Details
| Original language | English |
|---|---|
| Pages (from-to) | 827-849 |
| Number of pages | 23 |
| Journal | Computational mechanics |
| Volume | 66 |
| Issue number | 4 |
| Early online date | 14 Jul 2020 |
| Publication status | Published - Oct 2020 |
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.
Keywords
- Bayesian estimation, Brittle fracture, Inverse problem, Multi-field problem, Phase-field propagation
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Computational mechanics, Vol. 66, No. 4, 10.2020, p. 827-849.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A Bayesian estimation method for variational phase-field fracture problems
AU - Khodadadian, Amirreza
AU - Noii, Nima
AU - Parvizi, Maryam
AU - Abbaszadeh, Mostafa
AU - Wick, Thomas
AU - Heitzinger, Clemens
N1 - Funding Information: Open access funding provided by Austrian Science Fund (FWF). T. Wick and N. Noii have been financially supported by the German Research Foundation, Priority Program 1748 (DFG SPP 1748) in the subproject Structure Preserving Adaptive Enriched Galerkin Methods for Pressure-Driven 3D Fracture Phase-Field Models with the project No. 392587580. A. Khodadadian and C. Heitzinger acknowledge financial support by FWF (Austrian Science Fund) START Project no. Y660 PDE Models for Nanotechnology. M. Parvizi has been supported by FWF Project no. P28367-N35. Furthermore, the authors appreciate the useful comments given by the anonymous reviewers.
PY - 2020/10
Y1 - 2020/10
N2 - 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.
AB - 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.
KW - Bayesian estimation
KW - Brittle fracture
KW - Inverse problem
KW - Multi-field problem
KW - Phase-field propagation
UR - http://www.scopus.com/inward/record.url?scp=85087894180&partnerID=8YFLogxK
U2 - 10.1007/s00466-020-01876-4
DO - 10.1007/s00466-020-01876-4
M3 - Article
AN - SCOPUS:85087894180
VL - 66
SP - 827
EP - 849
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 4
ER -