An integral elasto-plastic constitutive theory

This paper proposes an integral elasto-plastic constitutive equation, in which it is considered that stress is a functional of plastic strain in a plastic strain space. It is indicated that, to completely describe a strain path, the arc-length and curvature of the trajectory, the turning angles at the corner points and other characteristic points on the path must be considered. In general, the plastic strain space is a non-Euclidean geometric space, hence its measure tensor is a function of not only properties of the material but also the plastic strain history. This recommended integral elasto-plastic constitutive equation is the generalization of Ilyushin, Pipkin, Rivlin and Valanis theories and is suited to research the responses of material under the complex loading path. The predictions of the proposed theory have a good agreement with the experimental results.