The image above shows five stress-strain curves for a polymer material called PEEK (Polyether Ether Ketone).  This test data was digitized from the paper by David Quinn, et al. (2013) : Development and Experimental Validation of an Advanced Nonlinear, Rate-Dependent Constitutive Model for Polyether Ether Ketone

User-subroutines were recently published on the SIMULIA Knowledge-Base (QA00000429005) to allow the Abaqus PRF model to replicate Bergström's Three Network Model.  Let us call this the "PRF_TNM" model.  Abaqus solver 2025 HF1 or later can be used. This post describes how the 3DExperience Material Calibration App can be used to calibrate the PRF_TNM model. In the post below we will discuss modeling this PEEK material with the Abaqus equivalent of Jorgen Bergström's Three Network Model.  You should probably read this earlier post with a good deal of background information.  Jorgen Bergström's Three Network Model.

The first video below shows the process of setting up this calibration in the 3DExperience Material Calibration App.  This video was created on May 26, 2026 using the public cloud R2026x HotFix 3.19.  The five test datasets were imported prior to starting the video, just to save some time.  

Steps in this process :

1. Use Abaqus make -library PRF_TNM_std.f                 to create the StandardU.dll   (do not rename this file)
2. Open the calibration app and import the test data as nominal stress-strain
3. Change to Numerical mode.
4. Select the Parallel Rheological Framework material model
   1. Under User Defined Features, add Include solution dependent variables (DEPVARS). 
   2. Under User Defined Features, add Include custom schema.
5. Select the Parallel Rheological Framework material model
   1. select the Hyperelastic model as user-defined.  Set the number of constants = 0
   2. select the Viscoelastic model as user.  Num networks =2.   Set the number of constants = 0
6. Import the Custom Schema file. The custom schema contains the reference values for the parameters. 
7. Import the StandardU.dll file
8. Under "Plots", turn the "Automatically update response data" back to on.

That previous video showed the setup process, but did not actually execute a calibration.  It used the reference values and showed that indeed the reference values produced a stress response that matched the test data fairly well.   

The image below shows a perturbed set of material model parameters.  The deactivated parameters (not used in the calibration) have been deactivated because these test datasets do not provide enough information to calibrate them.  

The image below is the completion of the calibration.  This calibration was run on May 26, 2026 using the public cloud R2026x HotFix 3.19.  It uses the Hookes-Jeeves optimizer using 5 cpus.  The blank white space in the Objective History (no graph) is a known bug in that version.

Reference paper:

Development and Experimental Validation of an Advanced Nonlinear, Rate-Dependent Constitutive Model for Polyether Ether Ketone (PEEK) by David J. Quinn, Jorgen Bergström and Sam Chow.

• December 2013

• Journal of Medical Devices 7(4):040908

          DOI:10.1115/1.4025831

The zip file below contains:

1. The Knowledge Base article (pdf).
2. The Knowledge Base user-subroutine source code. 
3. The test data that was digitized from the 2010 paper.  (5 csv files)
4. The Custom Schema .xml file.
5. An Excel file that converts from Jorgen's TNM parameters to the required PRF_TNM parameters. 
6. The 3DX exported file PEEK_Quinn_just_data
7. The 3DX exported file PEEK_Quinn_Start2.3dxml

The 3DX file PEEK_Quinn_Start2.3dxml contains the user-subroutines as a compiled StandardU.dll.  That works in today's version of 3DX, but may fail later in time because incompatibility between the .dll file and the version of Abaqus run by the material calibration app.   

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