Theory of plasticity without loading surface and associated flow law

Abstract

Based on the analysis of a hysteresis loop (circular diagram), three areas were highlighted which characterize the different behavior of the stresses, i.e. three types of stress are revealed. For each type of stress corresponding evolution equations are formulated which describe the anisotropic hardening. To describe the isotropic hardening the author introduces an evolution equation for the fourth type stresses. A stress deviator is defined as the sum of the stresses of four types. To describe the non-linear process of stress accumulation there is introduced a kinetic damage equation, based on the energy principle where the energy consumed to create damage in material considers as energy equal to the work of the second type stresses on the total strain space. The material functions are shown, the basic experiment and the method of identification of material functions are formulated.