Journal
COMPUTATIONAL MECHANICS
Volume 66, Issue 4, Pages 827-849Publisher
SPRINGER
DOI: 10.1007/s00466-020-01876-4
Keywords
Bayesian estimation; Inverse problem; Phase-field propagation; Brittle fracture; Multi-field problem
Funding
- Austrian Science Fund (FWF)
- German Research Foundation [DFG SPP 1748, 392587580]
- FWF (Austrian Science Fund) START Project [Y660]
- FWF [P28367-N35]
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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.
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