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Usermat: Linear viscoelastic model with geometric nonlinearity

Hello,

I have implemented a linear viscoelastic model using the user subroutine Usermat in Ansys.
I have used the classical paper: "Formulation and implementation of three-dimensional viscoelasticity at small and finite strains" of Kaliske & Rothert (Simo's approach) and it works fine for small deformations.

It is written in the documentation that in the case of a simulation with large strain (geometric nonlinearity), one must rotate the state variables.

I would like to simulate bending of layers (like a shell, but made of solid elements with only displacement as dof). 
Do I have to rotate the state variables because of possible large bending (rigid body motion) even if the local deformation (strain) is small (I activate the option "nonlinear geometric" in Ansys) or can I update the state variables as in the paper without rotation at the end of each time step?

If so, how should I do that. At the end of each time step, I just multiply the tensor of state variables with the rotation matrix and save then for the next time step? Do I have to rotate any other tensor or the old state variables at the beginning of the new time step?

many thanks

Xuxa

I am not familiar with the detail of the viscoelastic model and user subroutine Usermat in Ansys. I think two different problems may should be considered.

First, the objectivity of the constitutive law in finite deformation: When you choose an objective constitutive law, the strain measurement and the stress measurement (such as Green strain and PK2 stress) are defined uniquely and are objectivity. Then you calculate the objective strain through displacement (or rate form through velocity) based on the definition, where field displacement is interpolated by nodes displacement  in FEM implementation. So the calculated strain in interpolated form is objectivty, and you needn't rotate this varible. If the measurements definition contains the rotation term, the rotation calculation is needed for these measurements or varibles.

Second, the deformation assumptions of the layers: As you have mentioned, the shell model generally involves the deformaiton assumptions along the thickness direction. The deformation assumption (especially the stress assumption) usually implemented through modifying the institutive law matrix along the shell thickness direction. Then you need rotate the strain or rotate the constitutiive law matrix to be consistent with the thickness direction.

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