Abaqus / Viscoelasticity

[TJSS]

Hi Jorgen


I am a beginner in ABAQUS and I need to simulate a tire using viscoelastic proprierties of the rubber. At first, I know the Mooney Rivlin coeficients (C01 =0.825, C10 = 0.8 and D1 = 0.012) and I have the relaxation test data (concerning t, G(t)) and frequency sweep data (concerning G',G'',G* and freq.). However I do not know how could a set the long term modulus in the input file of ABAQUS.

I mean , if I write

*HYPERELASTIC, MODULI=LONG TERM,MOONEY-RIVLIN
0.825,0.8,0.0122
*VISCOELASTIC,TIME=FREQUENCY DATA
G''1/Ginf , 1-G'1/Ginf,,,freq1
G''2/Ginf , 1-G'2/Ginf,,,freq2
G''3/Ginf , 1-G'3/Ginf,,,freq3

G''k/Ginf , 1-G'k/Ginf,,,freqk

where the Ginf = long term modulus

But how can I find the value of Ginf to calculate G''/Ginf and G'/Ginf ?
If I write MODULI=INSTANTANEOUS instead of MODULI=LONG TERM, how could I calculate Ginf and consequently G''/Ginf and G'/Ginf?


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I tried to change the input file writing:

*HYPERELASTIC, MODULI=LONG TERM,MOONEY-RIVLIN
0.825,0.8,0.0122
*VISCOELASTIC,TIME=RELAXATION TEST DATA
*SHEAR TEST DATA,SHRINF = ratiog
gr1 , t1
gr2 , t2
gr3 , t3

grk , tk

where grk = G*(tk)/G(0) and ratiog = Ginf/G0

Usually,the value of Ginf can be found in the relaxation test data (it is the last measured point or interpolated after the last point) and G0 is the G(t=0), but if everything is normalized by G0, I must inform the G0, mustn't I ? How could I do that.

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For this material, as I had told, I have both the Sweep Frequency Test Data and a Relaxation Test Data. The problem is when a run a dynamic analysis model (first using the Sweep Frequency Data and after, in the same model, using the Relaxation Test Data), there a considerable difference between the responses (strain, stress, displacements, damping ...etc)

To simulate both tests , i made a virtual specimen with the same geometry of the real one and simulated a relaxation test. I noted when I used the option TIME=FREQUENCY DATA, the simulated specimen relaxed so fast and when I used the TIME=RELAXATION TEST DATA, the same specimen relaxed so long as similar as the same Relaxation Test.

My doubt is , when I set the viscoelastic properties in the ABAQUS, independent of the option (TIME = FREQUENCY DATA or RELAXATION TEST DATA), mustn´t the viscoelastic properties be the same ? For both cases, Abaqus estimates the PRONY Series Coefficients that define the viscoelasticity in frequency domain and the viscoelasticity in time domain !


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I hope you understand my doubt !

Could you indicate me a good and easy Literature ?

Thank you very much !

Best Regards


ThiagoSaccheto
(mechanical engineering)

[Jorgen]

That is one long question :)

Here are a few comments:
:arrow: How do you know the Mooney-Rivlin parameters? Typically the hyperelastic model is calibrated to very slow experimental data, which would correspond to the Ginf term.

:arrow: No you do not need to specify G0. The G0 respose is implicitly defined in your hyperelastic model.

:arrow: If you see significant differences between the two data sets in terms of model predictions, then that could indicate that your material is not linear viscoelastic, or that the experimental data has errors.

- Jorgen