Linking the fractional derivative and the Lomnitz creep law to non-Newtonian time-varying viscosity

被引:58
|
作者
Pandey, Vikash [1 ]
Holm, Sverre [1 ]
机构
[1] Univ Oslo, Dept Informat, POB 1080, NO-0316 Oslo, Norway
关键词
WAVE-EQUATION; THEORETICAL BASIS; CALCULUS; MODEL; VISCOELASTICITY; PROPAGATION; BEHAVIOR; ROCKS; MEDIA;
D O I
10.1103/PhysRevE.94.032606
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
Many of the most interesting complex media are non-Newtonian and exhibit time-dependent behavior of thixotropy and rheopecty. They may also have temporal responses described by power laws. The material behavior is represented by the relaxation modulus and the creep compliance. On the one hand, it is shown that in the special case of a Maxwell model characterized by a linearly time-varying viscosity, the medium's relaxation modulus is a power law which is similar to that of a fractional derivative element often called a springpot. On the other hand, the creep compliance of the time-varyingMaxwell model is identified as Lomnitz's logarithmic creep law, making this possibly its first direct derivation. In this way both fractional derivatives and Lomnitz's creep law are linked to time-varying viscosity. A mechanism which yields fractional viscoelasticity and logarithmic creep behavior has therefore been found. Further, as a result of this linking, the curve-fitting parameters involved in the fractional viscoelastic modeling, and the Lomnitz law gain physical interpretation.
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页数:6
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