Spatially-dependent material uncertainties in anisotropic nonlinear elasticity: Stochastic modeling, identification, and propagation

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This paper develops a stochastic model for the spatially-dependent material parameters parameterizing anisotropic strain energy density functions. The construction is cast within the framework of information theory, which is invoked to derive a least-informative model while ensuring consistency with theoretical requirements in finite elasticity. Specifically, almost sure polyconvexity and uniform growth conditions are enforced through proper repulsion constraints and regularization, hence making the forward problem of uncertainty propagation well posed. In addition, transformations arising from the linearization procedure are introduced for consistency and induce statistical dependencies in the primary variables. The latter include material moduli, a weight balancing between the isotropic and anisotropic contributions, and the angle defining the structural tensors. The identification of the model is subsequently performed, using an existing database on human arterial walls. Maximum likelihood estimators are obtained and provided for the adventitia, media, and intima layers, which enables the use of the proposed model as a generative surrogate for, e.g., training and classification in data-driven approaches integrating inter-patient variability. Finally, uncertainty propagation on a realistic, patient-specific geometry is conducted to demonstrate the efficiency of the stochastic modeling framework. ... [Read More]

Data Citation

Chen, P., & Guilleminot, J. (2022). Data from: Spatially-dependent material uncertainties in anisotropic nonlinear elasticity: Stochastic modeling, identification, and propagation. Duke Research Data Repository. https://doi.org/10.7924/r4rn3c061

Creator: Chen, Peiyi
Guilleminot, Johann
DOI: 10.7924/r4rn3c061
Subject: Random fields
Nonlinear elasticity
Uncertainty quantification
Information theory
Stochastic models
Publication Date: January 5, 2024
ARK: ark:/87924/r4rn3c061
Affiliation: Mechanical Engineering and Materials Science
Civil and Environmental Engineering
Publisher: Duke Research Data Repository
Type: Dataset
Related Materials: Chen, P., & Guilleminot, J. (2022). Spatially-dependent material uncertainties in anisotropic nonlinear elasticity: Stochastic modeling, identification, and propagation. Computer Methods in Applied Mechanics and Engineering, 394, 114897. https://doi.org/10.1016/j.cma.2022.114897
Funding Agency: National Science Foundation
Grant Number: DGE-2022040
CMMI-1726403
Contact: Johann Guilleminot: johann.guilleminot@duke.edu
Peiyi Chen: peiyi.chen@duke.edu
License: Creative Commons CC0 1.0 Universal
Title: Spatially-dependent material uncertainties in anisotropic nonlinear elasticity: Stochastic modeling, identification, and propagation
License: http://creativecommons.org/publicdomain/zero/1.0/
Repository: Duke Research Data Repository

Title	Date Uploaded	Visibility	Actions
README.pdf	2024-01-08	Public	Download
calibrated_material_parameters_media.png	2024-01-08	Public	Download
calibrated_material_parameters_intima.png	2024-01-08	Public	Download
calibrated_material_parameters_adventitia.png	2024-01-08	Public	Download
artery_mesh.e	2024-01-08	Public	Download

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