stress update

Hi everybody,

I am studying the plastic deformation of sheet metal. Recently, I study about stress update scheme in finite element analysis using return mapping method. For this problem, we can calculate the increment of stress components, Δσ for a given value of strain components Δε using elastic predictor - plastic correct scheme. Since Δε = Δεe +Δεp, first, we assume Δεp=0 and check the yield criterion. Then, we find Δεp to satisfy the yield criterion as well as the consistent condition.

However, I have a question as the follows