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