Bayesian inversion for anisotropic hydraulic phase-field fracture

authored by: Nima Noii, Amirreza Khodadadian, Thomas Wick
Abstract: In this work, we employ a Bayesian inversion framework to fluid-filled phase-field fracture. We develop a robust and efficient numerical algorithm for hydraulic phase-field fracture toward transversely isotropic and orthotropy anisotropic fracture. In the fluid-driven coupled problem, three primary fields for pressure, displacements, and the crack phase-field are solved while direction-dependent responses (due to the preferred fiber orientation) are enforced via penalty-like parameters. A new crack driving state function is introduced by avoiding the compressible part of anisotropic energy to be degraded. Next, we use a successful extension of the anisotropic hydraulic phase-field fracture as a departure point for Bayesian inversion to estimate material parameters. To this end, we employ the delayed rejection adaptive Metropolis–Hastings (DRAM) algorithm to identify the parameters. The focus is on uncertainties arising from different variables, including elasticity modulus, Biot's coefficient, Biot's modulus, dynamic fluid viscosity and Griffith's energy release rate in the case of the isotopic hydraulic fracture while in the anisotropic setting, we will have additional penalty-like parameters to be identified. Several numerical examples substantiate our algorithmic developments.
Organisation(s): Institute of Applied Mathematics
Institute of Continuum Mechanics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 386
ISSN: 0045-7825
Publication date: 01.12.2021
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, Physics and Astronomy(all), Computer Science Applications
Electronic version(s): https://arxiv.org/abs/2007.16038 (Access: Open)
https://doi.org/10.1016/j.cma.2021.114118 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{bff6fe3640834e9194069166b213d068,
title = "Bayesian inversion for anisotropic hydraulic phase-field fracture",
abstract = "In this work, we employ a Bayesian inversion framework to fluid-filled phase-field fracture. We develop a robust and efficient numerical algorithm for hydraulic phase-field fracture toward transversely isotropic and orthotropy anisotropic fracture. In the fluid-driven coupled problem, three primary fields for pressure, displacements, and the crack phase-field are solved while direction-dependent responses (due to the preferred fiber orientation) are enforced via penalty-like parameters. A new crack driving state function is introduced by avoiding the compressible part of anisotropic energy to be degraded. Next, we use a successful extension of the anisotropic hydraulic phase-field fracture as a departure point for Bayesian inversion to estimate material parameters. To this end, we employ the delayed rejection adaptive Metropolis–Hastings (DRAM) algorithm to identify the parameters. The focus is on uncertainties arising from different variables, including elasticity modulus, Biot's coefficient, Biot's modulus, dynamic fluid viscosity and Griffith's energy release rate in the case of the isotopic hydraulic fracture while in the anisotropic setting, we will have additional penalty-like parameters to be identified. Several numerical examples substantiate our algorithmic developments.",
keywords = "Anisotropic materials, Bayesian inference, DRAM algorithm, Fluid-saturated porous media, Hydraulic fracture, Phase-field approach",
author = "Nima Noii and Amirreza Khodadadian and Thomas Wick",
note = "Funding Information: T. Wick has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany{\textquoteright}s Excellence Strategy within the Cluster of Excellence PhoenixD, EXC 2122 (project number: 390833453). N. Noii has been funded by the Priority Program DFG-SPP 2020 within its second funding phase. The authors also appreciate useful comments given by the anonymous reviewers. ",
year = "2021",
month = dec,
day = "1",
doi = "10.1016/j.cma.2021.114118",
language = "English",
volume = "386",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}