Introduction
I very rarely use a hyperelastic material model in a FE simulation, but a lot of people do. Unfortunately, I see a lot of errors when people use a hyperelastic model. The theory of hyperelasticity is very simple, and I’m hoping that this article will help you avoid 5 of the most common mistakes. Let’s jump right to it!
Mistake #5
A common mistake is to not realizing that there are 2 types of hyperelastic models:
I1-based models
This includes:
- Neo-Hookean
- Yeoh
- Arruda-Boyce (Eight-Chain)
- Gent
- Marlow/Response Function
These models can be calibrated using uniaxial tension data only
Non I1-based models
This includes:
- Mooney-Rivlin
- Ogden
- Polynomial
- Extended Tube
- Hyperfoam
These models need experimental data from 2 or more different loading modes
If you use a non I1-based hyperelastic model then you NEED to use experimental data from 2 (or preferably 3) different loading modes. For example, uniaxial, biaxial, and shear.
A classic example of this mistake is shown in the figure to the right. This figure shows the results from a 2-term Ogden model calibrated to uniaxial tension data, but since that is not enough, the model ended up with really odd predictions in compression. Note that MCalibration now catches this error and presents a warning if you try to do this!
Mistake #4
Common mistake number 4 is to use too much experimental data when calibrating an I1-based hyperelastic model. I1-based hyperelastic models only need experimental data from one loading mode.
The following example shows predictions from an Ansys Arruda-Boyce Eight-Chain model that was calibrated to uniaxial tension data. The figure shows that the calibrated model predicts the response also in other loading modes.
If you use an I1-based hyperelastic model then you don’t need to run as many experiments, which will save you money!
Mistake #3
Common mistake number 3 applies to all material models, not only hyperelastic models. The mistake is to calibrate the material model to data with incorrect strain magnitudes. You should always plan ahead when you do experimental testing. Specifically ask yourself: what strain magnitude do I care about?
The figure to the right shows the predictions of the same material model that was calibrated in the Mistake #4 section above, but this time the experimental data has been truncated at 10% strain.
Clearly, if you calibrate the hyperelastic model to experimental data up to 40% strain, but in your real application you only see a max strain of 10%, then you will not get as accurate predictions.
Always use relevant strains in your material model calibrations.
Mistake #2
Hyperelastic material models are most often used for rubber-like materials, and rubber-like materials often exhibit Mullins damage. That is, the stress-strain response is a bit stiffer in the first few load cycles, and then reaches a steady-state response.
This figure shows experimental data for a chloroprene rubber with 15 pph carbon black. Even for this lightly filled rubber the stress response softens during the first few load cycles, this is the classic Mullins effect.
The common mistake that I see is that many engineers do not plan ahead for the Mullins damage. If you want to include Mullins damage in your material model then you need to experimentally characterize it. If you do not want to include it then you should condition your rubber specimens so that the Mullins damage is removed.
Mistake #1
And the number 1 mistake that I often see is that a FE engineer is using a hyperelastic material model when they should not. Hyperelasticity is easy to use, but often provide inaccurate predictions for real materials.
This figure shows the compressive load-unload response of the same chloroprene rubber that I presented in the Mistake #2 section above. You should always remember that virtually all polymers exhibit time-dependence during loading. So if you perform a load-unload experiment, the unloading response is often quite different than the loading response. This behavior cannot be captured using a hyperelastic material model.
You should always consider if it is better to use a viscoelastic or viscoplastic material model. In many cases it is worth the extra work! And with MCalibration it is easy to calibrate any time-dependent material model.
Summary
Here are 5 common mistakes when using a hyperelastic material model:
- Calibrating the hyperelastic model using not enough experimental data
- Calibrating the hyperelastic model using too much experimental data
- Calibrating the hyperelastic model to experimental data with too large or too small strains
- Not considering the Mullins damage
- Using a hyperelastic model when it is not appropriate
