Predicting the response of complex fluids to different flow conditions has been the focal point of rheology and is generally done via constitutive relations. There are, nonetheless, scenarios in which not much is known from the material mathematically, while data collection from samples is elusive, resource-intensive, or both. In such cases, meta-modeling of observables using a parametric surrogate model called multi-fidelity neural networks (MFNNs) may obviate the constitutive equation development step by leveraging only a handful of high-fidelity (Hi-Fi) data collected from experiments (or high-resolution simulations) and an abundance of low-fidelity (Lo-Fi) data generated synthetically to compensate for Hi-Fi data scarcity. To this end, MFNNs are employed to meta-model the material responses of a thermo-viscoelastic (TVE) fluid, consumer product Johnson’s® Baby Shampoo, under four flow protocols: steady shear, step growth, oscillatory, and small/large amplitude oscillatory shear (S/LAOS). In addition, the time–temperature superposition (TTS) of the material response and MFNN predictions are explored. By applying simple linear regression (without induction of any constitutive equation) on log-spaced Hi-Fi data, a series of Lo-Fi data were generated and found sufficient to obtain accurate material response recovery in terms of either interpolation or extrapolation for all flow protocols except for S/LAOS. This insufficiency is resolved by informing the MFNN platform with a linear constitutive model (Maxwell viscoelastic) resulting in simultaneous interpolation and extrapolation capabilities in S/LAOS material response recovery. The roles of data volume, flow type, and deformation range are discussed in detail, providing a practical pathway to multifidelity meta-modeling of different complex fluids.
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September 2024
Research Article|
July 24 2024
Data-driven constitutive meta-modeling of nonlinear rheology via multifidelity neural networks
Milad Saadat
;
Milad Saadat
a)
1
Department of Mechanical and Industrial Engineering, Northeastern University
, Boston 02115, Massachusetts
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William H. Hartt V
;
William H. Hartt V
a)
2
Department of Chemical and Biomolecular Engineering, University of Delaware
, Newark 19716, Delaware
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Norman J. Wagner
;
Norman J. Wagner
b)
2
Department of Chemical and Biomolecular Engineering, University of Delaware
, Newark 19716, Delawareb)Authors to whom correspondence should be addressed: wagnernj@udel.edu and s.jamali@northeastern.edu
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Safa Jamali
1
Department of Mechanical and Industrial Engineering, Northeastern University
, Boston 02115, Massachusettsb)Authors to whom correspondence should be addressed: wagnernj@udel.edu and s.jamali@northeastern.edu
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b)Authors to whom correspondence should be addressed: wagnernj@udel.edu and s.jamali@northeastern.edu
a)
Milad Saadat and William H. Hartt V contributed equally to this work.
c)
Also at: Chemical Engineering Department, Northeastern University, Boston, MA 02115.
J. Rheol. 68, 679–693 (2024)
Article history
Received:
February 07 2024
Accepted:
July 03 2024
Citation
Milad Saadat, William H. Hartt V, Norman J. Wagner, Safa Jamali; Data-driven constitutive meta-modeling of nonlinear rheology via multifidelity neural networks. J. Rheol. 1 September 2024; 68 (5): 679–693. https://doi.org/10.1122/8.0000831
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