**Thomas Cugnon**
@
on

Problem with the viscous prefactor in the Kelvin-Voigt model

Good morning,

I have some questions about the viscoelastic Kelvin-Voigt model implemented in VEDA :

1) In the VEDA comprehensive manual, Version 2.0, 2012, p88, I do not understand the reason why you divide by a factor 2 the calculation of the convolutional integral of the Dirac delta.

2) Furthermore, I implemented the model in Excel and Matlab but there seems to be a little difference with the results of the VEDA simulator due to the viscous prefactor. This would indicate that it may be wrong or wrongly implemented.

By simulating a sinusoidal wave, in order to fit your results, I need to change the prefactors into : 7/5 instead of 2 for the approach 7/20 instead of 0.5 for the retract meaning that the actual viscosity you are using in your simulation is 7/10 times the viscosity you define in your model.

By simulating a triangular wave, I even get different prefactors : 1 instead of 2 for the approach 0.25 instead of 0.5 for the retract indicating that the viscosity you are using is 2 times the one of your model.

Could you help me and get me in the right direction for this viscous prefactor?

Thanks a lot, sincerely,

T.Cugnon

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Daniel Kiracofe@ onHello Thomas. Regarding number 1. you are probably used to think of the Dirac delta as defined such that the integral from x = minus infinity to x = plus infinity of Delta(x) is equal to one. But this is not the integral that we are doing in this case. It is more like the integral from x=0 to x= plus infinity, which has a value of 1/2. I know it confused me a little at first too. I’ll put a note in the next version of the VEDA manual about this.

Regarding number 2, It is always possible that I missed something. It would help me out if you could give me more details about what you did. For example, what exact parameters were you using the VEDA tool, and exactly what did your matlab code look like? If you could send the matlab code, and/or any comparison plots, that would be helpful. You may e-mail me directly at drkiraco@purdue.edu if that is easier.

Daniel

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Thomas Cugnon@ onHello Daniel, thank you for your answer. Actually, I got mistaken by wrongly defining the oscillation amplitude, that is the reason why I had some problems. Now, both simulations give the same results and everything is clear in my mind. Thank you again, Thomas

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