I am trying to write a UMAT in Abaqus to simulate non-linear visco-elastic material response based on the paper attached below..

I have a small problem in understanding how the non-linear parameters (g0,g1,g2,a) of Schapery's equation (Ref pg 7) are calculated.. As I understand, they are functions of octahedral shear stress (sigma_bar) in the paper, which I think varies with applied stress (Correct me if I am wrong). Now here is where I don't understand..

In case I want to simulate creep test, I give a steady heaviside jump stress of say 30Mpa, then stress tensor is constant, meaning octahedral shear stress is constant as well. That essentially makes nonlinear parameters constant for every time step.

I am pretty sure I am overseeing something.. Please correct my understanding..

Thanks for your time

Regards

Shree

Update 1 :  I have been checking other research papers as well.. I find some(different) analytical expressions for those parameters (g0,g1,g2,a) in terms of stresses only.. For my UMAT, I need to compute stress increment based on given strain increment. How am i to compute them now? 

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