Constitutive model fingerprints in medium-amplitude oscillatory shear
- Univ. of Illinois at Urbana-Champaign, IL (United States)
Rheologists have expectations for signatures of linear viscoelastic properties, such as shapes of G'(ω) and G"(ω). Medium amplitude (or asymptotically-nonlinear) oscillatory shear (MAOS) provides additional nonlinear rheological information with low dimensional, well-defined material functions. Here, we develop expectations of signatures (or fingerprints) for the four asymptotically-nonlinear material functions associated with MAOS, [e1](ω), [e3](ω), [v1](ω), [v3](ω). Although the linear fingerprints may be identical for different models, the asymptotically-nonlinear fingerprints may be different in magnitude, frequency-scaling, curve shapes, and sign changes. To perform the analysis, we collect/translate a library of available analytical strain-controlled MAOS fingerprints for seven different constitutive models. Using this library, we identify general trends and highlight key differences of asymptotic-nonlinear viscoelasticity. Asymptotic nonlinearities for all models considered here obey the terminal regime inter-relations and frequency scaling predicted by Bharadwaj and Ewoldt. Unlike the positive linear viscoelastic measures, at least one of the four asymptotic nonlinearities changes signs with Deborah number (De). Following sign interpretations of Ewoldt and Bharadwaj, we show that nonlinearities tend to be driven by strain-rates at small De, and by strains at large De, a trend observed for nearly all the constitutive models studied here, the exception being the model for dilute rigid dumbbell suspensions. Some constitutive models exhibit multiple sign changes at intermediate De and there may be no universal behavior of asymptotically-nonlinear fingerprints in this regime. Therefore, frequency-dependent signatures can be material-specific. Furthermore, this will allow inverse problems to infer structure, select models, and fit model parameters using asymptotically-nonlinear signatures. To illustrate this aspect, we demonstrate a fingerprint matching exercise with experimental measurements on a transiently cross-linked hydrogel system. We find that currently available model fingerprints can match the qualitative magnitudes and frequency dependence, but not the signs of the experimental transient network response.
- 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
- Grant/Contract Number:
- FG02-07ER46471
- OSTI ID:
- 1875114
- Journal Information:
- Journal of Rheology, Vol. 59, Issue 2; ISSN 0148-6055
- Publisher:
- Society of RheologyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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