Time-strain separability in medium-amplitude oscillatory shear

Martinetti, Luca; Ewoldt, Randy H.

doi:10.1063/1.5085025

Title: Time-strain separability in medium-amplitude oscillatory shear

Journal Article · Tue Jan 29 00:00:00 EST 2019 · Physics of Fluids

DOI:https://doi.org/10.1063/1.5085025· OSTI ID:1607424

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Univ. of Illinois at Urbana-Champaign, IL (United States)

Here, we derive and study equations for the weakly nonlinear medium-amplitude oscillatory shear (MAOS) response of materials exhibiting time-strain separability. Results apply to constitutive models with arbitrary linear memory function $$\textit{m}$$(s) and for both viscoelastic liquids and viscoelastic solids. The derived equations serve as a reference to identify which models are time-strain separable (TSS) and which may appear separable but are not, in the weakly nonlinear limit. More importantly, we study how the linear viscoelastic (LVE) relaxation spectrum, H($$_\tau$$), affects the frequency dependence of the TSS MAOS material functions. Continuous relaxation spectra are considered that are associated with analytical functions (log-normal and asymmetric Lorentzian distributions), fractional mechanical models (Maxwell and Zener), and molecular theories (Rouse and Doi-Edwards). TSS MAOS signatures reveal much more than just the perturbation parameter A in the shear damping function small-strain expansion, $$h(_γ) = 1 + \text{A}_γ$$$$^2 + \mathcal{O}(_γ$$$$^4)$. Specifically, the distribution of terminal relaxation times is significantly more apparent in the TSS MAOS functions than their LVE counterparts. We theoretically show that this occurs because TSS MAOS material functions are sensitive to higher-order moments of the relaxation spectrum, which leads to the definition of MAOS liquids. We also show the first examples of MAOS signatures that differ from the liquid-like terminal MAOS behavior predicted by the fourth-order fluid expansion. This occurs when higher moments of the relaxation spectrum are not finite. The famous corotational Maxwell model is a subset of our results here, for which A = -1/6, and any LVE relaxation spectrum could be used.

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Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division

Grant/Contract Number:: FG02-07ER46471

OSTI ID:: 1607424

Journal Information:: Physics of Fluids, Vol. 31, Issue 2; ISSN 1070-6631

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 19 works

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