Viscoelastic material, prony series?

[rmettier]

I'm studying a model that I got as an example from a former co-worker.
She used a viscoelastic material, defined through a time-domain prony series. The three parameters are:

g_i= 0.99
k_i= 0
tau_i= 1000

I'm trying to understand what that series does. I've fiddled with the three parameters and nothing seems to make any difference in the results.

From what I've found while googling, g+k should be always less than 1, and I assume that tau is some kind of time parameter. Can someone give me a push in the right direction here?

 

[DanStro]

I am still learning about this as well so I may have this wrong. But this is how I understand it: the Prony series is a way of representing the viscoelastic response of the material as a series of springs and dashpots (generalized Maxwell model).

You may want to try adding more terms. For instance, if you create a material with the constants of:

g_i=0.4, k_i=0, tau_i=10
g_i=0.59, k_i=0, tau_i=1000

You'll get a very different curve than your original. Just remember that the g_i terms need to sum to less than 1, and the k_i terms need to sum to less than one also.

tau_i is the relaxation time of the material at a particular stress and temperature. A pretty good description is here:

http://www.vilastic.com/tech3.htm

The help file (sections 18.7,4.8.1, and 4.8.2 of the 6.8 documentation), and there are a couple of examples that are pretty useful too.

As I said I am still learning this too so I could have some misunderstandings in here.

HTH
Dan