MIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

The medium amplitude response of nonlinear Maxwell–Oldroyd type models in simple shear

Author(s)
Lennon, Kyle R; McKinley, Gareth H; Swan, James W
Thumbnail
DownloadSubmitted version (2.400Mb)
Publisher with Creative Commons License

Publisher with Creative Commons License

Creative Commons Attribution

Terms of use
Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/
Metadata
Show full item record
Abstract
A general framework for Maxwell–Oldroyd type differential constitutive models is examined, in which an unspecified nonlinear function of the stress tensor and rate-of-deformation tensor is incorporated into the well-known corotational version of the Jeffreys model discussed by Oldroyd. For medium amplitude simple shear deformations, the recently developed mathematical framework of medium amplitude parallel superposition (MAPS) rheology reveals that this generalized nonlinear Maxwell model can produce only a limited number of distinct signatures, which combine linearly in a well-posed basis expansion for the third order complex viscosity. This basis expansion represents a library of MAPS signatures for distinct constitutive models that are contained within the generalized nonlinear Maxwell model. We describe a framework for quantitative model identification using this basis expansion for the third order complex viscosity, and discuss its limitations in distinguishing distinct nonlinear features of the underlying constitutive models from medium amplitude shear stress data. The leading order contributions to the normal stress differences are also considered, revealing that only the second normal stress difference provides distinct information about the weakly nonlinear response space of the model. After briefly considering the conditions for time-strain separability within the generalized nonlinear Maxwell model, we apply the basis expansion of the third order complex viscosity to derive the medium amplitude signatures of the model in specific shear deformation protocols. Finally, we use these signatures for estimation of model parameters from rheological data obtained by these different deformation protocols, revealing that three-tone oscillatory shear deformations produce data that is readily able to distinguish all features of the medium amplitude, simple shear response space of this generalized class of constitutive models.
Date issued
2021
URI
https://hdl.handle.net/1721.1/138882
Department
Massachusetts Institute of Technology. Department of Chemical Engineering; Hatsopoulos Microfluids Laboratory (Massachusetts Institute of Technology); Massachusetts Institute of Technology. Department of Mechanical Engineering
Journal
Journal of Non-Newtonian Fluid Mechanics
Publisher
Elsevier BV
Citation
Lennon, Kyle R, McKinley, Gareth H and Swan, James W. 2021. "The medium amplitude response of nonlinear Maxwell–Oldroyd type models in simple shear." Journal of Non-Newtonian Fluid Mechanics, 295.
Version: Original manuscript

Collections
  • MIT Open Access Articles

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries
PrivacyPermissionsAccessibilityContact us
MIT
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.