Application of numerical differentiation to conversion of linear viscoelastic functions

Abstract

We propose a new method to calculate relaxation time spectrum (RTS) and enable conversions between viscoelastic functions. The exact relations between the viscoelastic functions are simply derived using complex analysis of the higher-order derivative of those functions. Hence, a stable numerical differential method is demanded to obtain genuine solutions without the interference of errors due to numerical analysis. In this study, we adopted the double-logarithmic B-spline and its recursive relation to obtain higher-order derivative. The proposed algorithm is tested and compared with previous methods, using simulated and experimental data. When creep data obtained through experiments are converted to dynamic moduli, significant improvement in the terminal behavior is observed compared to the previous method because the Runge phenomenon is significantly reduced using a low-order polynomial. Moreover, the spectra obtained for experimental data are almost identical to those obtained through a previously verified algorithm. Thus, our results agree well with both simulated data and experimental data.