Large Amplitude Oscillatory Shear From Viscoelastic Model With Stress Relaxation

2017 ◽  
Vol 84 (12) ◽  
Author(s):  
Alberto Garinei ◽  
Francesco Castellani ◽  
Davide Astolfi ◽  
Edvige Pucci ◽  
Lorenzo Scappaticci
Keyword(s):  
Shear Stress ◽  
Relaxation Time ◽  
Large Amplitude ◽  
Viscoelastic Model ◽  
Integral Form ◽  
Oscillatory Shear ◽  
Normal Stresses ◽  
Large Amplitude Oscillatory Shear ◽  
The Difference ◽  
Constitutive Parameters

The analytic response for the Cauchy extra stress in large amplitude oscillatory shear (LAOS) is computed from a constitutive model for isotropic incompressible materials, including viscoelastic contributions, and relaxation time. Three cases of frame invariant derivatives are considered: lower, upper, and Jaumann. In the first two cases, the shear stress at steady-state includes the first and third harmonics, and the difference of normal stresses includes the zeroth, second, and fourth harmonics. In the Jaumann case, the stress components are obtained in integral form and are approximated with a Fourier series. The behavior of the coefficients is studied parametrically, as a function of relaxation time and constitutive parameters. Further, the shear stress and the difference of normal stresses are studied as functions of shear strain and shear rate, and are visualized by means of the elastic and viscous Lissajous–Bowditch (LB) plots. Sample results in the Pipkin plane are reported, and the influence of the constitutive parameters in each case is discussed.

The Transition to Quasi-Periodicity for Molten Plastics in Large Amplitude Oscillatory Shear

1994 ◽  
Vol 116 (4) ◽  
pp. 446-450 ◽  
Author(s):  
D. W. Adrian ◽  
A. J. Giacomin
Keyword(s):  
Shear Stress ◽  
Stress Response ◽  
Large Amplitude ◽  
Average Molecular Weight ◽  
Oscillatory Shear ◽  
Large Amplitude Oscillatory Shear ◽  
Weight Average Molecular Weight ◽  
Amplitude Spectra ◽  
Shear Stress Response ◽  
Even Harmonics

Large amplitude oscillatory shear (LAOS) experiments on three grades of LLDPE including one commercial film blowing resin showed an interesting transition in the shear stress response to LAOS. The shear stress response is initially a nonsinusoidal standing wave which then undergoes a transition to quasi-periodicity. Many line-broadened odd and even harmonics were found in the shear stress amplitude spectra of the quasi-periodic responses. The transition time depends on shear strain amplitude and frequency, but it did not correlate with the weight average molecular weight of the LLDPE’s.

On a suspension of nearly spherical colloidal particles under large-amplitude oscillatory shear flow

2016 ◽  
Vol 791 ◽  
Author(s):  
Aditya S. Khair
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Shear Flow ◽  
Large Amplitude ◽  
Colloidal Particles ◽  
Deborah Number ◽  
Oscillatory Shear ◽  
Spherical Particles ◽  
Simple Shear Flow ◽  
Large Amplitude Oscillatory Shear

The dynamics of a dilute, monodisperse suspension of nearly spherical particles that undergo Brownian rotations in an oscillatory simple shear flow is quantified, as a paradigm for large-amplitude oscillatory shear (LAOS) rheology of complex fluids. We focus on the ‘strongly nonlinear’ regime of LAOS, defined by ${\it\beta}\gg 1$ and ${\it\beta}/{\it\alpha}\gg 1$, where ${\it\beta}$ is a dimensionless shear rate (or Weissenberg number) and ${\it\alpha}$ is a dimensionless oscillation frequency (or Deborah number). We derive an asymptotic solution for the long-time periodic orientation probability density function of the particles. Our analysis reveals that the orientation dynamics consists of ‘core’ regions of rapid oscillation (on the time scale of the inverse of the shear-rate amplitude), separated by comparatively short ‘turning’ regions of slow evolution when the imposed flow vanishes. Uniformly valid approximations to the shear stress and normal stress differences (NSDs) of the suspension are then constructed: the non-Newtonian contribution to the shear stress, first NSD and second NSD, decays as ${\it\beta}^{-3/2}$, ${\it\beta}^{-1}$ and ${\it\beta}^{-1/2}$, respectively, at large ${\it\beta}$. These stress scalings originate from the orientation dynamics at the turning regions. Therefore, it is the occasions when the flow vanishes that dominate the rheology of this paradigmatic complex fluid under LAOS.

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