An integral non-proportional cyclic plasticity model taking into account path dependences

Based on the general 5D plastic strain vector space, we previously developed an integral elasto-plastic constitutive theory in which the stress is expressed as a vectorial functional of intrinsic geometry of plastic strain trajectory in a non-Euclidean space of plastic strains. This paper presents a further discussion on the geometric descriptions in this theory and gives a practical model with loading path dependence for non-proportional cyclic plasticity. In the model, the hardening variables and the constitutive functional are assumed to be simply related to the accumulation of plastic strain component along the normal of stress trajectory and the geometric parameters of loading path. The simulations by the model are compared with the experiments in the references and a good agreement is obtained.