bsista
posted this
23 August 2018

Jonsys,

Curve-fitting is usually a nonlinear regression optimization problem which requires an "initial guess" (or the seed value) for the parameters that are being calculated. Highly nonlinear systems such as this one tend to have multiple local minima and the choice of initial guess can influence the local minima that the optimization algorithm will find. So, it is necessary to use physically realistic seed values for relaxation times. Just getting the order of magnitude in the ballpark can do the trick. One way of physically interpreting the Prony series is: the stress relaxation happens over a time and there may be multiple relaxation chains (mathematically, Prony terms) that may be contributing to this relaxation. So, a Prony term (Gi, Ti) may be interpreted as Gi fraction of the total stress relaxases over a time of Ti. This is a very loose interpretation of the math but it'll help in understanding the Prony series better.

For curve fitting, look at the timeline of your data. E.g., if you have data for a time of, say, 10^6 sec, and if you're using 3 Prony terms, then use seed values for time constants evenly distributed along that timeline (1s, 1e3s, 1e6s) or if you see a sharp dip at around 1e4 s then (1s, 1e4, 1e6) would be a good start. This way you'll have better chances of capturing the relaxation terms that are prominent along the timeline.

In general, you need not assign seed values for shear modulus and residual so don't tinker with them for now.