Fung orthotropic coefficients for hyper-elastic materials

[Emerry]

Hello every body,
I want to simulate an elastomer material. It's orthotropic. I want to use the Fung model but i don't know how to find the coefficients : b1111, b2222, b1122, ........ I have experimental data of the material but i don't know how to extract coefficients. Anyone has an idea ?

 

[Emerry]

No idea ? or suggestion ?

 

[IceBreakerSours]

Nonlinear curve-fitting. Any major scientific coding environment will let you do it. I am sure Google/YouTube will be very useful as well.

I am sure it works very well in some situations but, in general, I would not recommend using the Fung model. It is known to have convexity issues in some strain domains. Holzapfel and Ogden have proposed a potential (which happens to be based off of Fung and Deflino) for orthotropic tissues in 2016. I would suggest you use this energy function.

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[Emerry]

Hello !

Thank you IceBreakerSours. I developped the model in order to do curve fitting. At the end of my development, i have sigma1 = f1(b_ijkl,lamda1) and sigma2 = f2(b_ijkl,lamda2) where sigma_i correspond to the stress in the two directions and lamda_i the stretches. I have sigma_i and lamda_i from experimental data. The problem is that the b_ijkl that i obtained from the first equation (sigma1 = f1(b_ijkl,lamda1)) is not the same as the b_ijkl from the the second one. And i don't know how to do curve fitting for two curves. And I have not found it in the internet (google/youtube).

 

[IceBreakerSours]

As just one example, Matlab has a nonlinear curve fitting toolbox.

By the way, I do not remember off the top of my head but I think the B tensor must undergo additive decomposition before you can start computing stresses. Also, isn't the Fung orthotropic law already supported (i.e., available)? If so, why do you need to implement a UMAT? Even if implementation were necessary, why not do it in UANISOHYPER_XXXX?

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[Emerry]

Hello & happy new year every body,

IceBreakerSours> I do not implement a UMAT. You are right, Fung orthotropic law is already supported but I have to find the coefficients b_ijkl to make Abaqus working.
I just developped the model in order to do curve fitting and extract the coefficients.

Do you have any reference about fung model in abaqus, conference, journal ... a work made with fung model in Abaqus ? (preferably, using b_ijkl coefficients)

PS: Recently, i master the nonlinear curve fitting for 2 curves.

 

[IceBreakerSours]

Fung's papers are a pleasure to read and Fung's books are classics and a must-have for any student of soft tissue mechanics. Relatively more modern treatment in the cardiovascular space is by Jay Humphrey. Holzapfel's book is also very good to have. Wei Sun and Michael Sacks wrote a paper on using Fung's law for valve tissue. That one might be good to read.

Please know that Fung formulation is known to have convexity issues. Holzapfel/Gasser/Ogden wrote a paper on convexity of tissue mechanics material models more than a decade ago.

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[Emerry]

Thanks, i will take a look.

Do you know which one of those references has the same notation that used in ABAQUS ? and which one explains how to extract the coefficients (b1111, b1122,b2222,b1133,b2233,b3333, b1212,b1313,b2323, c, D for Fung orthotropic model /or/ C10, D, k1, k2, kappa for Holzapfel model) from experimental data.

Sorry, if my question seems to be obvious but i am a beginner for soft tissue. My recent simulation is multi-physic (fluid, contact, thermal, hyperelastic structure) and i have to deal with soft tissue.

 

[IceBreakerSours]

I think you need expert supervision; reading a book is not necessarily sufficient to fill gaps.

Estimation/finding material constants has nothing to do with tissue mechanics. It is nothing more than a curve-fitting exercise. I bet Google/YouTube will have tonnes of resources for you. However, in order to some idea of what the constants actually mean or what the bounds must be on their values as the convex optimization code is looking for an optimal set of constants, the context of tissue mechanics will play an important role.

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[DrBwts]

If you have experimental data & you have the constitutive equations then as IceBreaker has already mentioned you need to do some curve fitting.

This can be done with SciPy curve fitting functions if you're familiar with Python or you can use Matlab's curve fitting toolbox, or write your own code to do it.

Either way you'll have to teach yourself how to use these tools