FEA problem: hyperelastic material model unstable

[adlh01]

I'm trying to get a constitutive model for a material based on some uniaxial test results obtained from one of my professors. However, I'm not able to obtain a working model with the data. I get a warning message about the model becoming unstable at the following:

UNIAXIAL TENSION: 0.210E+00
UNIAXIAL COMPRESSION: -0.119E+00
EQUIBIAXIAL TENSION: 0.700E-01
EQUIBIAXIAL COMPRESSION: -0.880E-01
PLANAR TENSION: 0.140E+00
PLANAR COMPRESSION: -0.116E+00

From running a few simulations it seems clear the results are completely off, it's actually compressing when I apply a pulling force and other abnormal things like that.

The data itself doesn't appear to be too bad; the curve fitting didn't give me any issues on Ansys. Except there appears to be a part of the curve that goes below zero, as can be seen here:

Does anyone with experience with hyperelastic models know how I can try and make a stable hyperelastic model? Any tips and suggestions? Thank you.

I should add that I also tried with some curve fits that were less than adequate to see if at least those would appear stable, but I had problems with them too.

 

[SteamKing]

What looks suspicious is the lower left hand portion of the graph. It appears the material does not exhibit stable behaviour under zero stress.

 

[AlephZero]

If your experimental data has zero stress while the strain is increasing from 1.00 to 1.05, a plausible explanation is you are taking up the slack in the measurement system before you apply any load to the test piece. Or if you are testing something like an elastic cord, you are straightening it out rather than stretching it.

I suggest looking carefully at all the experi data to see if that is the case, then make your best guess at what is really "zero strain".

Trying to fit a smooth curve through measured data with a "kink" in the graph isn't goiing to work well, whatever type of material model you use.

If you really want to use the measured data "as is", try a material model where the stress-strain curve is just a series of straight line segments interpolated between the data points. I'm not an Ansys user but any reasonable nonlinear FE program should have that option avaialble.

 

[adlh01]

Thank you for the help. The data 'as is' was in itself a curve made from various other uniaxial tests. When I use the uniaxial tests all together, and run them through CFTOOL on Matlab, I am able to obtain material models that work correctly. So the problem appears to be resolved that way.

That being said, whether I use Matlab to obtain the coefficients of the model, or Ansys, there is still the possibility that I get 'negative slopes'. For example, if I use only some of the uniaxial tests, there might still be a negative slope at the beginning.

So my other question would be, is there any *easy* way (especially through Matlab or another available software) to do a least-squares fit where I have enough control/input into the process as to eliminate the possibility of negative curves? Because for obvious reasons, a fitted curve with a larger error but positive slopes (especially at the smaller strains) is preferable to a curve with a small error but a downward slope right at the beginning.

 

[afreiden]

As AlephZero suggested, your "negative" or zero slope nonsense at the beginning is probably not the actual response of the material. Rather, it is most likely your machine taking up the "slack." Why not just truncate off that portion and move your curve to the left by approximately .05?

Thank you for the help. The data 'as is' was in itself a curve made from various other uniaxial tests. When I use the uniaxial tests all together, and run them through CFTOOL on Matlab, I am able to obtain material models that work correctly. So the problem appears to be resolved that way.

That being said, whether I use Matlab to obtain the coefficients of the model, or Ansys, there is still the possibility that I get 'negative slopes'. For example, if I use only some of the uniaxial tests, there might still be a negative slope at the beginning.

So my other question would be, is there any *easy* way (especially through Matlab or another available software) to do a least-squares fit where I have enough control/input into the process as to eliminate the possibility of negative curves? Because for obvious reasons, a fitted curve with a larger error but positive slopes (especially at the smaller strains) is preferable to a curve with a small error but a downward slope right at the beginning.

 

[adlh01]

Let me clarify. The graph posted was a 'composite' curve made up of all the different data sets that I have and then fitted, but zero strain parts were badly butchered. I had been originally told to make some sort of composite of all the data, but instead I'm now simply using all the data sets.

Using different combinations of the data sets that I have, or using them all, I am able to obtain working coefficients using various Mooney-Rivlin and Yeoh models, with no 'negative slopes' or any such nonsense. But this isn't true of all the combinations, it's only true of some of them. In some combinations of data sets, there is still a tendency to do a 'negative' curve at the beginning, and often near the end of the data too. That's with Matlab. With the ANSYS Curve Fitting tool, the results are worse.

Looking at the ANSYS and Matlab results, the difference seems to be that MATLAB gives you the best fitted curve disregarding the physical constraint of a positive slope (at least in the beginning), whereas ANSYS gives you the best fitted curve disregarding not only that constraint, but the constraint of having the initial stress on zero strain be zero. Instead, the curve arbitrarily starts anywhere where ANSYS deems it fit.

So based on all that, I think the problems have more to do with the software and me having different definitions of what the best fit is, than any major problems with the data.

 

[afreiden]

So based on all that, I think the problems have more to do with the software and me having different definitions of what the best fit is, than any major problems with the data.

I disagree.

If you want the advice of a true expert, make a post on PolymerFEM. Jorgen Bergstrom will be happy to help you and will probably even give you a free copy of MCalibration, which is a software that can take your raw data and find your Mooney or Yeoh coefficients, and then even export to ANSYS.