Bayesian inversion for anisotropic hydraulic phase-field fracture

In this work, we employ a Bayesian inversion framework to fluid-filled phase-field fracture. We develop robust and efficient numerical algorithm for hydraulic fracture toward transversely isotropic orthotropy anisotropic the fluid-driven coupled problem, three primary fields pressure, displacements, crack are solved while direction-dependent responses (due preferred fiber orientation) enforced via penalty-like parameters. A new driving state function is introduced by avoiding compressible part of energy be degraded. Next, use successful extension as departure point estimate material To end, delayed rejection adaptive Metropolis–Hastings (DRAM) identify The focus on uncertainties arising from different variables, including elasticity modulus, Biot’s coefficient, dynamic fluid viscosity Griffith’s release rate in case isotopic setting, will have additional parameters identified. Several examples substantiate our algorithmic developments.