvature deformation trajectories, and which makes it possible to use the hypothesis of decomposition of total deformations in the theory of flow.