Visco-Hyperelastic Model vs BB Model.

[edo.me]

Hi Jorgen,
I'm pretty new in this field and I'm having an overview of the different ways to model RUBBERS in dynamic analyis.
This is my understanding up to now.
I'll be very grateful to you if you can check my post and give me a feedback about wrong or miss understood things.

VISCOELASTIC + HYPERELASTIC

TIME DOMAIN
-PRONY SERIES FITTING:
When from relaxation data test, Prony series coefficients are obteneid by fitting procedure, the fitting doesn't take into account the strain rate in which the strain increases from zero to the wanted value. An unit step is considered, even if in the reality we have a ramp.
STRAIN-RATE EFFECT on PRONY COEFFICIENTS
To take it into account the fitting should be done on the experimental stress value with an hereditary integral approach.
Even if the prony coefficients take into account the strain rate of the relaxation test, since just only one set of prony coeff can be specified, the strain rate dependency is poor and valid only for that strain-rate.
RATE EFFECT in RELAXATION TEST
If different relaxation test are considered with the same final strain, but different rates of appliaction, the 'different' decay stress behavior could give an idea about how linear viscoelastic the material is with respect to the rate effect.
AMPLITUDE EFFECT in RELAXATION TEST
If different relaxation test are considered with the same rate, but different final strain, the 'different' decay stress behavior could give an idea about how linear viscoelastic the material is with respect to the amplitude effect.

The VISCO-HYPERESLASTIC model can well represent a linear viscoelstic behavior (prony series) and the loading phase of histeretic loop at different strain rate (if the HYPERELASTIC MODEL works properly).
It is poor in representing the unloading condition, and for that reason the lost energy is bad estimated.

BB MODEL
The BB model has no these limitations. It is like an advance non linear viscoelastic model. Other parameters need to be specified and maybe a different way of testing the material is requiered.
The implementation of your model in Abaqus has some limitation (in Ansys as well?!) but if no linear effect are present it could be better than a VISCO-HYPERELASTIC Model. Does it work properly in dynamic analysis?

BR
Thank you a lot
edoardo

Edoardo Menga
Dynamic and Aeroelasticity
AIRBUS SA

[Jorgen]

Hello Edoardo,

I agree with most of your points. Here area a few specific comments:

* A linear viscoelastic material model can be calibrated in different ways. The most common approach is to use stress relaxation data. This approach typically do not include consideration of the applied strain rate during the loading phase. The influence of rate effects and amplitudes effects can be considered through various experiments, either relaxation, creep, or frequency-based dynamic mechanical analysis (DMA).

* As you said, the BB model that I developed is a non-linear viscoelastic material model that in most finite strain applications is more accurate than simple linear viscoelasticity. I typically use the BB model in all my FE modeling work of rubbers. I have developed my own implementation of the BB model for Abaqus (an ANSYS version is on the way) that has a number of improvements of the built-in BB model (called *Hysteresis in Abaqus). Specifically, it is available for Explicit simulations, allows for temperature dependence of the material, and it is also more robust.

If you are interested in predicting the response of rubbers, then I definitely recommend that you check out the Bergstrom-Boyce (BB) model.

-Jorgen

[jmg]

Dear Edoardo and Jorgen,

I've been working the last couple of months with the BB Model implementation in Ansys 12 and recently with the one in Abaqus. I run some models with uni axial loading to compare with the results published in Dr. Bergstrom papers. I can tell you that the Ansys implementation IS NOT WORKING properly. I've contacted Ansys by the end of last year and they issued a Class 3 error report. They were supposed to fix by March, but I didn't get anything and the person that I was in contact with is not replying my emails.
As I need to go on, I switched recently to Abaqus. The test models look much better. There are some slight differences but I believe that they arise from the fact the Abaqus implementation uses a 5 term expansion of the inverse Langevine function.
My goal is to calculate the dissipated energy for one cycle. For a uniaxial compression loading and unloading cycle (@ fixed strain rate) I calculated the dissipation using two different methods:
1) CENER (Dissipated Creep Energy Density) @ the end of the cycle
2) Integrating the Stress against LE (True Strain) for the whole cycle
I am struggling to find out why (2) is about one half of (1). I'll appreciate any suggestions!

Regards,

Joaquin M. Gutierrez
Graduate Research Assistant
Mechanical and Aerospace Engineering
West Virginia University
118A ERB, Morgantown WV 26506

[Jorgen]

Hello Joaquin,

Interesting comments. A few days ago I become a software alliance partner with ANSYS and I now have v12.1 on my computer. I am working on translating my library of user-material models to ANSYS format and I will absolutely validate the ANSYS implementation of the BB-model. Can you send me a private message explaining what problems you noticed with the ANSYS implementation?

If you integrate the CENER over the volume I would think that you should get the same dissipated energy as from integrating the stress-strain response for a complete cycle. I have not tried that test with the Abaqus built-in implementation. If you post your inp-file that you used to verify this, I will try to find the time to check this as well.

Thanks,
Jorgen