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 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 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.In this study, an optimized i distribution method for fitting master curves of viscoelastic materials based on Prony series model is proposed. The method is based on an optimization algorithm strategy to allocate the time coefficients along the time scale to obtain the best fit. The method is validated by using experimental data of temporomandibular joint disc, which presents a short-time and high relaxation rate viscoelastic curve. The method improves significantly the fitting of the viscoelastic curves when compared with uniformly distributed time fittings.Furthermore, the optimized coefficients are also used to obtain the complex moduli of the material using an analytical conversion, which are then compared with the experimental complex moduli curves of the material.