Thermodynamic point of view on constitutive models of rubber

[fourier]

Hello.

I have one question about constitutive models, like Arruda-Boyce, Bergstrom-Boyce etc.
Is where any possibility to prove the approach of constitutive models of strain energy function from a termodynamical point of view?

For example, if we have some constitutive model of strain energy function
A(a1,a2,...an). How you can prove that this model is termodynamically coordinated ? For example which ranges of parameters a1,...an made this model to be termodynamically proved( I those models should satisfy principal termodynamic identity and ranges of parameters which made
strain energy function positive).

Or maybe constitutive models is only engineering models, based on experimental data and statistics ?

What should I read about those questions?

Thank you.

[Jorgen]

The Arruda-Boyce (AB) and the Bergstrom-Boyce (BB) models have both been shown to satisfy the first and second laws of thermodynamics (the Clausius Duhem inequality), as long as the material parameters are chosen as reasonable values. For example, the Young's modulus has to be positive, etc.

I don't think anyone has carefully gone through and demonstrated within what ranges the complete set of parameters must be in order to satisfy classical thermodynamics.

- Jorgen

[fourier]

Ok, that's great. Could you recommend me the articles (or maybe books) where this satisfaction is performed? I'll use them as items at my bibliography.

[Jorgen]

I wrote a section about that in my PhD-thesis (http://www.polymerfem.com/modules.php?name=Downloads&d_op=viewdownloaddetails&lid=27).
You can likely also find a similar information about the AB-model in Prof. Boyce and Prof. Arrruda's theses.

- Jorgen