Hi everyone,
Its hard to describe my question just using the text format, so I attached a zip about it. Please download first.
Any comments would be helpful for me, I really appreciate you guys.
Thank you.
Okyle
Hi friends
It is inconvenient to download a zip file, so i uploaded the picture of my description to Flicker.
Look forwards to your response, than you all.
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Even larger picture: [url] 
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I dont quite follow your nomenclature.
The stress you need to calculate is the stress at time t+dt.
You are given the stress at time t.
Hence: stress(t+dt) = stress(t) + dstress
There is no need to double the initial stress.
-Jorgen
Thank you very much, Jorgen.
Let me make my question clearer: I want to calculate dstress, but I dont understand the expression (W*Sigma(t)-Sigma(t)*W)*delta t = R*Sigma*RT (just as the above picture describing).
How should I obtain R*Sigma*RT?
Or should I just throw this item (R*Sigma*RT), and calculate the dtress via dstress= the co-rotational stress increment?
I looked at your original equations again and the first equation in the image does not make sense. As you said, it would give twice the stress which does not make sense. Are you sure you wrote the equation right?
I also agree with your statement regarding: (W*Sigma(t)-Sigma(t)*W)*delta t = R*Sigma*RT. That does not make sense to me.
You can obtain R from the deformation gradient so you can calculate R*Sigma*RT if you like.
You need to make sure you stress update is consistent, which will depend on your material model formulation.
-Jorgen