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

By R. Ewoldt, G. H. McKinley. 2010

174 citations recorded by the source corpus.

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.

Subfields: Fluid Flow and Transfer Processes, Polymers and Plastics, Pulmonary and Respiratory Medicine

View Paper: https://www.semanticscholar.org/paper/35b7d5162441fc48a8c9d16aab907e8c5b87359b

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In Fluid Flow and Transfer Processes

In Polymers and Plastics

In Pulmonary and Respiratory Medicine

Citations in the corpus

A sequence of physical processes determined and quantified in large-amplitude oscillatory shear (LAOS): Application to theoretical nonlinear models (2012, unknown): “12 can be used not only to calculate the new nonlinearity parameter but also to calculate the perfect plastic dissipation ratio /, defined by Ewoldt et al. (2010).”
Small and large oscillatory shear properties of concentrated proteins (2021, background): “At high strains for SPI, self-intersections appear in the viscous Lissajous curve (shown in Appendix Figure A 4), which leads to secondary loops (Ewoldt & Mckinley, 2010).”
A unified approach to model elasto-viscoplastic thixotropic yield-stress materials and apparent yield-stress fluids (2013, methodology): “…plots have been used extensively in the presentation of large-amplitude oscillatory test data of yield-stress materials (e.g., Mas and Magnin 1997, Tiu et al. 2006, Ewoldt et al. 2008, Ewoldt and McKinley 2010, Ewoldt et al. 2010, Rogers et al. 2011, Rogers and Lettinga 2012, Rogers 2012).”
Large amplitude oscillatory shear of pseudoplastic and elastoviscoplastic materials (2010, methodology): “description of this phenomenon is given in a companion communication ( Ewoldt and McKinley 2009 ).”
A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS) (2011, background): “73 The utility of the Chebyshev representation was recently demonstrated in the explanation of secondary loops (self-intersection) of Lissajous curves, interpreting the behavior with elastic stress overshoot [140].”
Describing and prescribing the constitutive response of yield stress fluids using large amplitude oscillatory shear stress (LAOStress) (2013, methodology): “It is well known that, for a sinusoidal forcing, the energy dissipated within the material per cycle only depends on the first viscous Fourier coefficient (Ganeriwala and Rotz, 1987; Kalelkar et al., 2010; Ewoldt et al., 2010).”