This paper proposes a fractal viscoelastic element via He?s derivative, its properties are analyzed in details by the two-scale transform for first time. The is used to establish Maxwell-rheological model, which unifies creep equation and relaxation equation, includes classic elastic model classical as two special cases. sheds bright light on viscoelasticity, can find wide applications rock mec...

We present several new results on the kinetic, i.e., mesoscale, level of a continuum–kinetic–microscopic approach to multiscale modeling of complex fluids. We choose the microscopic level as Kramers’ bead-rod model for polymers, which we describe as a system of stochastic differential equations with an implicit constraint formulation. The associated Fokker-Planck equation is then derived, and a...

Strongly-coupled dusty plasmas often exhibit liquid behavior. Liquids behave as a viscous continuum in the hydrodynamic regime. However, in the kinetic regime of a liquid, viscous and elastic effects occur at the same time [1], i.e., the liquid is said to be viscoelastic. To characterize the viscoelasticity of a liquid, the complex viscosity, () = () i(), is often used, where the real a...