Be sure to read this post first:
Holzapfel-Ogden Anisotropic Hyperelastic Calibration
Diving a little deeper into the Holzapfel-Ogden calibration, and adding some additional details. Again, here is the equation for the strain energy potential :
The more you know about the equations and the role that the parameters play, the the more insight you will have into the calibration process. This will allow you to set better initial values, and set meaningful minimum and maximum bounds. In the work from Jiang Yao and her team, they looked at the stress-strain equations for the types of test data that they had available.
For the equibiaxial test data:
For the triaxial shear test data:
Looking at the FS mode and FN mode equations, they differ only by the last term, involving the parameters afs and bfs. This is also true for the equations for SF mode and SN mode. Recall that in the triaxial shear test data that there is virtually no difference between the FS & FN test data, nor for the SF & SN data. This would suggest that the parameter afs should be zero or near-zero. Also notice that for this set of test data, once afs is zero, then the parameter bfs cannot be determined.
Looking back at the equations, notice that all of the "a" parameters will have units of stress, while the "b" parameters are unit-less. Also, all of the "b" parameters are used in an exp(b) expression. As any "b" parameter becomes large, the corresponding exp(b) expression becomes very large. For this reason, it would be a good practice to supply a maximum bound on all of the "b" parameters, perhaps a value of 20 would be reasonable.
From the Abaqus Keyword docs:
From the Abaqus Materials section:
The calibration app allows the user to include the linearization stretch (see image below). Once selected, the linearization stretch shows up in the parameter list. While we have allowed it to be used as a design variable, it may be safer to turn it off as a design variable.
Side note: Abaqus was recently updated (2024 FD01) to allow the "b" parameters to be set = 0.0 The calibration app is a bit behind, but will also be updated to allow this in 2024 FD02.
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