November 13, 2015
|Dr. Thomas Wick
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Austria
|Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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Currently, fracture propagation is a major topic in applied mathematics and engineering. It seems to turn out that one of the most promisingmethods is based on a variational setting and more specifically on a thermodynamically consistent phase-field model. Here a smoothed indicator function determines the crack location and is characterized through a model regularization parameter. In addition, modeling assumes that the fracture can never heal, which is imposed through a temporal constraint, leading to a variational inequality system. The basic fracture model problem has been recently extended to pressurized and fluid-filled fractures. In the latter technique an additional flow equation of Darcy-type is formulated as a diffraction problem and accounts for flow in the fracture as well as the surrounding porous media. Thus, three unknowns are seeked: pressure, displacements and a phase-field variable. In the numerical solution, the fixed-stress splitting is employed to decouple flow and geomechanics. Moreover, in order to better capture the local fracture and flow dynamics, a predictor-corrector scheme for local mesh adaptivity is employed. Our proposed approach is substantiated with different numerical tests.