Hi, I have done some stress relaxation tests to study the viscoelastic behaviour of hydrogels. I am just wondering how to use stress-time data to find prony series constants required for material characterization. Please help.
The Prony method is described in detail in the attached entry of Wikipedia (see also the Prony series under Viscoelasticity - link also attached). In essence, the sampled data (the equidistant sampled function of interest in time) form the vector F, whose components are Fn, n = 0, 1, ..., N-1. From these components one constructs a matrix and a vector that together describe a linear matrix equation, the solution of which is a vector P whose components are Pm, m = 1, 2, ..., M. These components form the coefficients of an M-th order monic polynomial whose roots are used to construct matrices in matrix equations described in part by the coefficients {Fn | n}. The solutions of these equations combined with the roots of the above-mentioned monic polynomial, provide one with the necessary constants from which to determine all the parameters in the Prony series corresponding to N equidistant samplings in time of one's property of interest.
https://en.wikipedia.org/wiki/Prony%27s_method
https://en.wikipedia.org/wiki/Viscoelasticity#Prony_series
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