This post describes a new feature that will become available in R2024x FD01, on Feb 10, 2024.
The image above comes from the Abaqus Benchmark manual problem named "Anisotropic hyperelastic modeling of arterial layers". That manual section contains a realistic material model for the Holzapfel anisotropic hyperelastic model. The problem has been analyzed numerically by Gasser, Holzapfel, and Ogden (2006). The numerical study demonstrates the significant effect that dispersion of the collagen fiber orientations can have on the mechanical response of soft tissue. We have used that manual section to create some realistic "synthetic test data" for the adventitial layer of human iliac arteries. This post shares that synthetic test data and describes how one can calibrate the Holzapfel material model using the 3DX calibration app. The Holzapfel material model for calibration will be released in early 2024 with R2024x FD01.
As seen in the figure above, the material response is very soft at low stretches; only a small force is needed to achieve significant extension. Once the collagen fibers are approximately aligned with the loading direction, the material stiffens rapidly. It is assumed that two families of collagen fibers are embedded in the specimens, symmetrically arranged with respect to the axial and circumferential directions of the artery and with no component in the radial (thickness) direction. The angle between the mean orientation of the fibers and the circumferential direction is γ=49.98°. This angular orientation of the collagen fibers is input via the Abaqus *orientation feature.
First steps: We start by using 3 of the .inp files from the Benchmark manual:
1) adventitia_axial.inp This is a 1/8 model with a run-time of ~11 seconds.
Synthetic test data is (time, 2*U1, 4*CF1).
2) adventiti_circ.inp This is a 1/8 model with a run-time of ~11 seconds.
Synthetic test data is (time, 2*U1, 4*CF1).
3) adventitia_15deg.inp This is a full model with a run-time of ~91 seconds.
Synthetic test data is (time, U1, CF1).
These 3 Abaqus FE models use the k (Kappa, or fiber dispersion parameter) =0.226 value. These three files were modified for use with the calibration app.
All "Parts & Assemblies" attributes were removed (these are not supported in the calibration app)
All use of *Parameter attributes were removed (these are not supported in the calibration app)
Note: The "Holzapfel" (2006) model has been in the Abaqus solver for many years. In the 2022 version of Abaqus another version of the Holzapfel model, called the Holzapfel-Ogden was added. This Benchmark problem and this post are using the older Holzapfel-Gasser-Ogden (H-G-O) material model.
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 2022)
Here is an image of the initial setup of the calibration problem. The Holzapfel material model was added only to the FE mode of the calibration app. For this initial demonstration we chose to only include the axial and circumferential FE models in the objective function. We chose to do this because those models run in only ~11 seconds. All three models are loaded with a Cload (known applied load) and the measured response is the U1 displacement of that node.
The narrated video below shows the entire process of setting up this calibration.
Note in the image below, that since we excluded the 15 degree test data from the objective function, the calibration app does not run that simulation, thus cannot plot a response curve for it.
If we want to see the 15 degree (green) response curve, we can toggle it on (for the objective function), and then run an Evaluate. The Evaluate only takes about 116 seconds.
Note that the calibration has recovered the known material model parameters :
*Material, name=IliacAdventitia
*Anisotropic hyperelastic, Holzapfel, local directions=2
**
3.82e-3, 0.0, 996.6e-3, 524.6, 0.226
The zip attached contains:
1) An Excel file of the synthetic test data.
2) The 3 modified Abaqus .inp files.
3) A 3DExperience file named arterial_layer_start.3dxml. This requires version R2024 FD01 or later.
Back to: Sharing Material Test Data
Back to: Material Modeling and Calibration - An Overview and Curriculum
