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

Abstract

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 signaturesmore » 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.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]
  1. Univ. of Illinois at Urbana-Champaign, IL (United States)
Publication Date:
Research Org.:
Univ. of Illinois at Urbana-Champaign, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
OSTI Identifier:
1607424
Grant/Contract Number:  
FG02-07ER46471
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physics of Fluids
Additional Journal Information:
Journal Volume: 31; Journal Issue: 2; Journal ID: ISSN 1070-6631
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 36 MATERIALS SCIENCE; Mechanical stress; Relaxation time spectrum; Zener model; Polymers; Materials analysis; Viscoelasticity; Constitutive relations; Maxwell models; Series expansion; Oscillatory shear measurements

Citation Formats

Martinetti, Luca, and Ewoldt, Randy H. Time-strain separability in medium-amplitude oscillatory shear. United States: N. p., 2019. Web. doi:10.1063/1.5085025.
Martinetti, Luca, & Ewoldt, Randy H. Time-strain separability in medium-amplitude oscillatory shear. United States. https://doi.org/10.1063/1.5085025
Martinetti, Luca, and Ewoldt, Randy H. 2019. "Time-strain separability in medium-amplitude oscillatory shear". United States. https://doi.org/10.1063/1.5085025. https://www.osti.gov/servlets/purl/1607424.
@article{osti_1607424,
title = {Time-strain separability in medium-amplitude oscillatory shear},
author = {Martinetti, Luca and Ewoldt, Randy H.},
abstractNote = {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.},
doi = {10.1063/1.5085025},
url = {https://www.osti.gov/biblio/1607424}, journal = {Physics of Fluids},
issn = {1070-6631},
number = 2,
volume = 31,
place = {United States},
year = {Tue Jan 29 00:00:00 EST 2019},
month = {Tue Jan 29 00:00:00 EST 2019}
}

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Works referencing / citing this record:

The medium amplitude response of nonlinear Maxwell–Oldroyd type models in simple shear
journal, September 2021