2016/09/23 by Vikash Pandey, Sverre Holm · 5 citations
Chemical Engineering · Mathematics · Materials Science · #Rheology and Fluid Dynamics Studies #Fractional Differential Equations Solutions #Material Dynamics and Properties #Viscoelasticity #Creep #Power law #Newtonian fluid #Relaxation (psychology) #Fractional calculus #Thixotropy #Viscosity #Mechanics #Physics #Law #Materials science #Thermodynamics #Classical mechanics #Mathematical analysis #Mathematics #Composite material
paper · pdf · doi:10.1103/physreve.94.032606
openalex publication_date 2016/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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-varying Maxwell 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.