high deformation under high strain rate

[Jay]

We are analyzing an impact behavior of a rubber structure.
The hightest strain is about 0.3 and strain rate 10000/s.
We need to get some test data for simulation.
However we met some problems, maybe people here can give me some help.
1. We will use Hyperelastic and Viscoelastic model in ABAQUS. Is that a correct choice?

2. In experiment, should we do the experiments in high speed (strain rate 10000/s) to obtain the hyperelastic material property?

3. To obtain viscoelastic properties, should the test be done in high deformation (strain = 0.3) and high strain rate? Do we need to do both relaxation and creep test?

Thank you very much for giving us suggestions.

[Jorgen]

Hello Jay,

There are a few options to model strain-rate effects at those high strain rates. One is to use, as you described, Hyperelasticity and Viscoelasticiy. If you take this approach then you need to calibrate your model to data as close to the actual strain rates and strain levels as you can. The reason for this is that the viscoelasticity model that is available in ABAQUS can only capture the response of a rubber structure over a very small range of strain rates.

Another option, which is more accurate and general, is to use the *Hysteresis option in ABAQUS. This option is based on the Bergstrom-Boyce model which has been shown to capture the response of rubber for large ranges of strain rates, including between 0.01/s and 1000/s, using one set of material parameters :!:

To determine the material properties you can use experiments performed at different strain rates, or stress relaxation, or creep tests. Note that it more difficult to calibrate the Viscoelasticity model in ABAQUS since it is not going to give you accurate results both at a long term stress relaxation test and at an applied strain rate of 1000/s.

Best of luck.

[Jay]

Dear Dr. Bergstrom,

I spent some time reading ABAQUS manual and your articles, then I found that you did lots of great jobs. I am so lucky to discuss with a real expert here. I am new in this field, this website give me much help. :D

However, I still have some questions from your last reply.
1. Is Hysteresis model the same as the AB model in this website? According to the ABAQUS theory manual, the formula is from Arruda and Boyce(1993). I'd like to know the difference of the results from Hysteresis and BB model.

2. Does BB model and Hysteresis model work in strain rate 1000/s ? The highest strain rate in your paper is only 0.2/s. Do you have other verification studies?

3. It seems hard to determine Hysteresis material constans from tests. Does your UMAT of BB model support the evaluation of material constants from tests?

4. If we use Hysteresis or BB model, a unixal tesion test at different strain rate is enough to determine the material constants? Does the testing strain rate need to be 1000/s? (the highest strain rate in my structure is 1200/s)

5. To determine the hyperelastic material properties, should the tests be done in high speed? or usual static test is OK?

Thank you again for your help!

[Jorgen]

Jay, here are a few answers:

:arrow: The AB-model on this website is not the hysteresis model. The AB-model is a model developed by Arruda and Boyce for glassy polymers undergoing viscoplastic deformations. It turns out that Arruda and Boyce also developed a hyperelastic model: the 8-chain model. The BB-model is a model that I developed for Elastomer and rubber-like materials. One version of the BB-model is available in ABAQUS as the *Hystersis model.

:arrow: Yes, it turns out that the BB-model works even at strain rates of the order of 1000/s. This has been recently been shown by Steve Quintavalla and co-workers. The reason that the BB-model works for such a broad range of strain rates is that it based on the physical micromechanisms driving the rate-dependence of rubbery polymers.

:arrow: It is somewhat tricky to determine the material parameters for the BB-model. This is not a unique feature of the BB-model but a challenge with all advanced material models. I have developed techniques to automatically extract the material parameters from given experimental data. Although not yet available for public use, my software tools make the extraction of the material parameters simple.

:arrow: It is sufficient to use uniaxial tension tests at different rates to determine the material parameters. It is often valuable to record the stress both during loading and unloading. The reason it is sufficient to use uniaxial data to calibrate this general 3D-constitutive model is that it is based on the micromechanisms driving the material response. Other purely phenomenological models such as the Ogden or polynomical models do not have this very attractive feature. It is not necessary to perform the calibration experiments at the actual strain rate, but it does not hurt.

:arrow: You can use static (i.e. slow deformation rate) tests to determine the hyperelastic material properties (i.e. the equilibrium response of the material).

- Jorgen

[Jay]

You mentioned that viscoelastic model in ABAQUS is only for small strain.
But there is a large strain viscoelastic model in ABAQUS, is there any disadvantage of the model?

[Jorgen]

Hello Jay,

Yes, ABAQUS has a large strain linear visoelastic model. This model can be used for elastomers, but there are a few issues to keep in mind when doing this:
:arrow: The large strain viscoelastic model does not capture time-effects, rate-effects, and hysteresis well for real elastomers. If you are interested in obtaining accurate predictions then the large strain visoelastic model is not a good choice. The BB-model (*Hysteresis) is much better.
:arrow: The large strain viscoelastic model cannot predict Mullins effect
:arrow: It is difficult to capture temperature effects using the large strain viscoelastic model.

- Jorgen