hyperelastic model problems

[egal]

Dr. Bergstrom & all,

For a rubber material, I have uniaxial tensile, biaxial tension, planar tensile and volumetric compression data (pressure vs volume ratio). I tried to use abaqus/CAE to evaluate it and get parameters for ogden 2, Reduced 2nd polynomial models.

The fitted results are very good for all the four modes. However, ABAQUS/cae told me none of them are stable for any volume ratios for volumetric compression.

I tried also to use D1=2/k0, where k0 is initial bulk modulus and set D2=0 as default. Then used ABAQUS/CAE to evaluate it and got totally different pressure vs volume ratio curve compared to volumetric test data.

Can I trust abaqus/CAE since it predicted instablity? What should I do if I do not trust it? If I only use tensile, biaxial, planar test data, how can I get the D1,D2 with accurate results? The rubber is strongly constrained so that I can not use default value as k0/u0=20.

[Jorgen]

You mentioned that none of the calibrated material models were stable for any volume ratios in volumetric compression. Are you saying that the calibrated material models are not stable in volumetric compression at any strain?? That would certainly be a problem.

Is it possible that your four sets of experimental data are not consistent? That is, are you confident in the accuracy of our experimental results?

I typically don't use ABAQUS/CAE to find any material parameters. I like to have more control of the procedure that is used to find the parameters. In your case I would first find the appropriate volumetric material parameters, and then fix those parameters while determining the remaining parameters.

In this case you can also attempt to use an unconditionally stable hyperelastic model.

- Jorgen

[egal]

Dr. Bergstrom,

Yes, the only problem is that the volumetric compression not stable at any strain.

I am very confident with the test data and the material were tested by one of the best material labs. Besides, not only one of the materials has the same problem.

Is that possible that I send you the test data and you help me figure out? I can not publish the data here since I am not allowed.

---In your case I would first find the appropriate volumetric material
---parameters, and then fix those parameters while determining the
---remaining parameters.

Do you find the volumetric parameters by curve-fitting the volumetric test data to those volumetric equations in Theroy manual? I think I can do that, but how can I check the stability of these results as I have instablity issue? I am developing my own tool to calibrate the materials but it takes time and I need to use it now.
Instead, if I use the volumetric compressed data to get the approximate bulk modulus (it is quite linear). Then used D1=2/k, and set D2,3=0, I should get very close results, right? But I did not.

The unconditional hyperelastic models did not fit the volumetric test data well, actually it is very bad, while the volumetric deformation is very concernd for me.

Thanks and look forward to your answer.

[Jorgen]

Yes, I would curve-fit the volumetric data using the exact equations (as outlined, for example, in the theory manuals). You can check stability in the same way as ABAQUS does it: by applying certain strain histories and checking for Drucker's stability.

If you are OK publishing the data on this web site, then I can go through this exercise for you (although it might take me a week or so to finish). If you are not allowed to publish the data, then I can still help you, but I would have to charge for my time. Send me an email or private message (http://www.polymerfem.com/modules.php?name=Private_Messages&file=index&mode=post&u=3) if you are interested.

- Jorgen

[egal]

Thanks, I will try to do it myself firstly.