Abstrarct



Theoretical and experimental methods used for the determination of the area of applicability for the Prager and Hencky-Nadai-Il'yushin deformation theories were surveyed. Their disadvantages have been determined. The necessity of development of diverse approaches has been pointed out. Considering the advantages of methods of the rational continuum mechanics, a theoretical solution of such a problem based on the use of general constitutive relations for hardened elastoplastic materials simple in Noll's sense is presented. The reference configuration was adopted to be unstressed and nondeformed. Only the histories that involve active deformation with increasing plastic strains are considered. The strains and the symmetry type of the material properties are arbitrary. The processes and materials were defined, for which general constitutive relations are reduced to the equations of the deformation type. Approaches to their rigorous specialization have been worked out by imposing limitations on the material properties and the processes of deformation. Particular attention is given to the simulation of the finite and infinitesimal strains in isotropic materials. It has been shown under which assumptions the relations constructed reduce to the equations of the Prager and Hencky-Nadai-Il'yushin deformation theories. These assumptions determine rigorously the area of applicability for the plasticity theories mentioned.