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curve fitting indentation data

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(@umpd99)
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Joined: 15 years ago

I am trying to use finite element modeling of indentation experiments to extract hyperelastic material parameters. I am having a dilemma, when the tissue has residual strain, the model couldnt achieve the high nonlinear relationship between displacement vs reaction force as measured in the experiments.

I have tried several strain energy potential, such as Mooney-rivlin, and exponential type (W=C1[exp(C2(I1-3)]). If residual strain is zero, the displacement vs. reaction force can be very nonlinear (concave shape), however when the residual strain is high (stretch ratio>=1.2), the displacement vs. reaction force relation is either straight or convex.

I am not sure how could I model this nonlinearity with residual strain:confused:. Does anyone have any clue?

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(@jorgen)
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Sounds like you are working on a great project. I have been telling people for a long time now that indentation tests can be very useful if the results are interpreted correctly!

How do you impose or know what the residual strain is?
How anisotropic is the tissue that you are studying?
Also, I am curious, what tissue are you studying?
Have you tried to use an anisotropic hyperelastic material model?

-Jorgen

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(@umpd99)
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The material I am trying to find parameters is embryonic chick heart, the indentation test was done in micro-level.

I havent try anisotropic for this material, since the experiments indicated that it is basically isotropic.

The residual strain was applied by first stretch the tissue, while the stretch was maintained, the indentation was applied as displacement boundary condition.

The residual strain is a big deal for this project, because the tissue is actively growing, and large residual strain (>1.2 stretch ratio) was measured through cutting experiments.

My ultimate goal is to model it as viscoelastic material, but currently even the hyperelastic couldnt model the concave-up displacement-reaction force relation, adding viscoelasticity only makes the curve less concave and less stiff.

I am really stuck.

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(@jorgen)
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I dont know exactly what hyperelastic material models that you have tried, but I would not use a Mooney-Rivlin model (it will not be non-linear enough). Instead I would try the Yeoh model.

Can you provide a figure showing what force-displacement data you get experimentally, and what you get with your models?

-Jorgen

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Posts: 8
Topic starter
(@umpd99)
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Joined: 15 years ago

Thank you for your interest. I think you are right the strain energy function I tried may not be nonlinear enough especially in tension (when residual strain is high, tension parallel to surface is likely to govern the reaction force more than compression perpendicular to surface). Yeoh form is a great idea, I was trying Polynomial type yesterday. Hopefully by playing around the numbers I could find a good fit.
I am attaching an overlay of my model (blue) with the experimental data (red). I have tried two strain energy functions:
1) W=A/B*{exp[B(I1-3)]-1}
2) W=C10(I1-3)+C01(I2-3)

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(@jorgen)
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Joined: 5 years ago

The model prediction does not look that bad 🙂

Tweaking the material model might help.

-Jorgen

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Posts: 8
Topic starter
(@umpd99)
Active Member
Joined: 15 years ago

have tried yeoh model

Hi Jorgen, I have tried Yeoh model which gives me a better fit, but still not as ideal. I have also tried Arruda-Boyce model, which gives similar fit. I seem to have exhausted all the combinations, but couldnt achieve better fit than this. Will Ogden type be more nonlinear, I am wondering because it is giving me some convergence issues..

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