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Should Material Model Parameters be Unique?

Story

  1. You have some experimental data
  2. You calibrate a material model to the data (using MCalibration)
  3. You get some material parameters
  4. You then, for some reason, repeate the material model calibration using the SAME material model, but you end up with a different set of optical material model parameters
Questions:

Should you expect to get the same optimal material model parameters if you repeat a material model calibration?
Is there a problem if you don’t get the same material model parameters?

Example

To study this issue in more detail I selected a PolyUMod TNV model consisting of 2 Yeoh hyperelastic networks in parallel, see the material model set up in Figure 1.

Unique TNV Selection

Figure 1. TNV model set up.

The predicted stress-strain response of the TNV model with C10=1 for both networks is shown in Figure 2.

Figure 2. First TNV model prediction. C10 = 1.

Another example, using the same material model, is shown in Figure 3. In this example I set C10 for network 1 to be 0.5, and then I set C10 for network 2 to be 1.5. The figure shows that the predicted stress-strain response for this set of material parameters is exactly the same as for the first example shown in Figure 1.

This example shows that a material model with two different sets of material parameters can give exactly the same stress-strain predictions. In other words, there is no requirement that the optimal material model parameters always be unique if you repeat a material model calibration.

In Summary

  • The calibrated material model parameters do not need to be unique
  • Do not worry if:
    ➡️  You have enough high quality experimental data
    ➡️  The material model accurately represents the experimental data

Side Note

There are, of course, cases when you want and should expect the optimal material parameters to be unique. For example, If you calibrate a neo-Hookean hyperelastic model to a single uniaxial tension curve then there is only one optimal solution to the material model parameters. This type of unique solution typically only occurs for very simple material models. It is no guarantee it will happen for more advanced material models.

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