Evaluation of stress integration algorithms for elastic–plastic constitutive models based on associated and non-associated flow rules

• Four stress integration algorithms are formulated for AFR and non-AFR models.
• The formulations are general and include plastic anisotropy and hardening asymmetry.
• Backward Euler’s in implicit solver was 10 times faster than same in explicit solver.
• A recent explicit algorithm resulted in the fastest simulation in explicit solver.
• Backward Euler’s in implicit solver was faster than any explicit in explicit solver.

This paper presents in-depth analyses of four stress integration algorithms for finite deformation elastic–plastic constitutive relations. In particular, the four integration schemes were developed for both non-Associated Flow Rule (non-AFR) and Associated Flow Rule (AFR) in the continuum level of plasticity theory. The four integration schemes are (1) fully implicit backward Euler, (2) semi explicit convex cutting plane, (3) fully explicit classical forward Euler and (4) fully explicit forward Euler named Next Increment Corrects Error (NICE-1), which were implemented into the user material subroutines of finite element software ABAQUS. Analysis on numerical accuracy was carried out by using uniaxial tensile simulations at various orientations and time increments. The same analysis was also conducted for uniaxial tension/compression tests to investigate the effect of time increment on the calculated hardening curve. Finally, cylindrical cup deep drawing (manufacturing process which stamps a cylindrical cup) simulations were performed to compare computation time and accuracy for both AFR and non-AFR schemes for the evaluation of more realistic forming application. From the systematic comparative analyses, the following conclusions are made; (1) Caution should be exercised when finding an optimum time increment for explicit integration schemes. (2) The computation time and accuracy for both AFR and non-AFR are not much different when identical integration scheme is used. (3) For the simulation of large scale sheet metal forming applications, the explicit type stress integration algorithm can be a more practical choice considering that it does not deteriorate the computational accuracy and efficiency compared to the fully implicit algorithm.