Numerical testing on return map algorithms for von-Mises plasticity with nonlinear hardening based on a generalized midpoint integration scheme

We consider an associative von-Mises elastoplastic constitutive model in the realm of small deformations [1]. The model takes into account both linear isotropic hardening and linear/nonlinear kinematic hardening. The aim of the work is to test integration algorithms based on a return mapping concept and adopting a generalized midpoint integration rule. The method under consideration was originally proposed by Ortiz and Popov [2] and further studied in the simpler case of nonhardening materials by Simo [3]. The tested method guarantees yield consistency at the end of the time step and results linearly or quadratically accurate depending on the choice of the integration parameter. The numerical algorithm adopts a return map update based on a projection along the midpoint normal-to-yield-surface direction onto the endpoint limit surface. A testing on the method accuracy and precision is carried out by comparison with a new exponential-based integration algorithm [4]. The comparison is carried out solving zero-dimenisonal mixed prescribed stress-strain loading histories. Accuracy and precision are determined by plotting the instantaneous error graphs on stress and strain as well as iso-error maps on stress.