Bayesian inversion for anisotropic hydraulic phase-field fracture. (English) Zbl 1507.74408

Noii, Nima; Khodadadian, Amirreza; Wick, Thomas

Comput. Methods Appl. Mech. Eng. 386, Article ID 114118, 37 p. (2021).

Summary: 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.

MSC:

74R10	Brittle fracture
74S05	Finite element methods applied to problems in solid mechanics
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76S05	Flows in porous media; filtration; seepage

Keywords:

phase-field approach; hydraulic fracture; fluid-saturated porous media; anisotropic materials; Bayesian inference; DRAM algorithm

Software:

ParaDRAM; IPACS

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