Stress integration schemes for novel homogeneous anisotropic hardening model

Numerical formulations and implementation of stress integration algorithms in the elasto-plastic finite element method are provided for the homogeneous yield function-based anisotropic hardening (HAH) model. This model is able to describe complex material behavior under non-monotonic loading conditions. Two numerical algorithms based on the semi-explicit and fully implicit schemes are compared in terms of accuracy. To efficiently treat the yield locus distortion when the strain path changes, a multi-step Newton–Raphson method is proposed to calculate the first and second derivatives of the HAH yield surface. For the validation of the developed numerical algorithms, the r-value anisotropy is compared for the conventional yield model with classical isotropic hardening and for the HAH model. Moreover, detailed error analysis is presented using iso-error maps. The results show that the fully implicit stress integration algorithm based on the closet point projection method leads to better accuracy in general. However, the semi-explicit algorithm also provides comparable accuracy if an appropriate time increment is chosen. Furthermore in spite of the yield surface distortion, the developed numerical algorithms can successfully update stress with the equivalent level of the error for the conventional yield model.