Becker and Lomnitz rheological models: a comparison

TL;DR

This paper compares the Becker and Lomnitz rheological models, analyzing their viscoelastic functions, creep, and relaxation behaviors, highlighting their similarities and differences in retardation spectra.

Contribution

It provides a detailed comparison of the viscoelastic functions of Becker and Lomnitz models, including analytical and numerical insights into their creep and relaxation behaviors.

Findings

Both models have similar creep and relaxation time dependence.

They exhibit distinct retardation spectra despite similar overall behavior.

Analytical expressions are available for their spectra.

Abstract

The viscoelastic material functions for the Becker and the Lomnitz rheological models, sometimes employed to describe the transient flow of rocks, are studied and compared. Their creep functions, which are known in a closed form, share a similar time dependence and asymptotic behavior. This is also found for the relaxation functions, obtained by solving numerically a Volterra equation of the second kind. We show that the two rheologies constitute a clear example of broadly similar creep and relaxation patterns associated with neatly distinct retardation spectra, for which analytical expressions are available.