On the viscoelastic characterization of the Jeffreys–Lomnitz law of creep
On the viscoelastic characterization of the Jeffreys–Lomnitz law of creep
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DOI：
10.1007/s00397-012-0634-x
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发表时间：
2011-12
期刊：
影响因子：
2.3
通讯作者：
F. Mainardi;G. Spada
中科院分区：
文献类型：
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作者：
F. Mainardi;G. Spada
1958 年，Jeffreys（Geophys J R Astron Soc 1:92-95）提出了蠕变幂律，推广了 Lomnitz 早期引入的对数定律，将地球物理应用范围扩大到包括火成岩在内的类流体材料。然而，这个广义定律也可以应用于类固体粘弹性材料。我们通过允许其幂律指数 α 来重新审视杰弗里斯-洛姆尼茨蠕变定律，该指数通常限制在 0 ≤α≤ 1 到所有负值的范围内。这与粘弹性的线性理论一致，因为蠕变函数仍然是伯恩斯坦函数，即具有完全单调导数的正值，并具有相关的延迟时间谱。整个范围 α≤ 1 产生从无蠕变的胡克弹性固体到具有线性蠕变的麦克斯韦流体的连续转变，穿过具有对数蠕变的 Lomnitz 粘弹性体，这将类固体与类流体行为分开。此外，我们数值计算了弛豫模量，并提供了对应于杰弗里斯-洛姆尼茨蠕变定律扩展到所有α≤ 1的延迟时间谱的解析表达式。
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 exponentα, 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 rangeα≤ 1 yields a continuous transition from a Hooke elastic solid with no creepto a Maxwell fluid with linear creeppassing 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 allα≤ 1.