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MATHEMATICAL MODELING OF HYDRAULIC FRACTURE PROPAGATION IN POROELASTIC MEDIUM
Abstract
The paper presents the calculation of the trajectory of an axisymmetric fracture propagation in an isotropic poroelastic medium considering fluid leakage and viscosity. The problem was solved using the extended finite element method (XFEM). It allows to obtain solutions containing a displacement jump with the help of discontinuous functions, and solutions near the crack tip with special asymptotic functions. This method can simulate the process of initiation and propagation of a crack in the direction that is determined from the analysis of the stress state in the vicinity of its tip. The simulation used an approach based on phantom knots and the cohesive fracture law which takes into account the existence of a zone of material softening in front of the crack. This means that it is not necessary to determine the critical stress intensity factor. The calculated trajectories are in agreement with experimental data obtained in other studies during the formation of fractures in blocks of polymethylmethacrylate.
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