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An Extended Finite Element Method for Hydraulic Fracture Problems by Brice Lecampion is a Engineering article available to read on EtoBox.

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## Abstract In this paper, the extended finite element method (X‐FEM) is investigated for the solution of hydraulic fracture problems. The presence of an internal pressure inside the crack is taken into account. Special tip functions encapsulating tip asymptotics typically encountered in hydraulic fractures are introduced. We are especially interested in the two limiting tip behaviour for the impermeable case: the classical LEFM square root asymptote in fracture width for the toughness‐dominated regime of propagation and the so‐called 2⁄3 asymptote in fracture width for the viscosity‐dominated regime. Different variants of the X‐FEM are tested for the case of a plane‐strain hydraulic fracture propagation in both the toughness and the viscosity dominated regimes. Fracture opening and fluid pressure are compared at each nodes with analytical solutions available in the literature. The results demonstrate the importance of correcting for the loss of partition of unity in the transition zone between the enriched part and the rest of the mesh. A point‐wise matching scheme appears sufficient to obtain accurate results. Proper integration of the singular terms introduced by the enrichment

Who reads An Extended Finite Element Method for Hydraulic Fracture Problems?

Author

Brice Lecampion

Publisher

John Wiley and Sons; Wiley (John Wiley & Sons); John Wiley & Sons Inc.; Wiley (ISSN 1069-8299)

Published

2008

Language

EN

Field

Engineering (Physical Sciences)