Double-step midpoint methods for J2 plasticity with nonlinear hardening

We consider the J2 elastoplastic constitutive model in the realm of small deformations. The model takes into account both linear isotropic hardening and nonlinear kinematic hardening in the form proposed by Armstrong and Frederick [1]. The aim of the work is to test and compare a set of two quadratically accurate integration algorithms based on a return mapping concept and adopting different midpoint integration rules. The considered algorithms are respectively labeled as DMPT1nl and DMPT2nl. The two algorithms are based on the idea of dividing each time step in two substeps and of updating the solution substep by substep. A wide testing of the considered methods in terms of accuracy and precision using different time discretizations is carried out by means of mixed stress-strain loading histories [2].