The image above was taken from Stuart Nixon's post : An Implementation for a more Payne-ful Rubber Response!!
You probably want to browse that post first. Congrats to Stuart ! He was reading through a 2008 Abaqus Users' Conference paper (attached below) by Jorgen Bergstrom. Jorgen proposed something he called the "Dynamic Bergstrom-Boyce" model (DBB) in order to capture the Payne effect. Stuart recognized that he could achieve the same type of model using a PRF model with a special form of Mullins damage. After some consultation with Juan Hurtado, Stuart prototyped this using a UMullins user-subroutine. That special form of Mullins damage was implemented natively in Abaqus version 2025x FD02 and called :
*Mullins Effect, Definition = Slow Decay
Stuart also digitized the test data from Bergstrom's paper. The test data for Natural rubber is attached in the zip file at the bottom of this post. The test data is included in the file "Payne_Effect_Natural_Rubber_just_data.3dxml".
The image below shows the DMA test data loaded in the 3DX Material Calibration App. This data is from a dynamic amplitude sweep at constant frequency (1 Hz). The Material Calibration App requires that the dynamic strain amplitude (aka strain amplitude) be input as the "peak-to-peak" values.
In the video below, we start from the "just data" 3dxml file and import a PRF-Mullins model as created by Stuart Nixon. Next we run a calibration. This video was created on Oct, 5, 2025 using a development version of the Calibration App that will become R2026x FD01 (release to public on Feb 7, 2026).
The result of the calibration :
In the calibration video above, I showed a way to generate a time series from the DMA test data. There is another way to visualize the stress-strain behavior of a material model, that is using the "Range Response Data" feature, sometimes we just call this "RO" data (for Response Only). In the video below I use this Range Response Data feature to create three separate harmonics, all at 1 Hz, but with dynamic strain amplitudes of 0.002, 0.02 and 0.20 Then we can use these strain-time waveforms to plot the stress-strain curves from the known material model.
Note: There is this bug with Mullins effect: IR-1456606
An Abaqus analysis using a PRF material model with the combination of Hyperelastic + Nonlinear Viscoelasticity + Mullins effect can incorrectly underestimate the softening response of the material compared to that of an equivalent Hyperelastic + Linear Viscoelastic + Mullins definition. The discrepancy is more pronounced for the long term (equilibrium) response of the material. It can be resolved by multiplying the parameter “m” of the Ogden-Roxbourgh model or the “Uh” parameter of the Exponential and Slow decay models by the stiffness ratio of the equilibrium network.
This bug fix should appear in R2026x FD01.
Reference paper :
Zip file:
