Sounds like you have a challenging project! Here are a few comments:
- You don't have to worry too much about the Green-Naghdi stress rate. I instead recommend that you develop your own material model, a procedure for solving the material model equations, and then derive the tangent modulus for the UMAT. This, of course, can be a tall order.
- There are no particular changes that need to be implemented in the UMAT in order to switch from membrane elements to shell elements. You can typically guess a value for the transverse shear stiffness. It often does not have much influence on the results.
- As you have noticed, there are not many exemplar UMAT codes available. And the examples that are available typically do not support shell elements
However, I have done a lot of UMAT work for membrane and shell elements and would be happy to provide helpful suggestions.
Jorgen Bergstrom, Ph.D.