For the stress relaxation test, the applied strain is constant and the resulting stress is time dependent (relaxation).

Since the 3D RVE is considered as a material point, in my opinion the question should be:

How to define the displacement {u} on the RVE boundaries such that a constant strain will be imposed?

If x is a node on the RVE boundaries, then the following linear displacement test will define a constant strain [Epsilon]:

{u}=[Epsilon]{x}

you may study your model response under a sudden dilatational strain for example.

Hi Ahmad,

Thank you for your answer. I have used the equation you suggested in my model, but the strain will always increase from 0 to the values you defined in a step. So the question now becomes how to define "step" in Abaqus and how to make it converge. Now I am defining two steps. The first step is very short and the strain will be linearly increased to the constant value. Then, the second step keeps this constant strain. However, the attached updated umat has some convergence issues. Please let me know if you have any suggestions. Thanks a lot.

the the problem is in your umat...

one note: try to use time(2) instead of time(1) in your umat... hope this works

also I found several mistakes in your umat.. for example stran() is not updated stran..so you need to add stran + dstran when calculating the stress..

see umat in this link http://barbero.cadec-online.com/feacm-abaqus/Examples/Chapter_7/Ex_7.7/CAE_files/UMAT3DVISCO.FOR

Dear Ditho,

Thanks a lot for your reply. The link is very useful.

Thanks