A Bayesian estimation method for variational phase-field fracture problems
- PDF / 5,524,582 Bytes
- 23 Pages / 595.276 x 790.866 pts Page_size
- 59 Downloads / 216 Views
ORIGINAL PAPER
A Bayesian estimation method for variational phase-field fracture problems Amirreza Khodadadian1,3 · Nima Noii3 · Maryam Parvizi1 · Mostafa Abbaszadeh2 · Thomas Wick3 · Clemens Heitzinger1,4 Received: 16 October 2019 / Accepted: 17 June 2020 © The Author(s) 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 timeand 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 · Inverse problem · Phase-field propagation · Brittle fracture · Multi-field problem
1 Introduction This work is devoted to parameter identifications in fracture failure problems. To formulate fracture phenomena, a
B
Amirreza Khodadadian [email protected] Nima Noii [email protected] Maryam Parvizi [email protected] Mostafa Abbaszadeh [email protected] Thomas Wick [email protected] Clemens Heitzinger [email protected]
1
Institute of Analysis and Scientific Computing, Vienna University of Technology (TU Wien), Wiedner Hauptstraße 8–10, 1040 Vienna, Austria
2
Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran 15914, Iran
3
Institute of Applied Mathematics, Leibniz University Hannover, Welfengarten 1, 30167 Hanover, Germany
4
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
phase-field formulation for quasi-brittle fracture is used. The variational phase-field formulation is a thermodynamically consistent framework to compute the fracture failure process. This formulation emanates from the regularized version of the sharp crack surface function, which was first modeled in a variational framework in [1]. Regularized fracture phenomena are described with an additional auxiliary smooth indicator function [2], which is denoted as crack phase-field (here indicated by d). Along with a mechanical field (denoted by u), a minimization problem for the multi-field problem (u, d) can be formulated. The main feature of such a variational formulation is to approximate the discontinuities in u across the lower-dimensional crack topology with the phasefield function d. The resulting, regularized formulation leads to a diffusive transition zone between two phases in the solid, which corresponds t
Data Loading...
