Implementation of the XFEM for Hydraulic Fracture Problems

A new finite element has been implemented to incorporate the extended finite element method (XFEM) for the solution of hydraulic fracture problems. The proposed element includes the desired aspects of the XFEM so as to model crack propagation without explicit remeshing. In addition, the fluid pressure degrees of freedom have been defined on the element to describe the fluid flow within the crack and its contribution to the crack deformation. Thus the fluid flow within the crack and crack propagation are fully coupled in a natural way and are solved simultaneously. Verification of the proposed element has been conducted by comparing the finite element results with the analytical solutions available in the literature.

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