Development of a consistent hysteretic model with kinematic hardening and isotropic softening

A phenomenological plasticity based bilinear hysteretic model is developed to account for strength deterioration in cyclic loading. The kinematic hardening isotropic softening (KHIS) model is based on J2 plasticity theory and considers the material response to harden kinematically, but soften isotropically, according to a backbone curve that includes strength deterioration with a negative tangent slope. Therefore, the yield surface translates when the material hardens, but as the material softens the yield surface center location is anchored in place, while the size of the yield surface shrinks. A set of novel hysteretic rules is proposed to implement the strength deterioration in cyclic reversals to address the inconsistencies in backbone-curve-based phenomenological models. The yield point in a load cycle is always tracked by the backstress, and the maximum strength in any cyclic excursion is associated with the material strength at the point of the reversal. The material response between the yield point and the maximum strength is kinematic hardening, followed by isotropic softening after the peak response. The backstress tensor stays unchanged during softening, fixing the location of the yield surface center. The proposed changes to the hysteretic rules keep the yield point during the reversals consistent with kinematic laws and better represent the material behavior, and can be implemented into 1-, 2-, or 3-dimensional elements. A stress update algorithm is presented for implementing the model in a finite element (FE) code. A series of material point simulations verify the implementation of the model in an open-source FE code. The proposed model can be easily set up in an FE formulation by adding strain softening in the material constitutive relationships without further consideration of specific component failure modes. The model is validated against cyclic experimental tests on steel structural members, showing its capability to accurately simulate strength deterioration.