We use the image above in describing the behavior of the PRF model (Parallel Rheological Framework). There are several posts in the SIMULIA Community showing the calibration of the native PRF model.  The dashpots in the above diagram relate to the creep law / nonlinear viscous behavior of each of the 1 through N viscous networks. The UCREEPNETWORK user subroutine allows the user to specify their own nonlinear viscous law. 

 There is a UCREEPNETWORK user subroutine supplied along with this Abaqus Verification Manual section:  UCREEPNETWORK

The whole material model is listed here:

*MATERIAL,NAME=ABVISC
*HYPERELASTIC,ARRUDA-BOYCE,MODULI=INSTANTANEOUS
20., 7.
*VISCOELASTIC, NONLINEAR, NETWORKID=1, SRATIO=0.3, LAW=USER, PROPERTIES=4
2.5E-5,  4.0,  -1.0,  0.01
**

So, this is a PRF material model with a purely hyperelastic zeroth network and one viscous network whose behavior is given by the UCREEPNETWORK user subroutine.  In the user subroutine you will see that the material model is a Bergstrom-Boyce model and the material parameters can be given on the data line as:

        A   = props(1)
       dm = props(2)
       C   = props(3)
       E   = props(4)

This user subroutine data line interface mimics the older Law=Bergstrom-Boyce interface.  The newer one is called "BB Power Law". Only the newer one is supported as a native BB model in the 3DExperience platform.   

           Older (original) version, Law=Bergstrom-Boyce

         Newer version, Law=BB Power Law

Using the Abaqus .inp file from this Verification Manual section, I created some synthetic stress relaxation data from loadings at four different applied strain levels. The synthetic test data is attached to this post in the zip file at the bottom. 

In this first video, we start by importing and opening a 3dxml file that just has the synthetic stress relaxation test data.  We will then select the Arruda-Boyce hyperelastic model with the native Bergstrom-Boyce nonlinear viscous behavior.  We make the ReferenceStress parameter = 1 and the ReferenceStrainRate looks like the "A" parameter from the older BB model. A narrated video of calibrating the native PRF -BB model, using the public cloud, R2024x HotFix 3.11 (May 14, 2024):

Here is an image just before the native BB calibration:

And the image after the BB calibration

In this 2nd video, we import the compiled user subroutine and switch to the "User" Nonlinear Viscous Law

Here is an image at the end of the user subroutine calibration. All of the parameters have been recovered quite well. 

The zip file attached contains all the files needed to work through this example

Back to:  User Subroutine Calibration

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