# Network B in Bergstrom-Boyce Model

Hello,

I am working on a continuum project attempting to implement the BB model for PTFE material. I am inquiring about Network B in this model. I am not certain where the Fe deformation matrix is coming from. It is not explicitly stated in Bergstrom, Boyce (2005) paper. I am trying to match the model to experimental data using MATLAB. Could anyone provide some assistance?

Thank you,

Kate

Hello Kate - Welcome to the forum ?Â

I am not sure I fully understand your question. If your goal is to calibrate (find) the BB model parameters that match some experimental data, then I would recommend you using the MCalibration software. It is very easy to use, and you can get a free trial license by clicking on the button on the front page of PolymerFEM.com

If your goal is to create your own implementation of the BB model then I recommend that you read my Polymer Mechanics book, which contains (I think) a Python implementation of the BB model.

If you have a specific question about the **F**e tensor, then can you please provide a bit more details here?

-Jorgen

Hello Jorgen,

Thank you for your response. In regards to theÂ **F**e tensor, I am having difficulty understanding where to take data from. In particular, I am utilizing the (2005) paper to try and replicate your stress-strain plots for PTFE at -53 C. While using the BB model, network B calls for the 8-chain model (same as network A) except now the **F**e deformation matrix is being used. I am not exactly certain how to get this tensor. I am using the function Grabit in MATLAB to get data from the plots in order to try and replicate them via the BB model. When I attempt to model this data in MATLAB, my plot does not look as it should and I think the issue revolves around the deformation matrices. Hopefully that gives a little more specificity for the question. Â

Â

Attached are the plots I am attempting to replicate.

FIGURE 1: I am pulling data from the -53 C curve and using the true strain to form theÂ **F** tensor.Â

FIGURE 2: Pulling data from this curve to generateÂ **FeÂ **matrix?

FIGURE 3: My plots from MATLAB

Thanks for the images. I am starting to understand your question. You are right, the **F** tensor can be determined from the applied strain (well, at least the F_11).

The way to determine the Fe tensor is from:

\(\mathbf{F}^e = \mathbf{F} \left( \mathbf{F}^p \right)^{-1}\)

That is, you need to first calculate the Fp tensor (from the flow rate equation), and then you can calculate the Fe tensor.

-Jorgen

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