The weakly nonlinear response and nonaffine interpretation of the Johnson–Segalman/Gordon–Schowalter model

Ramlawi, Nabil; Bharadwaj, N. Ashwin; Ewoldt, Randy H.

doi:10.1122/8.0000122

Title: The weakly nonlinear response and nonaffine interpretation of the Johnson–Segalman/Gordon–Schowalter model

Journal Article · Tue Oct 20 00:00:00 EDT 2020 · Journal of Rheology

DOI:https://doi.org/10.1122/8.0000122· OSTI ID:1778691

^[1]; Bharadwaj, N. Ashwin ^[2];

^[1]

Univ. of Illinois at Urbana-Champaign, IL (United States)
Univ. of Illinois at Urbana-Champaign, IL (United States); Nike, Inc., Beaverton, OR (United States)

We derive new analytical solutions for the non-affine Johnson-Segalman/Gordon-Schowalter (JS/GS) constitutive equation with a general relaxation kernel in medium-amplitude oscillatory shear (MAOS) deformation. The results show time-strain separable (TSS) nonlinearity, therefore providing new physically-meaningful interpretation to the heuristic TSS nonlinear parameter in MAOS. The upper-convected, lower-convected, and corotational Maxwell models are all subsets of the results presented here. The model assumes that the microscale elements causing stress in the material slip compared to the continuum deformation. We introduce a visualization of the non-affine deformation field that acts on stress-generating elements to reinforce the hysical interpretation of the JS/GS class of models. Lastly, a case study is presented where previously published results, from fitting TSS models to MAOS data, can be re-interpreted based on the concept of non-affine motion of the JS/GS framework.

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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). Materials Sciences & Engineering Division; USDOE

Grant/Contract Number:: SC0020858; FG02-07ER46471

OSTI ID:: 1778691

Alternate ID(s):: OSTI ID: 1678798; OSTI ID: 1876430

Journal Information:: Journal of Rheology, Vol. 64, Issue 6; ISSN 0148-6055

Publisher:: Society of RheologyCopyright Statement

Country of Publication:: United States

Language:: English

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Title: The weakly nonlinear response and nonaffine interpretation of the Johnson–Segalman/Gordon–Schowalter model

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