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Characterizing viscoelastic materials via ensemble-based data assimilation of bubble collapse observations

Spratt, Jean-Sebastien and Rodriguez, Mauro and Schmidmayer, Kevin and Bryngelson, Spencer H. and Yang, Jin and Franck, Christian and Colonius, Tim (2021) Characterizing viscoelastic materials via ensemble-based data assimilation of bubble collapse observations. Journal of the Mechanics and Physics of Solids, 152 . Art. No. 104455. ISSN 0022-5096. PMCID PMC8177475. doi:10.1016/j.jmps.2021.104455.

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Viscoelastic material properties at high strain rates are needed to model many biological and medical systems. Bubble cavitation can induce such strain rates, and the resulting bubble dynamics are sensitive to the material properties. Thus, in principle, these properties can be inferred via measurements of the bubble dynamics. Estrada et al. (2018) demonstrated such bubble-dynamic high-strain-rate rheometry by using least-squares shooting to minimize the difference between simulated and experimental bubble radius histories. We generalize their technique to account for additional uncertainties in the model, initial conditions, and material properties needed to uniquely simulate the bubble dynamics. Ensemble-based data assimilation minimizes the computational expense associated with the bubble cavitation model , providing a more efficient and scalable numerical framework for bubble-collapse rheometry. We test an ensemble Kalman filter (EnKF), an iterative ensemble Kalman smoother (IEnKS), and a hybrid ensemble-based 4D-Var method (En4D-Var) on synthetic data, assessing their estimations of the viscosity and shear modulus of a Kelvin–Voigt material. Results show that En4D-Var and IEnKS provide better moduli estimates than EnKF. Applying these methods to the experimental data of Estrada et al. (2018) yields similar material property estimates to those they obtained, but provides additional information about uncertainties. In particular, the En4D-Var yields lower viscosity estimates for some experiments, and the dynamic estimators reveal a potential mechanism that is unaccounted for in the model, whereby the apparent viscosity is reduced in some cases due to inelastic behavior, possibly in the form of material damage occurring at bubble collapse.

Item Type:Article
Related URLs:
URLURL TypeDescription CentralArticle Paper
Rodriguez, Mauro0000-0003-0545-0265
Schmidmayer, Kevin0000-0003-0444-3098
Bryngelson, Spencer H.0000-0003-1750-7265
Franck, Christian0000-0002-2347-620X
Colonius, Tim0000-0003-0326-3909
Additional Information:© 2021 Elsevier Ltd. Received 10 August 2020, Revised 22 February 2021, Accepted 13 April 2021, Available online 17 April 2021. This work was supported by the National Institutes of Health, USA [grant number 2P01-DK043881]; and the Office of Naval Research, USA [grant numbers N0014-18-1-2625, N0014-17-1-2676]. CRediT authorship contribution statement: Jean-Sebastien Spratt: Conceptualization, Investigation, Methodology - data assimilation and bubble dynamics, Software, Writing - original draft, Writing - review & editing. Mauro Rodriguez: Methodology - bubble dynamics, Writing - review & editing. Kevin Schmidmayer: Conceptualization, Writing - review & editing. Spencer H. Bryngelson: Methodology - bubble dynamics, Writing - review & editing. Jin Yang: Software, Writing - review & editing. Christian Franck: Writing - review & editing, Supervision. Tim Colonius: Conceptualization, Methodology, Writing - review & editing, Supervision, Funding acquisition. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Funding AgencyGrant Number
Office of Naval Research (ONR)N0014-18-1-2625
Office of Naval Research (ONR)N0014-17-1-2676
Subject Keywords:A. Dynamics; B. Constitutive behavior; B. Viscoelastic material; C. Numerical algorithms; Data assimilation
PubMed Central ID:PMC8177475
Record Number:CaltechAUTHORS:20200908-152555309
Persistent URL:
Official Citation:Jean-Sebastien Spratt, Mauro Rodriguez, Kevin Schmidmayer, Spencer H. Bryngelson, Jin Yang, Christian Franck, Tim Colonius, Characterizing viscoelastic materials via ensemble-based data assimilation of bubble collapse observations, Journal of the Mechanics and Physics of Solids, Volume 152, 2021, 104455, ISSN 0022-5096,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105278
Deposited By: Tony Diaz
Deposited On:08 Sep 2020 22:32
Last Modified:12 Jul 2022 20:29

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