# 8-chain model question

Dear Dr. Bergstrom,

Im studying your BB model from your dissertation and papers, and I have a

few questions about a deformation tensor in your cauchy stress tensor

equation.

I have uniaxial stess-strain data of polymer, and so I can compute the lamda,

which is strech.

1. My question is how to calculate deformation gradient tensor without

assuming incompressible? In your recent paper about DNF model,

F = F_ve * F_p , and I dont know how to form F tensor using

strain data.

If incompressible is assumed, then probably,

F = [lamda 0 0,

0 1/sqrt(lamda) 0

0 0 1/sqrt(lamda)]

but, I dont think you assumed the incompressible material.

How do you obtain the deformation gradient tensor for calculation B_ve ?

Thank you very much.

Wonseok Yoon

I dont think I quite understand your question. The deformation gradient F is usually a given input. The tricky part is to figure out what part is F_ve and what part is F_p. To do that youl will need to use the flow equation (flow rule).

Does that answer your question?

- Jorgen

Thank you for your reply.

Im trying to build one-dimensional constitutive model for polymer using Matlab.

In your Ph.D dissertation, the dev[B*] tensor for stress model has the following form: (lamda^2 - 1/lamda) for one dimensional, incompressible material.

How did you calculate dev[B*] ? Not sure Im right but, my understanding is that deformation gradient tensor F has to have the following form in case of incompressible material.

F = [ lamda 0 0,

0 1/sqrt(lamda) 0,

0 0 1/sqrt(lamda)]

and the real question is How I can build the input F if I have only strain-stress data.

I appreicate your answer.

Regards,

Wonseok Yoon

You are on the right track. Heres one way to do it:

(1) lambda = exp(strain)

(2) F11 = lambda

(3) F22 = F33 = 1/sqr(lambda)

Since you are assuming incompressibility you need to make determine the undermined pressure term. This pressure term can be obtained from the boundary conditions.

- Jorgen

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