Mooney-Rivlin parameters

[sarthak]

Hi,

Are there any restrictions that both the co-efficients of the Mooney-Rivlin have be positive values?

Also, what hyperelastic models would you recommend for large strain shear analysis?

Thanks,
Sarthak

[Jorgen]

No, there is not rule that the two Mooney-Rivlin constants both have to be positive. Typically, however, you want to make sure that the material parameters that you select give a stable model for the strain magnitudes that you are interested in.

I am personally not a big fan of the MR-model. I prefer the neo-hookean, the eight-chain model, the Gent model, or the Yeoh model, if possible. I would try one of these models first for large strain shear predictions.

- Jorgen

[sarthak]

Hi Jorgen,

Thanks your reply. If there are no restriction on the material coeffiecients for the Mooney-Rivlin model...is there any restriction on the strain energy density function i.e. can W be increasing monotonically in the negative direction based on the material coefficients??

Thanks,
Sarthak

[Jorgen]

Yes, there are restrictions on the strain energy function. Most times when you use a hyperelastic material model you want your material to be stable, i.e. the stress should increase with increasing strain: [TeX:10cb6e830f]d\sigma \cdot d\epsilon > 0[/TeX:10cb6e830f]

Strain energy functions are typically positive definite. I don't quite follow your comment about "negative direction based on the material coefficients".

- Jorgen

[xaktsaroth]

Dear Sir,

I am looking for a book or publication that will show that the Mooney-Rivlin parameters can be negative. Do you know of any that I may look into.


regards,

[Squid81]

Have youfound the book? I need this info as well.

Thanks a lot.

Regards

[madhu]

Recently I found a extracts of a paper in ASTM which says for a stable MR material model,
1) Under uniaxial extension
• 3 parameter C11 > 0
• 5 Parameter C20 > 0
• 9 parameter C30 > 0
2) Equibiaxial extension
• 3 parameter C11 > 0
• 5 Parameter C02 > 0
• 9 parameter C03 > 0
3) Pure Shear
• 3 parameter C11 > 0
• 5 Parameter C20+C02+C11 > 0
• 9 parameter C30+C21+C03 > 0
This conditions work well on ANSYS. If this is satisfied we will not get any error. I was wondering what the physical & mathematical basis is for this.
Thanks all