A comparative view of Becker, Lomnitz, and Lambert linear viscoelastic models

TL;DR

This paper compares classical viscoelastic models by Becker and Lomnitz with a Lambert W function-based model, deriving new analytical and integral representations for their spectra.

Contribution

It introduces new analytical expressions and integral representations for the spectra of these classical and Lambert-based viscoelastic models.

Findings

Derived new relaxation spectrum expressions for Becker and Lomnitz models.

Provided novel integral representations for Lambert model spectra.

Enhanced understanding of model relationships through comparative analysis.

Abstract

We compare the classical viscoelastic models due to Becker and Lomnitz with respect to a recent viscoelastic model based on the Lambert W function. We take advantage of this comparison to derive new analytical expressions for the relaxation spectrum in the Becker and Lomnitz models, as well as novel integral representations for the retardation and relaxation spectra in the Lambert model.