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Difference between Standard push forward and Mixed push forward

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Hi all,

I am currently working on modeling OCA by Prony's series. And I am searching for the helping documentation of ABAQUS to see how Prony's series for viscoelasticity works. I find that in the version before v6.9, abaqus uses a Mixed push forward scheme for finite strain viscoelasticity:   

Yet for v6.9 and later versions it uses a Standard push forward scheme:

Can someone tell me the difference between them and will these two lead to different results?

Thank you.