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  • Simulation of soft open foam

    Dear Simulaters

    i have several but similar materials which i tested all at

    • compression (strain rates=0.666%/s ; 13,3%/s / max strain=66.6%)

    • simple shear (strain rates=0.666%/s ; 13,3%/s / max strain=33.3%)

    Some typical results can be seen in the attached picture "compression and shear as measured"

    Please notice:

    • i imported the measured stress-strain curves as “true stress / strain” but they were measured as “engineering” and not corrected before. If i import them as “engineering” MCalibration deforms them dramatically. I guess it is because MCalibration implies a Poissons ratio of 0.5 which is absolutely not true with this soft foams. I tried to add a “virtual test” of the Poissons Ratio as it was described in one of the tutorial videos but it only worked for high PR (like 0.499) but not for small ones like 0.1.

    • Both shear curves are from the same sample and were measured directly after one another. Unfortunatelly they don´t seem to have the same hyperelastic storage stiffness with just variing hysteresis around that as it is constitutive in the paper “Constitutive modelling of the large strai time-dependent behavior of elastomers” (if i got that right). MCalibration fits something between that two curves.

    • I tested all material models available to get a feeling and the Dynamic Bergström-Boyce made by far the best fits for the different load cases if considered separately.

    The curve fits can be seen in the pictures "compression alone" and "shear alone".

    • Subsequently i tried to fit all four cures together. I tried the following strategies:

    – First a curve fit of just the compression data while the shear curves were deactiveted. Then activating the shear data and deactivating the compression for a second curve fit. (see figure "final results")

    – Like above but the other way around (even worse than in the figure)

    – All four curves active from the beginning (see figure "final results")

    It seems to me that the Poissons ratio might be the biggest issue here.

    Dr. Berström kindly answered some of my questions some month ago before i started to measure and he recommended the models:

    • Micro Foam Model (the fit was not really good)

    • BB Foam (i did not find this model ?!?)

    • PN

    as the probably most suitable for my material while the “Dynamic Bergström-Boyce” might just not be suitable for compressable foams.So there are some more questions:

    • Is there a “BB Foam” model somewhere? Or do i have to modify the BB model to make it a Foam model?

    • If i have to use the PN model could someone give me a hint of how to start the model structure?

    many questions and i am thankfull for every advice, inquiries and hints

    Greetings from Bremen / Germany
    Andreas Gierse
    Attached Files

  • #2
    Here are my comments:

    • i imported the measured stress-strain curves as “true stress / strain” but they were measured as “engineering” and not corrected before. If i import them as “engineering” MCalibration deforms them dramatically. I guess it is because MCalibration implies a Poissons ratio of 0.5 which is absolutely not true with this soft foams. I tried to add a “virtual test” of the Poissons Ratio as it was described in one of the tutorial videos but it only worked for high PR (like 0.499) but not for small ones like 0.1.

    if you measured the true stress/strain then import it as such, if you measured the eng stress/strain then specify that when importing. MCalibration does not assume or impose any Poisson's ratio.

    When working with foams I recommend either measuring the Poisson's ratio, and then adding a "Poisson's Ratio" load case. OR, measure the transverse strain during the testing and then read in both the axial strain and the transverse strain. This will allow MCalibration to know the Poisson's ratio as a function of the applied strain. Note that this second option only works for uniaxial loading.

    Do you know what the Poisson's ratio is of your foam?
    Also, what is the mass density of you foam? (That is, what is approximately the void volume fraction)?

    If your material is has a "low" Poisson's ratio then you should not use a material model for elastomers, but instead use a material model developed for foams. The difference being the volumetric response.

    The most accurate model in your case will be the PN model. I would give it a structure that is similar to the DBB model, but use hyperfoam elastic elements instead of rubber elasticity type hyperelastic elements.

    Best of luck,
    Jorgen
    Jorgen Bergstrom, Ph.D. PolymerFEM Administrator

    Comment


    • #3
      Progress

      Dear Simulaters

      Thank you very much for the answers.
      I tried to use the informations; here is what i got:

      Answer Bergström:
      If you measured the true stress/strain then import it as such, if you measured the eng stress/strain then specify that when importing. MCalibration does not assume or impose any Poisson's ratio.

