A Bayesian estimation method for variational phase-field fracture problems

In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method. Parameter estimation is realized with a Bayesian approach. Here, the focus is on uncertainties arising in the solid material parameters and the crit...

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Published in:	Computational mechanics Vol. 66; no. 4; pp. 827 - 849
Main Authors:	Khodadadian, Amirreza, Noii, Nima, Parvizi, Maryam, Abbaszadeh, Mostafa, Wick, Thomas, Heitzinger, Clemens
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2020 Springer
Subjects:	Classical and Continuum Physics Computational Science and Engineering Engineering Original Paper Theoretical and Applied Mechanics Bayesian estimation Multi-field problem Phase-field propagation Brittle fracture Inverse problem
ISSN:	0178-7675, 1432-0924
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Abstract	In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method. Parameter estimation is realized with a Bayesian approach. Here, the focus is on uncertainties arising in the solid material parameters and the critical energy release rate. A reference value (obtained on a sufficiently refined mesh) as the replacement of measurement data will be chosen, and their posterior distribution is obtained. Due to time- and mesh dependencies of the problem, the computational costs can be high. Using Bayesian inversion, we solve the problem on a relatively coarse mesh and fit the parameters. In several numerical examples our proposed framework is substantiated and the obtained load-displacement curves, that are usually the target functions, are matched with the reference values.
AbstractList	In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method. Parameter estimation is realized with a Bayesian approach. Here, the focus is on uncertainties arising in the solid material parameters and the critical energy release rate. A reference value (obtained on a sufficiently refined mesh) as the replacement of measurement data will be chosen, and their posterior distribution is obtained. Due to time- and mesh dependencies of the problem, the computational costs can be high. Using Bayesian inversion, we solve the problem on a relatively coarse mesh and fit the parameters. In several numerical examples our proposed framework is substantiated and the obtained load-displacement curves, that are usually the target functions, are matched with the reference values. In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method. Parameter estimation is realized with a Bayesian approach. Here, the focus is on uncertainties arising in the solid material parameters and the critical energy release rate. A reference value (obtained on a sufficiently refined mesh) as the replacement of measurement data will be chosen, and their posterior distribution is obtained. Due to time- and mesh dependencies of the problem, the computational costs can be high. Using Bayesian inversion, we solve the problem on a relatively coarse mesh and fit the parameters. In several numerical examples our proposed framework is substantiated and the obtained load-displacement curves, that are usually the target functions, are matched with the reference values.In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method. Parameter estimation is realized with a Bayesian approach. Here, the focus is on uncertainties arising in the solid material parameters and the critical energy release rate. A reference value (obtained on a sufficiently refined mesh) as the replacement of measurement data will be chosen, and their posterior distribution is obtained. Due to time- and mesh dependencies of the problem, the computational costs can be high. Using Bayesian inversion, we solve the problem on a relatively coarse mesh and fit the parameters. In several numerical examples our proposed framework is substantiated and the obtained load-displacement curves, that are usually the target functions, are matched with the reference values.
Audience	Academic
Author	Abbaszadeh, Mostafa Heitzinger, Clemens Khodadadian, Amirreza Noii, Nima Parvizi, Maryam Wick, Thomas
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BackLink	https://www.ncbi.nlm.nih.gov/pubmed/33029034$$D View this record in MEDLINE/PubMed
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Keywords	Bayesian estimation Multi-field problem Phase-field propagation Brittle fracture Inverse problem
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Snippet	In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method....
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SubjectTerms	Classical and Continuum Physics Computational Science and Engineering Engineering Original Paper Theoretical and Applied Mechanics
Title	A Bayesian estimation method for variational phase-field fracture problems
URI	https://link.springer.com/article/10.1007/s00466-020-01876-4 https://www.ncbi.nlm.nih.gov/pubmed/33029034 https://www.proquest.com/docview/2449262588 https://pubmed.ncbi.nlm.nih.gov/PMC7510934
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