Vector properties of elasto-plastic processes of deformation over plane trajectories of moderate curvature

Various hypotheses proposed within Ilyushin plasticity theory framework and expressed in terms of ODE and multple integrals are studied. One of the key aspects of this approach is a classification of constitutive equations by the complexity of loading for which a certain relation is suitable. Some relations of markedly different forms are proposed for a group of strain paths with moderate curvatures; this group is the most general kind of stress-strain relations in this classification. In the present paper the connections between those relations are discussed.