Bayesian inversion for anisotropic hydraulic phase-field fracture

Noii, Nima; Khodadadian, Amirreza; Wick, Thomas

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.

Citation

Noii, N., Khodadadian, A., & Wick, T. (2021). Bayesian inversion for anisotropic hydraulic phase-field fracture. Computer Methods in Applied Mechanics and Engineering, 386, Article 114118. https://doi.org/10.1016/j.cma.2021.114118

• Journal Article Type: Article
• Acceptance Date: Aug 12, 2021
• Publication Date: 2021-12
• Deposit Date: Feb 25, 2025
• Journal: Computer Methods in Applied Mechanics and Engineering
• Print ISSN: 0045-7825
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 386
• Article Number: 114118
• DOI: https://doi.org/10.1016/j.cma.2021.114118
• Keywords: Phase-field approach; Hydraulic fracture; Fluid-saturated porous media; Anisotropic materials; Bayesian inference; DRAM algorithm
• Public URL: https://keele-repository.worktribe.com/output/1079478
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0045782521004497
• Additional Information: This article is maintained by: Elsevier; Article Title: Bayesian inversion for anisotropic hydraulic phase-field fracture; Journal Title: Computer Methods in Applied Mechanics and Engineering; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.cma.2021.114118; Content Type: article; Copyright: © 2021 Elsevier B.V. All rights reserved.