Prony Series Conversion

[Jorgen]

This pdf-file summarizes a simple mathematical approach that can be used to determine the Prony series from dynamic storage and loss modulus data.

[sb47584]

Can you please help me out in calculation the shear relaxation Modulus for ramp loading equation by nano indentation method...

Just tell me the equations to be used for the calculation for ramp laod

[heavenarmy]

Hi Jorgen,


Stumble across your site through google... What can I say, a most helpful site and it is motivating me to restart my experiment to design a elastomeric shock absorber.

Forgive me for asking, but can you provide examples or tutorials with actual data to illustrate how this can be done?



This pdf-file summarizes a simple mathematical approach that can be used to determine the Prony series from dynamic storage and loss modulus data.

[Jorgen]

I am afraid that I don't have any tutorials to share :(
Best of luck,
Jorgen

[manfred]

see for example at http://www.viscodata.de/

[bhag.gupta@trelleborg.com]

Interesting document and useful for using it with MARC. I have one basic question. As I understand by this document that the master curve data ( E vs Time) generated at a reference temperature Tr , is used to generate the Prony's constants which are used in MENTAT along with the WLF constants, C1 and C2. This input, as I understand, will be good for any temperature, as far as the viscoelasticity part of the modeling is concerned. Is this correct?
If so, we will still have to model the material by, for examole, Ogden method, and the constants (moduli and exponents) which should be valid for any temperature.

Thanks.

Bhag

[Jorgen]

Yes, you will still need to use a hyperelastic model (e.g. the Ogden model). The linear viscoelasticity part only controls the viscous flow response.

If you want to predict the response at different temperatures you will still need to use a hyperelastic model that can handle different temperatures.

- Jorgen

[jplawler]

Hi Jorgen -

Thanks for the how-to .pdf file. One question though: does the omega in your equations refer to rad/s or Hz? The units don't seem to cancel.

Perhaps this is just understood, or clarified in the ABAQUS manual which I don't have.

Thanks much.

- John

And by the way, I very much enjoyed your class last month in Burlingame. Learned a heck of a lot in 2 days.

[Jorgen]

Hi John, Good to hear from you.

The equations are written in terms of rad/s. The units look fine to me: omega * tau becomes dimensionless (tau is a characteristic time).

Thanks,
Jorgen