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Erschienen in: Rheologica Acta 2/2010

01.02.2010 | Rapid Communication

On secondary loops in LAOS via self-intersection of Lissajous–Bowditch curves

verfasst von: Randy H. Ewoldt, Gareth H. McKinley

Erschienen in: Rheologica Acta | Ausgabe 2/2010

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Abstract

When the shear stress measured in large amplitude oscillatory shear (LAOS) deformation is represented as a 2-D Lissajous–Bowditch curve, the corresponding trajectory can appear to self-intersect and form secondary loops. This self-intersection is a general consequence of a strongly nonlinear material response to the imposed oscillatory forcing and can be observed for various material systems and constitutive models. We derive the mathematical criteria for the formation of secondary loops, quantify the location of the apparent intersection, and furthermore suggest a qualitative physical understanding for the associated nonlinear material behavior. We show that when secondary loops appear in the viscous projection of the stress response (the 2-D plot of stress vs. strain rate), they are best interpreted by understanding the corresponding elastic response (the 2-D projection of stress vs. strain). The analysis shows clearly that sufficiently strong elastic nonlinearity is required to observe secondary loops on the conjugate viscous projection. Such a strong elastic nonlinearity physically corresponds to a nonlinear viscoelastic shear stress overshoot in which existing stress is unloaded more quickly than new deformation is accumulated. This general understanding of secondary loops in LAOS flows can be applied to various molecular configurations and microstructures such as polymer solutions, polymer melts, soft glassy materials, and other structured fluids.

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Fußnoten
1
e3/e1< −1 corresponds to negative total stress at maximum positive strain γ = γ0, i.e., the material does not resist deformation but rather pushes towards further deformation. We are unaware of any observation of this type of behavior.
 
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Metadaten
Titel
On secondary loops in LAOS via self-intersection of Lissajous–Bowditch curves
verfasst von
Randy H. Ewoldt
Gareth H. McKinley
Publikationsdatum
01.02.2010
Verlag
Springer-Verlag
Erschienen in
Rheologica Acta / Ausgabe 2/2010
Print ISSN: 0035-4511
Elektronische ISSN: 1435-1528
DOI
https://doi.org/10.1007/s00397-009-0408-2

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