A return-free integration for anisotropic-hardening elastoplastic models

This paper develops a numerical integration for an elastoplastic model for hardening materials which has an anisotropic yield surface, and displays asymmetric behavior under tension and compression yielding. The model also captures nonlinear isotropic and kinematic hardening and softening behavior. The developed numerical integration, called return-free integration, automatically updates the stress on the yield surface during the plastic phase, hence it is capable of simulating the behavior of the anisotropic-hardening material model exactly. Furthermore, the return-free integration for the material model is examined through the analysis of consistency errors, average errors, and iso-errors. The influence of the non-zero initial condition of stress, pre-straining path, and loading paths on the consistency error is explored. The convergence analysis of average error is investigated and the iso-error maps are established. All error analysis demonstrates the return-free integration for the proposed model with the anisotropic yield surface and the nonlinear isotropic-kinematic-mixed hardening rule is stable, acceptable, and reliable.