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prony series calibration

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Posts: 10
Topic starter
(@Gafeaerorerly)
Active Member
Joined: 15 years ago

Hello everyone!

I am trying to model a linear viscoelastic material (pmma) in ABAQUS. I have frequency dependent data (complex modulus and complex poisson ratio as a function of frequency) and I have procceded to model it in the time domain.

ABAQUS models the material (pmma) but does not give the right results. I am studying stress waves in bars made of pmma and it is well known that material damping of the waves is suppose to be present.However, this is not the case.

I employed the evalution option in ABAQUS inorder to compare the material created by abaqus to that of my data and I found out that they were well apart.

My questions are, firstly, could this be a problem with ABAQUS calibrating the prony series coefficient form my data?Secondly,since it is not a problem with my data because they have been used elsewhere with success, could I possibly calibrate the prony series coefficient myself (e.g. following the prony series conversion paper by Dr Bergstrom)? If so could anyone point me towards an easy to understand explanation on implementing a good minimisation algorithim?Lastly, am I going totally towards the wrong direction?:oops:

Thanks so much in advance

GB

17 Replies
Posts: 3998
(@jorgen)
Member
Joined: 4 years ago

Hi GB,

First, just to clarify, PMMA is not a linear viscoelastic material. It is a material that in certain circumstances can be represented using a linear viscoelastic model.

I think that your approach sounds fine. My guess is that there is nothing wrong with the Abaqus calibration of the Prony series parameters. You mentioned that the Abaqus evaluation option provides data that is not the same as the experimental data. How different where the two data sets? Is it possible that the experimetal data that you have cannot accurately be represented using a linear viscoelastic model?

If you want you can, as you mentioned, also calibrate the model your self. Regarding minimization algorithms, I propose the Nelder-Mead Simplex Algorithm in Matlab (and other math programs).

-Jorgen

17 Replies
Posts: 10
Topic starter
(@Gafeaerorerly)
Active Member
Joined: 15 years ago

Firstly, thanks for the clarification, it was essential that i understood that point. My working conditions does allow me to approximate the behaviour as linear.

I really cant see were the problem stems from. The evaluation option gives results that are way apart. I am still in the procces of sorting out a minimization algorithim inorder to define the prony series parameters directly.

The theory of linear viscoelasticity states that the Fourier transform of the stress and strain are related by a complex modulus as a function of frequency. In ABAQUS, if it is possible to define the shear and bulk modulus as function of frequency as well as their longterm and instantenous values, then it is possible to put this in a form in which abaqus can calibrate the prony series parameters. These forms are, for example, for the complex shear modulus real(wg*)=Gl/Gi, were Gl is the loss shear modulus(imaginiary part of the complex shear modulus) and Gi is the lonterm modulus. We also have imag(wg*)= 1-Gs/Gi, were Gs is the storage modulus(real part of the complex shear moodulus).

So if I have the complex modulus and complex piosson ratio, I am able to define both Gs and Gl. Put them interms of (wg*) real and imaginary, and do the the same for the complex bulk modulus. This I have done but still with no good results. please help!!

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Posts: 3998
(@jorgen)
Member
Joined: 4 years ago

Can you present present an image of the experimental frequency data, and a figure of the calibrated model evaluated to the experimental data?

-Jorgen

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Posts: 10
Topic starter
(@Gafeaerorerly)
Active Member
Joined: 15 years ago

Thank you very much. I finally found out what was wrong (some errors in the data). If you still want to see the figures from the evaluation option before and after correction was made, then please let me know. Once again thank you, I will be back either with more questions or answers.:p

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Posts: 6
(@vision_valley)
Active Member
Joined: 15 years ago

Hello GB, I am having the similar problem. I do have reduced frequency nomogram for EAR C1002 material (i.e complex modulus vs. frequency) data.I am using ANSYS 11.0 and there is only way to define viscoelastic material is to enter time vs modulus data (creep test relaxation datas which i dont have ) for curve fitting and obtain prony parameters.
I went through the Dr. bregstorm paper to get prony parameters from storage or loss modulus relation with frequency but i could figured out how to guess initial parameters.

Please, tell me is there any way to obtain directly the prony parameters in ABAQUS with frequency vs modulus data. Or please tell me how to use optimization technique to obtain prony parameters.
Thank you GB

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Posts: 10
Topic starter
(@Gafeaerorerly)
Active Member
Joined: 15 years ago

Hello!

Can I please clarify some things, you have data of the complex modulus versus frequency? ANSYS allows only creep test data to be used to calibrate the prony series terms. You cannot figure out how to obatain the prony series terms through a curve fitting technique.

If this is the case then to the first question the answer is yes. You can in Abaqus obtain the prony series parameter from complex modulus data. I would refer you to ABAQUS USER MANUAL section 17.7.1. There is an explanation on how to do this. If any problem then let me know.

The answer to second question is also yes. It is possible to implement a curve fitting technique on a software like Matlab. If you look at the nature of the function which defines the complex modulus data(also available in the above reference), you will be able to think of the right technique to obtain the prony series terms.

Hope this was helpful.

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