hyperelastic material models and shell181

[reetu]

I am trying to model a hyperelastic material using shell181 element in Ansys. I provide uniaxial stress-strain test data and fit a Mooney-Rivlin model to it. The fit is very good. However, in the final solution, I find that the material stress and strain do not relate as per the defined behavior. Example: if strain is 7%, the stress should ideally be 200 kPa but the computed value is 2000 kPa.

I can understand that if various deformation modes are not accounted for in the test data, there will be deviations of simulation results from experimental ones. But what can be the reason for differences between the input data and output data in terms of stress-strain.

Any help is greatly appreciated.

Thanks
Reetu

 

[cbrn]

Hi,
I think you have the answer in your very post: you have uniaxial test data, but if, for example, your phenomenon has a very important part of hydrostatic-type sollicitation, your data is absolutely not appropriate and you will "see" no matching between results and theory (but also note that hand-calculating hydrostatic stress with uniaxial test properties is also not correct...).

Regards

 

[cbrn]

Hi,
... I forgot: also ensure that you have Large Deflection turned on; generally when coping with hyperelastic materials it is unlikely that the Small Deformations hypothesis is fulfilled.

Regards

 

[reetu]

Hi cbrn

I have been thinking about this and it does seem likely that uniaxial test data is the cause of the problem. I do have large deflection analysis turned on.

However, another question that plagues me here is:
what happens when we take a linear material modulus corresponding to uniaxial test data. Whatever holds true for non-linear case should also hold true for a linear model (for the same problem) and hence,the stress and strain in the final solution should not relate by stress=E*strain (E=young's modulus). But this is NOT the case. All stresses and strains do correlate by this formula for a linear material modulus case. It is kind of confusing at this point. Am I missing something here?

Thanks for your time. I appreciate it.

 

[cbrn]

Hi,
a non-lin analysis (where non-linearity is due to material properties) will give the same results as a linear one as long as the force field is such as to "call" an equilibrium solution (internal stress/strain field) which is still in the linear part of the material properties. In this case, but ONLY in this case, your statement "whatever holds true for a non-linear... also holds true for a linear..." is valid.
With materials such as rubber, the linear part is almost inexistent: with some constitutive laws, you define a Young's Modulus "E" anyway, but it is intended as "initial tangent modulus", because even for very small strains the response of the material immediately departs from linearity. With these materials, linear analyses are almost meaningless.
The hyperelastic constitutive laws (Mooney-Rivlin is only one of the possible, I'd say one of the easyest to setup but not always the most suitable - it depends on the material!) are NOTHING like a "sigma=E*epsilon", which is linear by definition.

Hope this sheds some light... I hope I haven't confused you even more!...

Regards

 

[reetu]

Hi cbrn

I understand what you are saying. stress=E*strain is not valid for non-linear problem. But then, stress is related to strain through a constitutive matrix which would consist of hyperelastic material constants determined using a non-linear material model. So, basically strains would be computed first and the stress would then be based on these strains and the constitutive matrix. Hence, for any value of strain, the stress should be determined by the stress-strain curve. When we say that if all modes of deformation are not accounted for in the test data, the results do not match experimental ones, my interpretation of the statement is the following:

suppose stress-strain curve is determined on the basis of a uniaxial test and the FE problem is solved. Then a force is applied to the body and a load-deflection curve is determined(and the force is not a uniaxial one). The stress-strain obtained from this experiment would not match the FE results obtained on the basis of uniaxial data. May be I am wrong here..I have had little experience with non-linear material models. Would you know of a good text in this field?

 

[reetu]

Hi

I also wanted to add that I am operating (in my FE model)within the range of strain specified in my test data to fit the material model.

 

[reetu]

Hi,

Another question that I have regarding Mooney-Rivlin model fitting to experimental data in Ansys:

Once we fit the Mooney-Rivlin (or any other model) to the stress-strain data in Ansys, is that the final material defining step. Or should we also provide a value of elastic modulus. I have seen that being done for cases where only the Mooney-Rivlin constants are provided and curve fitting is not done. But I am not sure how to go about with a model fitting case.

Any insights into this and any available literature would be greatly appreicated.
Thanks
Reetu

 

[cbrn]

Hi,
1- yes, I believe your interpretation is correct. I mentioned as an example the hydrostatic stress field because it happened to me to cope with a similar problem where I had only uniaxial data but the problem had an important (though not prevalent) hydrostatic component. Though the analyses provided good info for what we were searching, no comparison with "real field" tests was possible. On the other hand, another simulation of a quasi-uniaxial case showed agreement with experimental data well within 10%, which is really not bad for an hyperelastic non-linear simulation.
2- sorry, right now I don't remember. But I'm sure you easily find this info in the ANSYS Theory Manual and in the Advanced Analysis Guide.

Regards

 

[reetu]

Hi cbrn,
Thanks for the inputs.

This is the part of the code dealing with material model specification

MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,PRXY,1,,.49
TBFT,EADD,1,UNIA,file_UNIA_1.exp
TBFT,FADD,1,HYPER,MOON,3
TBFT,SOLVE,1,HYPER,MOON,3,1
TBFT,FSET,1,HYPER,MOON,3
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,DENS,1,,1100e-6 !g/mm3

I want to find out if EX also needs to be specified in this model. Would you be able to post part of your code that dealt with specifying the material properties by fitting experimental data to a non-linear model?

Also, with the uniaxial test data that you supplied to the FE code, were you able to look up the stress-strain relationship in the final solution. For a given strain, did the stress value from the FE computation correspond to the point on the test curve.

Thanks
Reetu