Hi guys
I have trouble with prony series. Could you give me sample calculation by prony series, if I have stress relaxation data in order to know shear modulus (G)?
Please.
Best Regard
Dear Yudha Lesmana;
You can apply hereditary integral method for your calculation.
Follow this article link
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20000052499.pdf
Hi, you have to perform a a kind of least-squares fit of the Prony-series to your experimental data. This ist not as easy as it seems to be. This is a highly nonlinear fit-problem for finding the coefficients of your series. There are many approaches in the literature to solve this numerically.
One method to mention is published by: R.D. BRADSHAW and L.C. BRINSON: A Sign Control Method for Fitting and Interconverting Material Functions for Linearly Viscoelastic Solids; Mechanics of Time-Dependent Materials 1: 85–108, 1997. This article gives you also a good overview.
Your dataset is a bit short and sub-optimally sampled. So, a reasonable number of prony-series elements will also be small in your case. usually, for time domain fitting 1-2 series elements per decade are sufficient. in most cases one has to choose the time-constants a priori. I had relaxation data over 1e6 seconds, and good results with n=10 elements.
To my experience, for a good fit you should provide logarithmic spaced samples (or a log spaced selection of datapoints). otherwise, evenly spaced samples will concentrate in log-scale somewhere and locally overweight these parts of your data in the fit for your prony series.
You should check your Prony-fit in logscale, as in linear scale the quality is often hard to prove (as you can see in my attached example diagrams)
Dear Yudha Lesmana,
you may find helpful data in paper attached (in Russian only).
All the best
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