Holzapfel-Ogden anisotropic hyperelastic calibration is a new feature added to the FE mode in the calibration app for R2024x FD01 (release date for the public cloud, Feb 10, 2024). 

Note:  The "Holzapfel" (2006) model has been in the Abaqus solver for many years, this has now been renamed to Holzapfel-Gasser-Ogden. In the 2022 version of Abaqus another version of the Holzapfel model, called the Holzapfel-Ogden was added.

Set DEFINITION=HOLZAPFEL-GASSER-OGDEN to use the Holzapfel-Gasser-Ogden strain energy potential.

Set DEFINITION=HOLZAPFEL-OGDEN to use the Holzapfel-Ogden strain energy potential (new in Abaqus 2022).

The bulk of this work was done by my colleague Jiang Yao for the Living Heart project.  This work follows the paper by Sommer, et, al, Biomechanical properties and microstructure of human ventricular  myocardium  2015      http://dx.doi.org/10.1016/j.actbio.2015.06.031

The image above shows a series of six triaxial shear tests performed on the myocardium tissue, as detailed in Sommer, et al, and other papers.  Sommer also shows biaxial testing which we will use here as well.

Holzapfel-Ogden Form

The form of the strain energy potential is based on that proposed by Holzapfel and Ogden (2009) for modeling passive mechanical response of myocardium tissue, which is an orthotropic material:
 

For the work here, we will consider the tissue as incompressible, thus D=0.  There are 8 deviatoric material parameters:    a, b, af, bf, as, bs, afs, bfs

The test data is digitized from the Sommer paper. The biaxial data was digitized from Figure 8(a).  The triaxial shear test data was digitized from Figure 13(a). Here is a summary of the test data:
 

The earlier work by Jiang Yao and her team was performed with the general purpose optimization software, Isight, and used FE unit-cube models to generate the stress responses. There are 7 experiments and 7 matching FE unit-cube Abaqus models.  Although the figures in the Sommer paper show stress as Cauchy stress, I have imported the digitized test data as nominal stress / nominal strain.  This may cause some small differences in the results, but the work here is for demonstration purposes.

The work by Jiang Yao showed calibrations to just the equibiaxial test data, then just to the shear data, then a final calibration to all the test data. I have repeated all of that work using the calibration app, but for brevity will just show the final results here in this post.

Here is a slide showing the final calibration results from Jiang Yao and her team. Units on the "a" parameters are MPa.
 

The image below comes from a development version of the calibration app that will be released in Feb, 2024.  This is not a calibration, but an "Evaluate" using the parameters determined by Yao and team (shown above). The resulting stress-strain curves (below) for the 8 responses match very well with the curves from Jiang Yao (above).  The aggregate R2 value for this solution is = 0.9402.
 

Because this material model was created with myocardium tissue in mind, the parameters shown above are used as the initialization parameters in the calibration app. 

The zip file below contains the 3dxml file (can only be opened by R2024x FD01 and later) and the 7 Abaqus unit-cube model .inp files.  These files are set up in units of MPa.

Back to:  Sharing Material Test Data

Back to:  Material Modeling and Calibration - An Overview and Curriculum