How to solve for the internal variables in nonlinear viscoelastic problem

[Stinky]

Dear All,

I want to write an user material subroutine to solve for nonlinear viscoelastic problem, such as the model in "A theory of finite viscoelasticity and numerical aspects" by Stefanie Reese and Sanjay Govindjee. The problem is after I defined the number of history terms in Umati1, what command lines should I use to solve the nonlinear implicit evolution equation in UmatL1, the method I want to use to solve for that evolution equation is Newton Raphson iteration. I guess I am not familiar of how to use commands in FEAP to solve an nonlinear equation inside user subroutine.

Thank you very much for your kindly attention.

Stinky

[Prof. R.L. Taylor]

Look in the directory /elements/material/small for the routine modlsd.f -- then look for the viscoelastic module viscoe.f -- this will show you how the linear model is solved.  You will need to assign storage for the history arrays needed for the integration (do this in your umati routine).

[Stinky]

Thank you very much Prof. Taylor, I will look into that file.
Best,

Stinky

[Prof. S. Govindjee]

To implement the finite viscoelastic model of R&G, it will actually be better to look at how the finite (isotropic) plasticity is done in FEAP.  The reason being that the finite plasticity involves many of the same manipulations as the R&G model due to the similar multiplicative splits.

[Stinky]

Thank you very much Prof. Govindjee, I will check that file in detail also~

Best,
Stinky

[chengxf]

To implement the finite viscoelastic model of R&G, it will actually be better to look at how the finite (isotropic) plasticity is done in FEAP.  The reason being that the finite plasticity involves many of the same manipulations as the R&G model due to the similar multiplicative splits.

I would like to ask if there should be a plus sign instead of a minus sign before the last term of formula B15 in the R&G's paper

[Prof. S. Govindjee]

Looking at Appendix B, it does seem that you are correct (assuming the other equations in the Appendix are correct).  If I have time later, I will check more carefully.
You can always test this kind of issue with a simple computation that perturbs the only the volumetric part of the deformation.