BB model

[Muzialis]

Jorgen,

I have read your PhD thesis but there is some background I am missing.

What represented the need for modelling originating from the characterization of the behaviour at a molecular scale ( 8 chains, the treatment of reptational dynamics in yours model, etc.)?

In other words, what can not be captured by a sufficiently complex viscoelastic model? A witty answer could be that such a complex model can not exist, but I am sure you have a much deeper explanation, for which I would be the most grateful.

Have a nice weekend and my apologies if the frequently (excessively?) abstract nature of my queries clashes with the general style of this forum, whicj I evidently enjoy a lot.

Best Regards

Muzialis

[Jorgen]

I don't quite follow your question. I would say that the model that I developed as part of my PhD thesis work is a "complex viscoelastic model". Another way, perhaps, to answer your question is to mention that in the mechanics and materials group at MIT (where I got my PhD) it is more or less required to have any new constitutive model connected to the micromechanisms that drive the material response.

- Jorgen

[Muzialis]

Jorgen.

my question was arguably very badly posed as I of course appreciate your model is a complex viscoelastic one.
My question originay
ied from a book about non linear viscoelasticity I am reading: it has been stated that a non linear viscoelastic constitutive equation (e.g. expressing strain and stresses as a polinomial function of their time derivatives) can be fitted to whatever strain and strain rate range, the only obstacle being the number of terms and the numerical complexity.

That is why I wondered about the reasons behind the physical characterization in your model.

Many thanks

Muzialis

[Jorgen]

I am afraid that I am still not sure I understand your question. Can you elaborate more? What book are you referring to?

- Jorgen

[Muzialis]

Hi Jorgen,

I will certainly try to explain myself better.
The book I mentioned is "Creep and Relaxation of Nonlinear viscoelastic materials",N. Findley, J.S. Lai, K. Onaran, but these thoughts sneaked into my mind even earlier.

Basically my understanding is that every differential equation of the form

sigma(t)= f(eps(t), eps(t)', higher order strain derivatives with respect to time)

defines a viscoelastic material.
A linear model corresponds to a linear differential equation.

The point is, is not possible to numerically determine a differential equation to suit, in the sense of minimizing the error over a range of strain histories, an arbitrary material behaviour?
Of course the difficulty would be in determining the general form of the non linear equation before focusing on the coefficents, but of course I am not suggesting this is the clever solution to the mistery of life.

The approach does not look trivial still seems both tempting and not impossible, in principle .

Hope this clarifies, many thanks for your time.

All the best

Muzialis

[Jorgen]

Aha, I think I see what you are suggesting, and I agree that it is probably possible to develop a model using that approach. However, I guess that it is quite challenging to come up with a robust model that works well in multiaxial deformations states with arbitrary strain histories. If you give it a shot, let us know how it went!

- Jorgen

[Muzialis]

Jorgen,

thank you as usual for your thoughts.
Should I try I will certainly let you know.

Best Regards

Muzialis