Pre-requisite:  Linear and Nonlinear Viscoelasticity

There are several posts here on the e-Learning resource center on Prony series linear viscoelasticity.  Prony series viscoelasticity has been in Abaqus for many years. 

This is the second post about transitioning from linear viscoelasticity to the use of nonlinear viscoelasticity.  In the first post, Linear and Nonlinear Viscoelasticity, we show the use of the PRF (Parallel Rheological Framework) model to capture a slight, or mild, amount of nonlinearity in the viscous behavior of an elastomer.  You should read that post before continuing with this one.

In this example, we use some test data provided by Axel Products for a polypropylene material.  This polypropylene exhibits more nonlinearity in its viscous behavior than the elastomer of our previous post.  In the attached PDF document, we show some of the test data we have for this particular polypropylene, then we march through the process of calibration.  In all of our examples, we like to paint a recipe, or strategy, for the calibration process. In our examples on calibration of the PRF model, we start with first creating a hyperelastic-Prony viscoelastic model.  We do that because it is easy to do and helps us: i) show that the material exhibits nonlinear viscous behavior, and ii) form a basis for some of the PRF parameters. 

In these two PRF examples we follow this same recipe:

1) Use high strain-rate test data to establish the instantaneous hyperelastic model parameter(s).

2) Use the lowest level stress relaxation test data to create a hyperelastic-Prony series linear viscoelastic model

3) Show that the linear viscoelastic model does not capture the behaviors at higher strain excitations

4) Use the Prony series parameters to establish some of the PRF model parameters.

5 ) Use optimization to find all of the PRF model parameters.

 The attached PDF document steps through each of these phases of the calibration recipe.

The PPC3TF2 Polypropylene test data used in this example is attached as a zip file.  This zip file contains data for the highest rate test and the 4 stress relaxation tests.  The high rate test data is called "partial" because I used just that part of the dataset up to about 20MPa.

The fuller set of test data for PPC3TF2-Black can be found here: Washington Penn Polypropylene, tested by Axel Products

In the process described above, we talk about converting from a Prony series to a degenerate PRF model. Details of this conversion are documented in the attached PDF file "Mapping_from_Prony_to_PRF_parameters.pdf"

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