Vector Properties of Elastoplastic Processes of Deformation along Plane Paths of Moderate Curvature

Abstract

Various hypotheses proposed with the Il’yushin plasticity theory framework and expressed in terms of ODEs and multiple 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.