Hello Jorgen (and others),

Please help me: I am trying to write USERMAT (3D) subroutine of hyperelastic material for ANSYS. Since I am relatively new in this area I started with neo-hookean model, however I still have huge convergence problems of my subroutines.

Details:

- First I calculate rotation matrix R (from def. grad.) and transform deformation gradient F into corotated coordinate system. Then I calculate Cauchy stress tensor and material elasticity tensor C (C is obtained numerically - based on Second Piola-Kirchhoff stress and central difference method). Finally i transform C into spatial elasticity tensor (through Piola transformation) and condense it into matrix notation required by ANSYS.

- For one-element analysis there is no problem - everything is OK (simple tension, simple shear, rotation, ...) and convergence is great. For multi-element analysis convergence difficulties occur. I really cannot reach the same convergence capability as for the build-in models in ANSYS (even for neo-Hookean model).

- Moreover, if I increase number of substeps (e.g. for displacement controlled multi-element simple tension test), the convergence becomes worse and worse :-(. This I did not observe for build-in models.

Note: If I use analytical form for material elasticity tensor C, the convergence problems still remain the same.

Questions:

1/ What is probable cause of my convergence problems? Could it be caused by rounding errors due to too long calculations? Should it be related to not sufficiently straighforward calculation? Or there must be something wrong in my code?

2/ Is there any possibility to calculate directly the spatial elasticity tensor (to avoid Piola transformation of C)? Does anybody have any refferences to that formulation (e.g. for neo-hookean model)?

3/ Should I try to convert my USERMAT subroutine into UMAT subroutine for abaqus? Could I expect any improvement of such (non)convergency of my code under ABAQUS enviroment or should I first concentrate on the debugging process of my current USERMAT code under ANSYS?

Hope that I clearly described my problem and thank you A LOT for ANY advice - I am really puzzled now :-(.

Paul