Peculiarities in Applying the Theory of Elastoplastic Processes at Complex Loading along Curvilinear Deformation Trajectories

Abstract

The approach to mathematical modeling of complex loading processes is based on the two ideas given by A.A. Il’yushin. One of them is called the Il’yushin three-term formula and sets the type of the differential dependence that connects the stress and strain deviator vectors in two- or-three-dimensional complex loading processes The second idea determines the type of the five-dimensional deformation trajectory of constant curvatures. The development of these ideas led to a new constitutive equation and to a new approach to mathematical modeling of complex loading processes. For the analysis of complex loading processes with deformation trajectories of zero curvature, Vasin’s material functions were introduced. These functions are at the center of the mathematical model. They are used for the representations of functionals and formulas for dissipative stresses and for an explicit representation of the stress vector. In this paper the features of applying the new approach to the processes with constant curvature trajectories are studied.