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nonlinear elastic part of Bergstroem Boyce Model, convergence problems

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Posts: 20
Topic starter
(@meta82)
Eminent Member
Joined: 16 years ago

HI,

I have implemented the nonlinear elastic part (Network A) of the Bergstroem Boyce model (2001) in a UMAT. I am using a forward difference approximation with a perturbation of the deformation gradient for the elasticity tensor (Sun 2008, Miehe 1994). At this stage I am comparing my user material subroutine with the Abaqus built-in Arruda-Boyce model using a 1-element cube. When I apply a prescribed displacement then the two approaches deliver very similar results (stresses).

In a second step I applied a constant load. The simulation using the UMAT did not converge. However looking at the results did not reveal any obvious issues. I then thought that there is a flaw in the formulation of the elasticity tensor. So far I have not found one. I then applied a constant load using the built-in Abaqus model and to my surprise the simulation did not converge either. I am at the moment a bit confused as to what could be wrong.

Has anyone any suggestions?

Thanks a lot,

Andreas

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Posts: 3998
(@jorgen)
Member
Joined: 5 years ago

Is it possible that the load that you applied is too high? If the load is too high then the resulting displacement might be very large which can cause problems.

Can you give more info about the Sun, 2008, reference?

-Jorgen

3 Replies
Posts: 20
Topic starter
(@meta82)
Eminent Member
Joined: 16 years ago

Hi Jorgen,

I first had 1 N/mm2, so not very large....The cube is 25x25x25mm. I then gradually decreased the pressure. I had to go down to 0.05N/mm2 to make it work. This of course resulted in almost no displacement/stress...

Then I used the unsymmetric parameter in the step definition and the Abaqus built-in model converged. Subsequently, I did the same for my UMAT simulation, but it still did not converge. In the message file it said that elements are highly distorted... they werent really distorted, but the cube rotated around its vertical axis while the pressure was applied (I constraint the vertical displacement of the bottom and the lateral displacement of one node of the cube). The same happens with the Abaqus built-in model but isnt causing any problems.

I then completely fixed the bottom surface of the the cube and suddenly the simulation using my UMAT converged! However, this is not what I want at this point (now I also have shear stresses).

So it seems that my UMAT has problems with rigid body rotation. I think that I have read about this issue before, but I am not exactly sure what I would have to do to solve it.

Here the exact reference:

Numerical Approximation of Tangent Moduli for Finite Element Implementation of Nonlinear Hyperelastic Material Models. Wei Sun, Elliot L. Chaikof, Marc E. Levenston, Journal of Biomechanical Engineering 2008

Thanks,

Andreas

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Posts: 3998
(@jorgen)
Member
Joined: 5 years ago

A rigid body rotation issue is sometimes caused by an improper material model formulation that does not satisfy objectivity. Since you are implementing a hyperelastic model that is known to be fine, that should not be a problem, though.

-Jorgen

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