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We propose a novel algorithm for integrating the standard rate form of plasticity in which the state variables are gradually returned onto the yield surface by a series of implicit plastic correction stages. Its features are discussed in relation to the Closest Point Projection Method (CPPM) and the Cutting Plane Method (CPM). As in CPPM, it is straightforward to derive a consistent tangent operator for the proposed method. Like in CPM, it uses the successive linearization of the yield function about the current state to evaluate the state variables. The proposed integration method can be easily implemented in existing finite element analysis frameworks since the required first and second order derivatives are similar to those required in CPPM. Several numerical tests are performed using von Mises plasticity and linear hardening rules. Single material point tests reveal that the proposed algorithm provides near identical stress remapping to that of CPM and CPPM. For the classical perforated sheet benchmark with both linear isotropic hardening and linear kinematic hardening, CPM, CPPM and the proposed methods produce near identical results. For the combined hardening, a slight disparity between the results from CPPM with the other two methods is observed. Further, the multi-element tests demonstrate that the consistent tangent operator of the proposed method is on par with that of CPPM.

computation; numerical methods; algorithm