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Title:Low dimensional intrinsic material functions uniquely identify rheological constitutive models and infer material microstructure
Author(s):Bharadwaj, Narayanan Ashwin Kumar
Advisor(s):Ewoldt, Randy H.
Department / Program:Mechanical Sci & Engineering
Discipline:Mechanical Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Material functions
large-amplitude oscillatory shear (LAOS)
Oscillatory deformation
Chebyshev coefficients
intrinsic nonlinearities
LAOS nonlinearities
oscillatory shear
Abstract:Rheological material functions are used to form our conceptual understanding of a material response. For a nonlinear rheological response, the associated material functions span a high-dimensional space. A theoretical framework is developed to outline lowdimensional measures for describing asymptotic nonlinear responses in large-amplitude oscillatory shear (LAOS). Nomenclature is introduced to provide physical interpretations for these newly developed intrinsic measures under both shear strain-control (LAOStrain) and shear stress-control (LAOStress) protocols. Analytical solutions are surveyed for these intrinsic signatures of constitutive model responses to imposed large-amplitude oscillatory shear strain (LAOStrain) and translated into the language of intrinsic Chebyshev coefficients to allow for comparison and conceptual interpretation. Considered constitutive models include that of a third order fluid, corotational Maxwell model, Giesekus model, and other specific models for polymer melts, rodlike polymer solutions, and emulsions. New analytical results are derived for two transient nonlinear-elastic network models; finitely extensible nonlinear elastic (FENE) and wormlike chain (WLC) models. A library of analytical intrinsic LAOStrain fingerprints is thus generated. The intrinsic signatures for all these models are only a function of the imposed frequency and a nonlinear parameter, if any. Interesting sign changes are observed in the intrinsic signatures across constitutive models that help compare and contrast between. Under a defined deformation protocol, a numerical approach may be required to converge on solutions to constitutive equations that may not have an analytical solution. A robust numerical scheme is thus developed for quick and efficient extraction of intrinsic LAOStrain nonlinearities for nonlinear constitutive models. The proposed numerical algorithm is used to extract intrinsic LAOStrain material functions for the single mode pompom model and the intrinsic signatures are compared for different combinations of the associated nonlinear parameters. With slight modifications, the numerical scheme is applicable for any differential or integral constitutive model. They are equally flexible to accommodate for increased iii nonlinearities in the system arising from modifications to constitutive equations in their current form. The utility of these measures is demonstrated by experimentally measuring the frequencydependent intrinsic LAOStrain nonlinearities for a polymeric hydrogel (PVA-Borax). Techniques for accurate extraction of the subdominant intrinsic measures are presented. Physical interpretations are provided through the obtained intrinsic signatures of the PVABorax system. The four measured intrinsic nonlinear fingerprints are compared with the available analytical and numerical library of intrinsic fingerprints. The matching process identifies a unique constitutive equation, fits the nonlinear model parameter, and implies molecular- and micro-scale structure in the material.
Issue Date:2013-02-03
Rights Information:Copyright 2012 Narayanan Ashwin Kumar Bharadwaj
Date Available in IDEALS:2013-02-03
Date Deposited:2012-12

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