Foam Viscoelastic Modeling

[PaulG]

Dr. Bergstrom,

First of all I want to thank you for setting up this site! There is a lot of critically important information here that is otherwise very difficult to dig up! :D

I am currently working with ABAQUS to model polymer foams.

These foams are compressed at a strain rate of 2.5/s, but our test equipment is limited to a (reliable) maximum rate of just 0.05/s.
I have ability to do creep testing and DMA however.
My samples are approx. 50x50x30mm blocks, with the indention on the thinnest side, and will see strains of 20-50%.
One of my foams is viscoelastic, while the rest are elastic.

My problems are these:
The samples are a simplified version of the object I am trying to model. Due to the geometric complexity of the final model I am forced to use ABAQUS/Explicit as Standard cannot cope with the complex contact conditions.
As a must, I have to model the rate-dependant behaviour up to 2.5/s, so I have been currently using the *hyperfoam & *visco with a Prony series from DMA (on a small (20x10x3mm) sample). The model requires static-state stress-strain data, this is simple to get from the elastic material, but what rate should a viscoelastic material be tested at as it is does not have a static-state response? (I have uniaxial tension/compression, planar compression and volumetric tests)

The second part of my problem is that I would like to model the mullins effect, but this is incompatible with the *visco option. I think you have mentioned elsewhere that the BB hysteresis model can take mullins into account, but I assume that as it is a rubber model (and can only be used with hyperelastic) it will not model the foams high compressibility - am I correct?

And the last part:
I'm currently using the *visco option for both the (hyper)elastic and viscoelastic foams due to there being a large amount of undissipated energy in the model during and after indentation. The time scale is too long for the bulk visco options to have any significant effect (even with very high coefficients), and a large fraction of the jobs fail due to wave speed errors (they shake themselves apart) without the *visco option. Is there another way of reducing the medium-high freqency vibration other than using a doctored viscoelastic response? (this method is practical, but its accuracy is questionable).

If you have got this far then thank you for reading my little essay! Any advice or pointers will be greatly appreciated,

Yours,

Paul Gibbs.

[Jorgen]

Hi Paul,

Good questions. I have done a lot of work on foams lately and will start publishing my results later this year. (My first presentation will actually be at the ABAQUS Users' conference in Boston in May this year).

First two general comments. I have noticed in my own experiments with foams that the rate-dependence can be quite different in different loading modes, e.g. smaller in compression than in shear, etc. To truly understand and characterize a foam material it is hence often recommended to perform the experiments in different loading modes.

Secondly, I have also used the *hyperfoam with the *Visco option in some of my work. My reason for using that model is that it is a good reference material for the built-in capabilities of ABAQUS. I then compared that model with other foam models that I have developed.

Now to your questions.

About deformation rates. Traditionally it is recommended to use the slowest possible deformation rate for the experiments that will be used to extract the hyperelastic response. What I typically do, however, is to fit the material model to the experimental data without the help of ABAQUS. That is, I have implemented the equations in Matlab and then use the minimization algorithms of Matlab to find the best set of material parameters. My experience is that this approach is much more general and powerful than using ABAQUS for the parameter extraction.

About Mullins effect. One of the models that I have been developed is an extension of the BB hysteresis model in which the eight-chain hyperelastic model has been replaced by the hyperelastic hyperfoam model. This simple substitution gives a very simple and robust model that in my tests have been shown to be more accurate than the *Hyperfoam + *Visco combination model. One additional advantage of this BB-foam model is that it directly enable the incorporation of Mullins effect (both the Ogden-Roxbury and the Qi-Boyce models) and temperature effects.

About stability. Do you expect to see high wave speed vibrations in your real parts? If not, I suspect that they are simply numerical issues that you should be able to fix. Do you use mass scaling in your simulations? Do you have the right mass density?

- Jorgen

[PaulG]

Jorgen,

I shall certainly be keeping an eye out for those papers!
I had planned to do multi-mode testing, but only to get the base stress-strain curve, I will have to look into more varied rate-dependancy testing too.

As for the stability problems I'm having, I have checked all the densities are correct and have been playing around with mass scaling for some time. I can generate similar effects by using a large amount of mass scaling and re-calculating it every increment, but the instability can also be generated in jobs where the scaling is switched off. I dont see any high speed vibrations in the real parts.

It appears to be coming from the contact (kinematic, penalty and general all have similar effects), and is increased when using rigid-deformable over deformable-deformable contact. It certainly occurs when parts penentrate, but the addition of viscoelasticity vastly reduces the effect:

Video (http://www-staff.lboro.ac.uk/~mmpjg/NoVisco_Visco.avi) (one on the right has *visco)

I think my next step will be to introduce some damping into the contact.

(I have done some high speed video testing on the parts and they are very similar to the ABAQUS model, except for the higher freqency vibrations).

Paul.[/url]