Energy dissipation in linear viscoelasticity
Abstract
We compare the specific dissipation $Q^{-1}\left( ω\right) $ for the Becker, Lomnitz, and Lambert models in linear viscoelasticity. Graphically, the specific dissipation of these models behaves similarly as ω→ 0+ and ω→ +∞. Furthermore, we obtain analytic formulas for the asymptotic behavior of $Q^{-1}\left( ω\right) $ in the Becker and Lomnitz models as ω→ 0+ and ω→ +∞, where the latter limit coincides with the specific dissipation of the Maxwell model. We also derive a novel closed-form expression for the specific dissipation in the generalized Becker model, $Q_{ν}^{-1}\left( ω\right) $, when the parameter $ν\in \left( 0,1\right] $ is rational. When ν→ 0, we recover the specific dissipation of the Maxwell model, whereas when ν=1, we recover that of the original Becker model. In addition, we derive two new closed-form expressions for the specific dissipation for the extended Jeffreys--Lomnitz model $Q_{α}^{-1}\left( ω\right) $, the first being valid for $α\in \left( 0,1\right] $, and the second for $α\in \left( -\infty ,1\right] $. When α→ 0, we recover the specific dissipation of the Lomnitz model, whereas when α=1, we recover that of the Maxwell model. Finally, we conclude that the asymptotic behavior of $Q_{α}^{-1}\left( ω\right) $ as $ω\rightarrow +\infty $ coincides with the specific dissipation of the Maxwell model. Keywords:
Versions
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BibTeX
@misc{gonzalezsantander2026energy,
title = {{Energy dissipation in linear viscoelasticity}},
author = {Juan Luis Gonzalez-Santander and Francesco Mainardi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05465},
eprint = {2609.05465},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05465},
}
RIS
TY - UNPB
TI - Energy dissipation in linear viscoelasticity
AU - Juan Luis Gonzalez-Santander
AU - Francesco Mainardi
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.05465
UR - https://arxiv.org/abs/2609.05465
AB - We compare the specific dissipation $Q^{-1}\left( ω\right) $ for the Becker, Lomnitz, and Lambert models in linear viscoelasticity. Graphically, the specific dissipation of these models behaves similarly as ω→ 0^+ and ω→ +∞. Furthermore, we obtain analytic formulas for the asymptotic behavior of $Q^{-1}\left( ω\right) $ in the Becker and Lomnitz models as ω→ 0^+ and ω→ +∞, where the latter limit coincides with the specific dissipation of the Maxwell model. We also derive a novel closed-form expression for the specific dissipation in the generalized Becker model, $Q_{ν}^{-1}\left( ω\right) $, when the parameter $ν\in \left( 0,1\right] $ is rational. When ν→ 0, we recover the specific dissipation of the Maxwell model, whereas when ν=1, we recover that of the original Becker model. In addition, we derive two new closed-form expressions for the specific dissipation for the extended Jeffreys--Lomnitz model $Q_{α}^{-1}\left( ω\right) $, the first being valid for $α\in \left( 0,1\right] $, and the second for $α\in \left( -\infty ,1\right] $. When α→ 0, we recover the specific dissipation of the Lomnitz model, whereas when α=1, we recover that of the Maxwell model. Finally, we conclude that the asymptotic behavior of $Q_{α}^{-1}\left( ω\right) $ as $ω\rightarrow +\infty $ coincides with the specific dissipation of the Maxwell model. Keywords:
ER -