Energy Dissipation in Linear Viscoelasticity

We compare the specific dissipation Q−1ω 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−1ω 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, Qν−1ω, when the parameter ν∈0,1 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 Qα−1ω, the first being valid for α∈0,1, and the second for α∈−∞,1. 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 Qα−1ω as ω→+∞ coincides with the specific dissipation of the Maxwell model.