A Novel Implicit Stress Integration Algorithm and its Verification Using von Mises and Drucker Prager Plasticity.

We introduce a novel fully implicit algorithm for integrating the rate form of plasticity, and compare its main attributes with Closest Point Projection Method (CPPM) and Cutting Plane Method (CPM). Inspired by CPM, the field variables such as stress, hardening modulus are expressed as functions of the plastic consistency parameter, and yet the field variables are treated as implicit. The latter was conceived by the superior performance of CPPM. The proposed method possesses a consistent tangent operator that is straight forward to obtain. The mathematical formulation and the geometric details of the return mapping show that the proposed method is a distinct algorithm. Numerical tests are carried out to verify, and explore the accuracy and computational performance of the proposed method. The benchmark tests for single material point integration indicate that the accuracy of the proposed method is as good as CPPM in the case of von Misses plasticity, while it is slightly lower in the case of Drucker Prager plasticity with nonlinear pressure dependent elastic constitutive relations. Further, the multi-element tests demonstrate that the consistent tangent operator of the proposed method is on par with that of CPPM, both in accuracy and numerical performance.