Prony series and parameters ??

[eddydonc0]

Hello everybody,

My English is poor but I try to be understood.
My question is about *viscoelastic in Abaqus ?
I have a polyurethane to study (E=4Mpa and 55Shore A hardness). I just have the compression test in experimental. How to obtain information on its viscous behavior?
In Abaqus, the prony series is used. How to obtain a relation between E the elastic modulus and G the shear modulus in a creep test data to obtain the prony parameter?
What's excactly the shear test data in abaqus to determine the prony parameter?

Thank's for all the answer.
Eddy

[Jorgen]

Hi Eddy,

What kind of compression test data do you have? The easiest way to determine the Prony seriers is to perform stress relaxation experiments.

For polyurethane you can often assume that the material is incompressible and hence convert the Youngs modulus to a shear modulus by dividing by 3, i.e. mu ≈ E / 3

Best of luck,
Jorgen

[eddydonc0]

Hi Jorgen,

Thank's to the answer !
I use a test piece of diameter 29mm and heigth 13mm for the compression test. The information is the stress-strain curve ! The strain speed is constant !
I think that i can do a relaxation test !

Eddy

Ps : your website is excellent !

[marrpi]

Hello,

I am trying to do a stress-strain analysis of a polymer part and I would like to use the viscoelastic material model (in ABAQUS).

I think you can define viscoelastic material model by using one of these procedures:
- giving shear and/or volumetric creep and relaxation data.
- by direct specification of Prony series parameters.
- material subroutine.

Please correct me if I am wrong.

My question is: if you have experimental data from a tensile creep tests, how can you transform it in the coefficients required by ABAQUS?.

Is the following process correct?:

1.From the tensile creep test I get the instantaneous tensile modulus E(t)
2.Using the relation G=E/(2(1+poisson ratio)) I get the instantaneous shear modulus G(t).
3.The instantaneous shear compliance is obtained by J(t)=1/G(t)
4.The normalized shear compliance is obtained by j(t)=J(t)/J(0)

Thank you very much

[Jorgen]

Your 3 ways to define a viscoelastic material for ABAQUS seem right. But I don't quite follow your procedure to find the shear relaxation function from creep data. What do you mean when you say "Instantaneous tensile modulus E(t)"? To me the word instantaneous to specifies time=0.

Your step 1 and 2 are fine. But #3 is only true in the limit when the time goes to zero.

In general, you can obtain the stress relaxation modulus from creep data by solving a Laplace convolution integral, or through a numerical solution scheme. You should also know that ABAQUS can find the appropriate Prony series from experimental creep data for you.

Best of luck,
Jorgen

[marrpi]

Thank you very much for your answer.

I would like to comment some points about it. I made a mistake by using the term "instantaneous" :oops: , what I ment was E(t)=tensile modulus at any time (1 hour, 100 hours): E(t)=(test tensile stress)/(strain stress at time t)


And I was not trying to find the shear relaxation function. I am trying to define viscoelastic behaviour by specifying creep test data. The problem is that ABAQUS ask for shear creep data and I have tensile creep data, and I don't know how I can find what ABAQUS call normalized shear compliance (j(t)) and long term shear compliance from my test data.

I hope I have better explained my question now.

[Jorgen]

For many elastomers you can assume that the deformation response is incompressible, hence for these materials the shear compliance is 1/3 of the tensile creep data.

- Jorgen

[sana]

Hi I have a load displacement curve on a bony shell which I want to model using ABAQUS viscoelastic model.

Can the prony series coefficients be determined using the load displacement curve? If so how is it done?
If not what additional test data would I need?

[Jorgen]

The Prony series parameters can be determined from load-displacement data at different strain rates, but it is often easier to determine the Prony series from a stress relaxation test.

You can determine the actual parameters either using a built-in feature in ABAQUS, etc., or write your own conversion tool using Matlab.

- Jorgen

[littleabaqus]

Hi Jorgen!

I have a similar question about the topic in this post..
I am currently trying to model stress-relaxation behavior in Abaqus,
based on data received in the lab from a stress-relaxation experiment.
For the experiment, we measured the dimensions of a material, and
compressed it through a displacement that was a percentages of its
original thickness.

The results from the lab experiment have been analyzed, producing stress
vs strain curves off several different percentages, and also I was able to
determine the instantaneous and equilibrium moduli. My question is
regarding inputing this data into the viscoelastic material section. I have
already set everything up, and the problem I am having is with the
shear test data input. For my complience modulus I am using the value
of equilibrium/instantaneous modulus. And for the y values, I am dividing
the stress by the equilibrium modulus, and plotting it against the
appropraite time. I keep getting errors when right clicking the material
and trying to evaluate. It says the material failed, or test failed. My
y-values are negative, and the compliance modulus looks acceptable..
I'm think I have a problem with the y-value I'm using... Is the stress
divided by the equilibrium modulus for those points correct, or am
I missing something here?

Thanks, I really appreciate it!!

Best,
littleabaqus

[Jorgen]

Hmm, I think that you want to divide the stress with the instantaneous stress at the beginning of the stress relaxation (not the equilibrium modulus). That way your normalized stress starts from 1 and goes down towards 0.

- Jorgen