TY - JOUR

T1 - Bayesian inversion for anisotropic hydraulic phase-field fracture

AU - Noii, Nima

AU - Khodadadian, Amirreza

AU - Wick, Thomas

N1 - Funding Information: T. Wick has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’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.

PY - 2021/12/1

Y1 - 2021/12/1

N2 - 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.

AB - 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.

KW - Anisotropic materials

KW - Bayesian inference

KW - DRAM algorithm

KW - Fluid-saturated porous media

KW - Hydraulic fracture

KW - Phase-field approach

UR - http://www.scopus.com/inward/record.url?scp=85114327526&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2021.114118

DO - 10.1016/j.cma.2021.114118

M3 - Article

AN - SCOPUS:85114327526

VL - 386

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

M1 - 114118

ER -