13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- element model. Another reason could be that a static fracture rather than a propagating fracture is simulated here. Improved prediction can be expected with including the crack tip element that captures the crack tip singularity correctly. Figure 6 shows the stress field and crack opening profile of a center-cracked tension plate subjected to uniform tensile stress of 1.0 MPa. The width of the plate is 40 m and the half length of the crack is 5 m. The corrected stress intensity factor [22] is I =3.995 MPa m K . The calculation of the stress intensity factors is performed with the domain form of interaction integral. The computed stress intensity factors are I =3.954 MPa m K , and 8 II =3.8 10 MPa m K . Figure 6. Stress and crack opening profile of a center-cracked tension plate 6. Summary The application of the extended finite element method to the hydraulic fracture problems has been presented. The discrete governing equations for the coupled fluid-fracture problem have been derived. A user element based on the XFEM has been implemented in ABAQUS, which 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 introduced and assigned to the appropriate nodes of the proposed element to describe the fluid flow within the crack and its contribution to the crack deformation. Verification of the user-defined element has been made by comparing the FEM predictions with the analytical solutions available in the literature. The preliminary result presented here is a first attempt to the promising application of the XFEM to the hydraulic fracture simulation. Acknowledgements The author would like to thank Dr. Rob Jeffrey for the support of this work. Furthermore, the author thanks CESRE for support and for granting permission to publish. References [1] R. J. Clifton, A. S. Abou-Sayed, On the computation of the 3-D geometry of hydraulic fractures, in Proceedings of the SPE Symposium on Low Permeability Gas Reservoir, Denver, Richardson, 1979, pp. 307-313. [2] A. Settari, M. P. Cleary, 3-D simulation of hydraulic fracturing, Journal of Petroleum Technology, 36(1984) 1177-1190. [3] L. Vandamme, J. H. Curran, A 3-D hydraulic fracturing simulator, International Journal for Numerical Methods in Engineering, 28(1989) 909-927.
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