In 1958, Jeffreys (Geophys J R Astron Soc 1:92–95) proposed a power law of creep, generalizing the logarithmic law earlier introduced by Lomnitz, to broaden the geophysical applications to fluid-like materials including igneous rocks. This generalized law, however, can be applied also to solid-like viscoelastic materials. We revisit the Jeffreys–Lomnitz law of creep by allowing its power law exponent α, usually limited to the range 0 ≤ α ≤ 1 to all negative values. This is consistent with the linear theory of viscoelasticity because the creep function still remains a Bernstein function, that is positive with a completely monotone derivative, with a related spectrum of retardation times. The complete range α ≤ 1 yields a continuous transition from a Hooke elastic solid with no creep (α→−∞) to a Maxwell fluid with linear creep (α=1) passing through the Lomnitz viscoelastic body with logarithmic creep (α= 0), which separates solid-like from fluid-like behaviors. Furthermore, we numerically compute the relaxation modulus and provide the analytical expression of the spectrum of retardation times corresponding to the Jeffreys–Lomnitz creep law extended to all α ≤ 1.

On the viscoelastic characterization of the Jeffreys-Lomnitz law of creep

MAINARDI, FRANCESCO;G. SPADA
2012

Abstract

In 1958, Jeffreys (Geophys J R Astron Soc 1:92–95) proposed a power law of creep, generalizing the logarithmic law earlier introduced by Lomnitz, to broaden the geophysical applications to fluid-like materials including igneous rocks. This generalized law, however, can be applied also to solid-like viscoelastic materials. We revisit the Jeffreys–Lomnitz law of creep by allowing its power law exponent α, usually limited to the range 0 ≤ α ≤ 1 to all negative values. This is consistent with the linear theory of viscoelasticity because the creep function still remains a Bernstein function, that is positive with a completely monotone derivative, with a related spectrum of retardation times. The complete range α ≤ 1 yields a continuous transition from a Hooke elastic solid with no creep (α→−∞) to a Maxwell fluid with linear creep (α=1) passing through the Lomnitz viscoelastic body with logarithmic creep (α= 0), which separates solid-like from fluid-like behaviors. Furthermore, we numerically compute the relaxation modulus and provide the analytical expression of the spectrum of retardation times corresponding to the Jeffreys–Lomnitz creep law extended to all α ≤ 1.
2012
F. MAINARDI; G. SPADA
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/128288
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