A novel formulation for integrating nonlinear kinematic hardening Drucker-Prager’s yield condition

The Drucker-Prager’s plasticity model obeying nonlinear kinematic and linear isotropic hardenings is considered. A new integration formulation is suggested that is based on definitions of angles between the strain rate and the shifted stress, and between the shifted stress and back stress in the deviatoric plane. This method will reduce the constitutive relations to five ordinary differential equations (ODEs). For solving this system of ODEs, the embedded pairs and local error estimation schemes along with FSAL property are used. As a result, an integration scheme is developed with automatic error control. The updated stress produced by the proposed numerical scheme is consistent with the yield condition. Finally, a broad set of numerical tests are carried out to investigate the accuracy and efficiency of the suggested technique.