Linear elastic -> Hyperelastic coefficient conversion

[thanoon]

Hello,

I am currently working on modeling soft tissue. I got as only data the Young modulus E=2500 Pa and the poisson ration =0.499 (incompressible material).

They ask me to work with the hyperelastic model so I need to understand if the is an equivalence between hyperelastic and linear elastic coefficient. I will be working with Mooney rivlin model so I need C_10 and C_01.
Can someone help me?

Regards
David

[Jorgen]

If all you know are E and nu (and you cannot perform additional tests), then you should not use a Mooney-Rivin model but a Neo-Hookean model.

The shear modulus for the NH model is E/3.

-Jorgen

[thanoon]

If all you know are E and nu (and you cannot perform additional tests), then you should not use a Mooney-Rivin model but a Neo-Hookean model.

The shear modulus for the NH model is E/3.

-Jorgen

Thank you very much for this answer. Is there a paper/book where I can get this information in order to cite it?

David

[Jorgen]

You can site me :)

It is actually easy to derive (perhaps you don't need to cite it):

:arrow: The Poisson't ratio of most rubbers and soft tissues is typically close to 0.5 (that is incompressible).

:arrow: The shear modulus is given by (see most intro to solid mechanics books):
mu = E / (2 * (1 + nu))

If you insert nu=0.5 you will get mu = E/3...

-Jorgen

[amitmane]

What is the incompressibility parameter used in Neo-Hooken model ? how to derive it?

[sandeep18784]

Hello Dr. Jorgen

As i told you, I have hardness value for rubber and nu = 0.5(rubber is incompressible). You asked me use Neo-Hookean form. I needed two parameters C10 and D1

So I converted hardness 's' into E as per ref formula E = 0.0981(56+7.62336s)/0.137505(254-2.54s)

I will get Shear modulus µ0 = E/2(1+nu). and from this i will calculate C10 = µ0/2

D1 = 0 for incompressible in abaqus/standard,

So I will have both C10 and D1

please tell me if this approach is right....

Thank you in advance..

[Jorgen]

That sounds right.

-Jorgen