Low dimensional intrinsic material functions uniquely identify rheological constitutive models and infer material microstructure

Material functions;large-amplitude oscillatory shear (LAOS);Oscillatory deformation;Chebyshev coefficients;intrinsic nonlinearities;LAOS nonlinearities;oscillatory shear

Bharadwaj, Narayanan Ashwin Kumar ; Ewoldt ; Randy H.

关键词: Material functions;    large-amplitude oscillatory shear (LAOS);    Oscillatory deformation;    Chebyshev coefficients;    intrinsic nonlinearities;    LAOS nonlinearities;    oscillatory shear;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/42175/Narayanan%20Ashwin%20Kumar_Bharadwaj.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Rheological material functions are used to form our conceptual understanding of amaterial response. For a nonlinear rheological response, the associated material functionsspan a high-dimensional space. A theoretical framework is developed to outline lowdimensionalmeasures for describing asymptotic nonlinear responses in large-amplitudeoscillatory shear (LAOS). Nomenclature is introduced to provide physical interpretationsfor 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 modelresponses to imposed large-amplitude oscillatory shear strain (LAOStrain) and translatedinto the language of intrinsic Chebyshev coefficients to allow for comparison and conceptualinterpretation. 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 twotransient nonlinear-elastic network models; finitely extensible nonlinear elastic (FENE) andwormlike chain (WLC) models. A library of analytical intrinsic LAOStrain fingerprints isthus generated. The intrinsic signatures for all these models are only a function of theimposed frequency and a nonlinear parameter, if any. Interesting sign changes are observedin the intrinsic signatures across constitutive models that help compare and contrastbetween.Under a defined deformation protocol, a numerical approach may be required to convergeon solutions to constitutive equations that may not have an analytical solution. A robustnumerical scheme is thus developed for quick and efficient extraction of intrinsic LAOStrainnonlinearities for nonlinear constitutive models. The proposed numerical algorithm is usedto extract intrinsic LAOStrain material functions for the single mode pompom model andthe intrinsic signatures are compared for different combinations of the associated nonlinearparameters. With slight modifications, the numerical scheme is applicable for any differentialor integral constitutive model. They are equally flexible to accommodate for increasediiinonlinearities in the system arising from modifications to constitutive equations in theircurrent form.The utility of these measures is demonstrated by experimentally measuring the frequencydependentintrinsic 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 PVABoraxsystem. The four measured intrinsic nonlinear fingerprints are compared with theavailable analytical and numerical library of intrinsic fingerprints. The matching processidentifies a unique constitutive equation, fits the nonlinear model parameter, and impliesmolecular- and micro-scale structure in the material.