Optimal discrete-time Prony series fitting method for viscoelastic materials

Viscoelastic models based on Prony series are usually used due to easy implementation in finite element analysis codes. The experimental data are fitted to a Prony series using a user-chosen number of terms represented by two coefficients. The time coefficients \(\tau _{i}\) are previously fixed in the time scale to determine the second parameter of the model. Usually, a homogeneous distribution in the logarithmic-time scale is used for \(\tau _{i}\). When short-time curves must be fitted or the relaxation curve shape is not uniformly distributed in time, the homogeneous distribution of time coefficients could be a significant drawback, since a large number of coefficients might be needed or even a reasonable fitting is not possible.