Semi-implicit Integration of Constitutive Equations with Non-linear Mixed Hardening

In this study, a stress updating method is formulated in a semi-implicit way for the von Mises plasticity model with the Chaboche nonlinear isotropic hardening and the Armstrong-Frederick kinematic hardening in the regime of the small deformations. For this purpose, the exponential map integration method is utilized. Then, in order to investigate the correctness, accuracy and convergence of the new proposed method, the numerous numerical tests are carried out and their results are compared with previously accepted methods. The results show considerable increasing in accuracy of the presented method and the second-order convergence rate of the method. On the other hand, in this research, the derived relationships have been presented in a way that it is possible to extract data from any desired point during the plastic step; finally, it is studied that selecting the data of which point of the elastoplastic loading step leads to the most accurate results.