Viscoelastic behavior of polymer foams

Hi all,

I am trying to simulate the strain dependent material behavior of rigid polyurethane foams (density > 200 kg/m). My focus is on uniaxial compression. Using MCalibration for determining material parameters worked well so far for constant strain rate, but some problems have arised now that I use 2 different strain rates for calibration. By using the Parallel Network Model, I have set up a material model that combines Hyperfoam with linear viscoelastic flow. I am using Hyperfoam here because it fits the experimental curves the best as long as I am calibratin only 1 curve.

1) Concerning the combination of Hyperfoam and viscoelastic flow I mentioned I have question: In Abaqus the linear viscoelasticity modul needs 3 parameters g,k,tau. The optimization in MCalibration does not include g, k but only tau. Instead I get mu, nu and alpha when only using hyperfoam and mu, alpha and beta when using hyperfoam combined with viscoelastic flow. How does that correlate? Also, the fittnes results are quite poor. Any suggestions?

Calibration results:

using hyperfoam combined with viscoelastic flow:

using only hyperfoam:

2) Last but [B]most important[/B]: Is this a proper way to determine the Prony Series Parameters (g,k,tau) from my strain dependent uniaxial compression test results? I know there is a way that works without having creep or relaxation data... this is the only thing I can imagine so far. Is there a way to determine these parameters for Abaqus without using MCalibration? I guess I dont need another way if question 1 is answered properly 🙄

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[*]Flow type 501 in the Parallel Network (PN) model is for a linear viscoelastic network with one Prony series term. That was how I designed it, but as I think about it, it is certainly possible to create another flow element that is linear viscoelastic and supports multiple Prony series terms. NOTE: you can create a PN model that supports multiple Prony series terms by using multiple parallel networks.
[*]You may want to try to use a non-linear flow element (for example Power-Law Flow). That should increase the model accuracy.
[*]MCalibration can calibrate any Abaqus material model, including hyperelastic with linear viscoelasticity. To do that you currently need to use the Abaqus Template material model feature.
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-Jorgen