Reuss Method For Large Deformations

[sharathchav]

Hello All,
I am understanding to find a solution for this problem I am facing from couple of months. Please give me your insights.
Problem:
Suppose I have two neo-hook materials of different strengths connected in Series (as in Reuss).
What will the effective modulus for the resultant material be under 'Large Deformations'
We have tried to calculate the effective modulus under Large Deformations and found that the effective modulus would be lesser than the two individual Neo-Hook Materials. Is this a special case for Large Deformations? Please let us know.
Thanks!

[Jorgen]

Yes the effective modulus will be less than the two individual NH models.
If you go through the derivation, then you should be able to figure out an expression for the effective modulus (I have not done that exercise)...

-Jorgen

[sharathchav]

Dear Dr.Jorgen,
Thanks for the reply. I am now working on implementing Homogenisation schemes like Reuss Method, Voigt Method, Mori-Tanaka Method etc on TPEs.
But for the case of Large deformations, the constitutive equations change and my code is not working for this case.
Can we reason this using Continuum Mechanics concept.
In uniaxial stretch , in Large deformations, the effective stretch = stretch of NH1 * Stretch of NH2
Is it correct, can you please let me know why it is so.