Fung orthotropic coefficients for hyper-elastic materials
Fung orthotropic coefficients for hyper-elastic materials
(OP)
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 ?
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 ?





RE: Fung orthotropic coefficients for hyper-elastic materials
RE: Fung orthotropic coefficients for hyper-elastic materials
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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RE: Fung orthotropic coefficients for hyper-elastic materials
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).
RE: Fung orthotropic coefficients for hyper-elastic materials
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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RE: Fung orthotropic coefficients for hyper-elastic materials
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.
RE: Fung orthotropic coefficients for hyper-elastic materials
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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RE: Fung orthotropic coefficients for hyper-elastic materials
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.
RE: Fung orthotropic coefficients for hyper-elastic materials
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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RE: Fung orthotropic coefficients for hyper-elastic materials
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 :D