Introduction
Calibrating an anisotropic material model, even an advanced non-linear anisotropic viscoplastic material model, does not have to be difficult. In this article I will show how you can quickly calibrate basically any anisotropic material model. The calibration is surprisingly easy once you have sufficient experimental data. In the example below I will use experimental data for a polyethylene film material. Read on for the details!
Experimental Data
Figure 1 shows the experimental data data that was used in this study. The material was tested in uniaxial tension at 3 different strain rates. The fastest rate was 100X faster than the slowest rate. The material was tested in two different orientations: (1) Machine Direction, MD, which will be aligned with the local 1-direction; and (2) Transverse Direction, TD, which will be aligned with the local 2-direction. The figure shows that the large strain response is strongly anisotropic, and the yield stress may be weakly anisotropic.
Figure 1. Experimental data for a PE film material.
Note that when reading in the experimental data in MCalibration it is important to specify the loading mode (and direction) correctly. In this case the three tests that were performed in the transverse direction were specified as “Uniaxial (2-dir)”, see Figure 2.
Figure 2. The TD tests were specified to be “Uniaxial (2-dir)”.
Material Model
There are many potential material models that can be applied to the PE that is examined in this study. The goal here is not to examine the predictive performance of a bunch of different models, but simply to demonstrate the calibration procedure for one material. Here I selected to focus on the PolyUMod TNV model. As I have shown in a number of recent articles (PA66, PVC, etc), this model is excellent at predicting the response of isotropic thermoplastics. In this article I will show that this model can also accurately predict the response of anisotropic polymers. Figure 3 shows the material model selection in MCalibration. Since I don’t have unloading data I simply selected a two network TNV model consisting of a HGOB (Holzapfel-Gasser-Ogden-Bergstrom) anisotropic hyperelastic network, and Yeoh network in series with an anisotropic Power flow element.
Figure 3. TNV model setup in MCalibration.
To simplify the calibration I manually adjusted some of the material parameters. I specifically made the following adjustments:
- For the equilibrium network (id=7), I set
k11=0.01,k2=0.001. That is, I provided a little bit of “fiber stiffness” in the local 1-direction. - For the flow network (id=3), I set
C20=C30=0,F=H, and activated searching forG. The meaning of the Hill parameters are discussed in another article.
Calibration Results
The selected material model was calibrated using the automatic calibration approach in MCalibration. The final calibration results are shown in Figure 4. The final material model captures the anisotropic behavior of the PE material very well. The average error in the model predictions is 6.8%.
Figure 4. Predictions from the final calibrated material model.
The final calibrated material model can then be exported to the material model options shown in Figure 5.
Figure 5. Export the final material model.
Final Comments
- Calibrating an anisotropic viscoplastic material model requires suitable experimental data, and a suitable material model.
- Once the experimental data and the material model has been specified, the actual calibration is easy.
