# Prony Series from Dynamic Storage and Loss Modulus

Lately I have received a few requests for information about how to determine the Prony series from dynamic vibrational data in the form of the loss modulus and the storage modulus. The Prony series is typically needed in order to specify the linear viscoelastic behavior in FE programs. The attahed pdf-file describes a method to determine the necessary Prony series parameters from dynamic data.

SImplex method?

[QUOTE=Jorgen,96]Lately I have received a few requests for information about how to determine the Prony series from dynamic vibrational data in the form of the loss modulus and the storage modulus. The Prony series is typically needed in order to specify the linear viscoelastic behavior in FE programs. The following [URL= https://polymerfem.com/polymer_files/Prony_Series_Conversion.pdf ]pdf-file[/URL] describes a method to determine the necessary Prony series parameters from dynamic data.

The pdf states that we can use Simplex method for minimization of error, but isnt Simplex method only for linear problems? Isnt the equation here non-linear?

The simplex method that I mentioned here is also called the Nelder-Mead method and it suitable for non-linear optimization problems.

-Jorgen

hello Prof Jorgen

i am working with nonlinear viscoelastic material and i want to develop a VUMAT subroutine to capture stress relaxation and strain rate dependent behavior of Bio-material and i am new in the VUMAT so i want some basic code for the same

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