Hysteresis and relaxation model

[miguel_roque]

Hello Dr. Bergstrom,

I have been reading the model that you have developed, because i want to implement it. The problem is that i don't understand how to find the deformation gradient (elastic and viscous) of chain B.

Best regards,

Miguel Roque

[Jorgen]

Hello Miguel,

The way to find the deformation gradients of network B is to use the viscoelastic rate equation ("flow rule") in order to determine how much of the applied deformation is viscoelastic.

Best of luck,
Jorgen

[miguel_roque]

Hello Dr. Bergstrom,

First off all, thank's for your reply.

I have i question, you said that the way to find the deformation gradients of network B is using the "flow rule", but i don't know this rule and how to apply it. Could you please explain it, giving the steps that i have to make?

Thank's in advance,
Miguel Roque

[ashu28]

As an initial step, try explicit scheme. Start assuming everything to be elastic. Calculate gammapdot and Dp (you may find relevant equations in the model you are interested in). Update Fp and calculate stress. This is the general way to go about it, may vary a bit depending on the particular model.


Ashu

[miguel_roque]

Hello Ashu,

I still don't understand how to determine the deformatin gradients for network B. You said that i should start assuming everything to be elastic, but how do i reach to the viscous and elastic deformations gradients for network B? And what do you mean with Dp and Fp, i´m not quiet following. I'm very new on this matter

Miguel Roque

[ashu28]

Which paper are you exactly refering to ??
Also, I would recommend looking into the refereces is going to help you a lot in understanding the development of a series of models for elastomers and thermoplasts as well.


Ashu

[ashu28]

Which paper are you exactly refering to ??
Also, I would recommend looking into the refereces is going to help you a lot in understanding the development of a series of models for elastomers and thermoplasts as well.
In case you have some specific problems, feel free to ask.

Ashu

[miguel_roque]

The paper i'm refering to, is the thesis of Jorgen Bergstrom, "Large Strain Time-Dependent Behavior of Elastomeric Materials". My problem is i don't know how to find the deformation gradients (elastic and viscous) of network B.
Dr. Bergstrom already said that i must use the "flow rule" but i don't know how to do it. I will try to find some information in the references, but if you could advance something more i would be thankful.

Miguel Roque

[Jorgen]

Miguel,

I agree with ashu28 about first using an explicit solution approach. I have to admit that I was purposely somewhat imprecise in my statement in order to indicate that finding the deformation gradient of the viscous part of network B is somewhat involved. The approach is to figure out how to update Fbv for a given time increment dt with a given F. All you need to perform the calculations are written in my papers, although the equations are written to indicate the theory and not to demonstrate various integration schemes. Perhaps there is a need to write a paper outlining the implementation in more detail.

Feel free to ask specific questions about the implementation of the BB model.

- Jorgen

[miguel_roque]

Dr. Bergstrom,

I have some questions about finding the estimated equilibrium curves/ equilibrium stress. I think this will help to find the deformation gradient of network B.

1- How can i estimate the equilibrium locus, in order to determine the material contants for the eight-chain model?
2- Are the equilibrium curves calculated from the eight-chain model?
3- Time-dependent stress = Total Stress - Equilibrium Stress ?
4- Is network B given by the Time-dependent stress/strain?

Thanks in advance,
Miguel Roque.