Construction of Constitutive Relationships of the Deformation Theory for Simple in Noll's Sense Hardening Materials with Elastoplastic Behavior.

Based on the theory of simple hardening materials with elastoplastic behavior, the general constitutive relationships of the deformation theory of plasticity are mathematically strictly constructed for arbitrary continuous, piece-wise continuously differentiable deformation trajectories, any strains and symmetry types of the material properties. Two conditions under which this is possible are considered. The approaches to a strict specialization of general constitutive relationships of the deformation theory of plasticity have been developed by imposing restrictions on the material strains, deformation processes and properties. In this case, the restrictions on the properties of materials formalize the data obtained in the experimental investigations. A series of both new and known constitutive relationships have been constructed that are arranged into a hierarchy according to the level of complexity of the response to deformation. The area of applicability of the derived physical equations has been defined. Special attention has been given to the modeling of finite and infinitesimal strains of isotropic materials. [ABSTRACT FROM AUTHOR]