      See Fig.1

      The first picture shows five times the same datafile:
      Blue - imported as TRUE Strain and Stress; looks just like the Force - Displacement curves of my measurment did.
      Red - imported as ENGINEERING Strain and Stress; as the stress decreases dramitically it seems like the cross sectional area must have changed. As the poissons ratio is very small (if not zero) the cross sectional area did not change and at least the stress values should remain the same ... shouldn´t they? What is my mistake here? Also strain values greater then »1« are unconventional to me but might be ok.
      Green (and hiding a red curve) - as ENGINEERING Stress and Strain but not as »uniaxial« but as »confined compression« to simulate the low Poissons Ratio ... well, doesn´t seem suitable.

      As the Poissons Ratios are very small for this materials (see below) i do not understand what makes the changes between True and Engineering. Doesn´t »True« just consider the true cross sectional area of the deformed specimen? Which should nearly be constant at small Poissons ratios?
      For the later tests i used the data imported as »True« becuase the curve fits are much better...(see below) i hope it is physically plausible!

      Answer Bergström:
      When working with foams I recommend either measuring the Poisson's ratio, and then adding a "Poisson's Ratio" load case. OR, measure the transverse strain during the testing and then read in both the axial strain and the transverse strain. This will allow MCalibration to know the Poisson's ratio as a function of the applied strain. Note that this second option only works for uniaxial loading. Do you know what the Poisson's ratio is of your foam?

      Unfortunatelly i did not measure it ... but: Optically the foam did not deform laterally as i compressed it uniaxially; the PR must be very small.
      Looking at measuremets of others (Milles, Gilchrist; The effects of heat transfer and Poisson´s Ratio on closed cell polymer foams / Viot, Beani, Lataillade; Polymeric foam behavior under dynamic compressive loading / etc.) it seems like the PR is very small or even zero even for closed cell foams.
      Now, to get the simulation running i guess i have to assume the PR to be between 0.0 and 0.2 for my materials untill i can measure it.

      Answer Bergström
      Also, what is the mass density of you foam? (That is, what is approximately the void volume fraction)?

      The densities of my foams are between 30 - 40 kg/m³ that gives void volume fractions of gas between 97% and 98% ... very soft foam!

      Answer Bergström
      If your material is has a "low" Poisson's ratio then you should not use a material model for elastomers, but instead use a material model developed for foams. The difference being the volumetric response.The most accurate model in your case will be the PN model. I would give it a structure that is similar to the DBB model, but use hyperfoam elastic elements instead of rubber elasticity type hyperelastic elements.

      I tested all three Hyperfoam models available ([8][18][20]) and added Neo-Hookean´s as parallel stiffnesses and virtual Poissons Ratio tests just to find out what might work.Here is the best i got when importing as »Engineering Stress/Strain«

      See Fig. 2

      (Hmm...?!?)
      And the best result i got with »True Stress/Strain«. In this case i added a virtual Poissons Ratio of 0.1 (which seems to be a realistic on / i also tested with PR´s of 0.05, 0.15, 0.2)

      See Fig. 3

      Well, its not perfect but it might be a good basis for a static model...what´s your guess?

      And finally my current attempt for a DBB like model using Hyperfoam stiffnesses. The »Chaboche« requires a linear elasticity (with temperature dependency):

      See Fig. Materialmodel

      And the best result so far:

      See Fig. 5

      Of course this is not yet satisfying but it allready took about ten simulations and manual adjustments of several parameters to get it to this point (and it doesn´t seem absolute absurd).

      As always: i am very thankfull for any comment and advice about how to go on.
      Am i on the right way?
      What do you think about the “True” and “Engineering” issue?

      Greetings from Bremen
      Andreas Gierse
      Attached Files

      Comment


      • #4
        As I mentioned in my previous post: If your experiments are measuring the eng strain and eng stress, then you import them as such. And similar for true stress and true strain.

        There is a feature in MCalibration to switch the plot back and forth between eng stress-eng strain, and true stress-true strain. That feature is only influencing the graph.

        Internally all calculations are done properly based on the type of stress and strain you provided.

        Unless your experimental data contain the transverse strain, switching back and forth between eng and true values is based on volume conservation, which is not valid for your foam. So you should either provide experimental data for the transverse strain, or only plot the engineering strain and the engineering stress.

        -Jorgen
        Jorgen Bergstrom, Ph.D. PolymerFEM Administrator

        Comment

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