A comparative study of constitutive algorithms for 3D rate-dependent single crystals

To better predict the polycrystalline behavior at large deformations, a robust time integration algorithm at the single crystal level is of vital importance. The present paper analyzes often-used integration approaches for rate-dependent single crystal plasticity in the area and classifies them into three representative approaches. Three different formulations are grouped into the first approach, which is based up the deformation gradient. The second approach is defined in terms of the slip rates. A modification is proposed to alleviate the numerical stabilities to the second approach upon analyzing the Jacobian. Comparisons between these two approaches show that they demonstrate very similar phenomenology in terms of kinematics and kinetics.