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 -