A new semi-implicit formulation for multiple-surface flow rules in multiplicative plasticity

We derive the equations of the multiplicative decomposition in the context of finite strain plasticity with elastic isotropy and arbitrary (isotropic and anisotropic) flow rules. We include multiple surface yield criteria and mixed control of stress components, a requirement for special stress states such as plane stress or uniaxial stress. Ductile damage and fracture are also considered. The approach is also appropriate for symmetric single-crystal flow rules. A direct integration of the rate equations is performed as well as smoothing of the complementarity conditions with the Chen-Mangasarian function. The resulting problem is smooth and always converges quadratically, typically requiring fewer steps than return-mapping algorithms. Exceptional robustness is observed. Illustrative examples are shown in 2D, shells and 3D analyses confirming the combination as very effective for the class of problems considered.