Introduction
In this article I will give my recommendations for what experiments to run if you want to calibrate a material model for a rubber. I have found a lot of misinformation about this, and here I will try to give a modern answer to this. To make my recommendations are useful as possible, I divided them into 3 different applications:
Dynamic (Frequency) Loading
- Frequency domain FE simulations
- Super small strains (<1%)
Slow Monotonic Loading
- Time domain simulations
- Monotonic loading at one strain rate
- Finite strains
General Loading
- Time domain simulations
- Any strain history
- Finite strains
In the following sections I will propose test plans for each of these applications.
Dynamic (Frequency) Loading
Run the following Dynamic Mechanical Analysis (DMA) tests:
- First perform a strain amplitude sweep at constant frequency (about 1 Hz). This is used to establish the strain range in which the material response is strain amplitude independent. The material will be linear viscoelastic only in this strain range.
- Run a frequency sweep in order to measure the storage modulus (E’) and loss modulus (E’’) data.
- Repeat the frequency sweeps if you are interested in calibrating a WLF or Arrhenius type time-temperature superposition (TTS) model.
The results from these tests can be used to calibrate a linear viscoelastic material model.
Slow Monotonic Loading
Run the following monotonic uniaxial tension tests:
- Uniaxial tension using a dog-bone shaped specimen (e.g. ASTM D638 Type IV).
- Deform the specimen to large strain.
- Repeat the test 2 to 3 times using different specimens (in order to determine the experimental variability).
This data can be used to calibrate an I1.-based hyperelastic material model like the Arruda-Boyce or Yeoh model. Some people claim that you should also perform tests in 2 other loading modes (biaxial, shear, etc). This is NOT necessary as long as you use a I1-based hyperelastic material model.
General Loading
Run the following cyclic uniaxial tension tests:
- Load to 5% strain, hold the strain for 1 min, unload to a force that is close to 0;
- then continue to load to 10% strain, hold the strain for 1 to 10 min, unload to a force that is close to 0;
- then continue to load to 50% strain, hold the strain for 1 to 10 min, unload to a force that is close to 0;
- finally either load to failure in tension, or unload to zero.
- Repeat this experiment 2-3 times (using different specimens) in order to determine the experimental repeatability.
- The testing should be performed using ASTM D638 type IV (or similar) dogbone-shaped specimens.
- All loading and unloading should be performed at a constant engineering strain rate of about 0.01/s to 0.1/s.
- Repeat each load cycle 2 or 3 times if you are interested in also calibrating a Mullins damage material model.
This data can be used to calibrate an I1-based non-linear viscoelastic material model.
- Repeat the testing at multiple temperatures if needed.
- Use MCalibration to calibrate a suitable material model to experimental data.
