A systematic approximation of discrete relaxation time spectrum from the continuous spectrum

Abstract

Most of viscoelastic models contain linear and nonlinear viscoelastic parameters and the linear viscoelastic parameters correspond to relaxation time spectra of materials. The relaxation spectra can be classified into continuous and discrete ones. Discrete relaxation time spectrum is more convenient to simulate multi-mode models than continuous one because it demands shorter calculation time. It has been demonstrated that the continuous spectrum is uniquely determined in views of theoretical (Fuoss and Kirkwood, 1941; Davies and Anderssen, 1997) [1,23] as well as empirical approaches (McDougall et al., 2014) [5]. Whereas, it is reported that different algorithms for discrete spectrum infer the different results from the same data (Malkin and Masalova, 2001) [14]. This is the study on a systematic method for discrete spectrum on the basis that a discrete spectrum must be consistent with the continuous one. We suggest a simple method to extract discrete relaxation spectrum as a systematically approximated continuous spectrum by means of the Levenberg–Marquardt method. The new algorithm is tested and compared with previous algorithms using synthesized model spectra and experimental data.