Rheologica Acta, Vol.51, No.9, 783-791, 2012
On the viscoelastic characterization of the Jeffreys-Lomnitz law of creep
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 alpha, usually limited to the range 0 a parts per thousand currency signaEuro parts per thousand alpha a parts per thousand currency signaEuro parts per thousand 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 alpha a parts per thousand currency signaEuro parts per thousand 1 yields a continuous transition from a Hooke elastic solid with no creep to a Maxwell fluid with linear creep passing through the Lomnitz viscoelastic body with logarithmic creep , 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 alpha a parts per thousand currency signaEuro parts per thousand 1.
Keywords:Creep;Relaxation;Linear Viscoelasticity;Jeffreys-Lomnitz law;Completely monotone functions;Bernstein functions;Laplace transform