Material Model Calibration
When you work with material models it is always important to think about the type and quality of experimental data that you have. I wrote a blog post about this called “Smart Testing of Polymers“, you should check that out if you have not already. In this post I will focus on a very specific question: is it better to run multiple stress relaxation tests, or one cyclic test with stress relaxation segments? By “better” I mean which of these two approaches enable a more accurate material model calibration. To investigate this I selected experimental data for a thermoplastic elastomer (TPE). The material was tested at monotonic tension at two different strain rates, and using two cyclic tests with multiple stress relaxation segments. The following figures show the experimental data.
From the cyclic tension tests with stress relaxation segments I also extracted the time-stress response during the relaxation segments. This type of stress relaxation data can be directly included in MCalibration by using the load case type “Stress Relaxation Data (time, stress)”.
The key questions that I'm trying to answer here is if it is better to use the complete stress-strain data files from the cyclic tests, or if it is better to use the extracted stress relaxation data.
To help answer this question I calibrated the PolyUMod TNV model, from the same parameter starting point, to 4 different combinations of the experimental data:
- Only the monotonic experimental data
- Monotonic data with the set of extracted stress relaxation behaviors
- The 4 original experimental data files
- The 4 original experimental data files with also the set of extracted stress relaxation behaviors
The following sections contain the results.
Calibration 1: Monotonic Data
As expected, the TNV model does not accurately capture the recovery response during unloading when calibrating to only monotonic tension data.
Calibration 2: Monotonic Data with Stress Relaxation
Also in this case the calibrated TNV model does not accurately capture the unloading response. This is to be expected since no experimental unloading data was provided to guide the calibration.
Calibration 3: The Four Original Data Files
The calibration results look really good.
Calibration 4: The Four Original Data Files with Stress Relaxation
The calibration results look really good.
Summary
| Calibration Data Set | Error in Predicted 4 Data Sets | Error in Predicted Stress Relax | Error in Predicting All |
|---|---|---|---|
| Monotonic | 3.06% | 2.96% | 2.99% |
| Monotonic + Relax | 2.87% | 1.07% | 1.72% |
| Original 4 Data Sets | 2.25% | 1.80% | 1.96% |
| Original 4 Data Sets + Relax | 1.79% | 1.02% | 1.30% |
- It is better to have more data than less data when calibrating a material model.
- The experimental data need to be relevant, "balanced", and focused on the features of interest.
- The answer to the question “Is stress relaxation or cyclic loading better?” depends on the material model.
- For simple material models, stress relaxation and cyclic tests with stress relaxation segments are equally useful.
- For advanced material models (like the TNV model), cyclic tests with stress relaxation segments are better!
Video about material model calibration:
