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Stress update scheme in platicity

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

At a stress stage, if we knew the value of the next plastic strain increment, Δεp Can we calculate the stress increment, Δσ?

 

I try to answer this question for a couple of days. But, it seems to be out of my knowledge. I hope some bodies can help me find the solution.

Any comment or suggestion is really appreciated.

Thank you for your reading.

 

 

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