What is the best suitable Viscoplastic Flow Rule (Wright-Batra, Bodner-Partom, Johnson-Cook ...etc) for modeling and capturing a shear bands in ductile metals ?
Wright-Batra and Johnson-Cook are both accurate enough. W-B predicts no significant change in the shear band width with shear stress, as J-C does. J-C is easier to implement in commercially available software, so I would suggest using J-C.
More info: Batra RC, Chen L, Shear band spacing in gradient-dependent thermoviscoplastic materials, Computational Mechanics, 23 (1999) 8-19
Thank you very much, your answer is very helpfull. Can you help me more by sending a simple code that include J-C rule or a document to implement this rule
The strain gradient effect must be considered for determining the shear band width. A material length scale can be introduced by rate-dependency; however, it arises in dynamic problems. In quasi-static condition, a gradient (local) constitutive model is required.