A rheological model for materials which support coexistent shear rates
by
R.L. Fosdick and C. Balan
in
Int. J. Nonlinear Mech., 35, 1023-1043, 2000.
Category: Journal Article
Keywords: Viscoelastic #uid; Di!erential model; Material instabilities; Yield stress
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Abstract:
In this work we study a version of the three constant di!erential-type Oldroyd constitutive relation which allows distinct objective time derivatives for the extra stress and the stretching. We integrate the constitutive equation and determine an equivalent history integral representation for this model for the general class of viscometric motions. For certain choices of the material parameters and initial conditions, we "nd that this model allows for the development of shear rate discontinuities in the #ow domain as a steady viscometric #ow is achieved. Correspondingly, we also give evidence that intense shear rate oscillations may occur during the transient period as an impulsively started viscometric #ow in a channel tends to a steady state under a constant critical shear stress. This critical shear stress lies in an interval of values for which the material experiences the phenomenon of `#ow yieldinga. A qualitative comparison with experimental data is made for certain creams and greases. The material instabilities inherent in this constitutive theory for viscometric motions are suggestive of the instabilities that occur in many viscoelastic #uids such as sharkskin patterns, wavy fracture, and spurt #ow.
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