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Recently, mesh-free methods are increasingly utilized in solving various types of boundary value problems. Much research has been done on mesh-free methods for solving differential equation problems including crack and also obtained satisfactory results. Among these methods, reproducing kernel particle method (RKPM) has been used increasingly in fracture mechanic problems. The �-integral and the stress intensity factor (SIF) are the most important parameters for crack problems. In this study �-integral has been used to calculate the SIF in the crack tip. The mode � SIF at the crack tip in a work-hardening material is obtained for various dilation parameters using RKPM. A comparison between two conventional treatments, visibility and diffraction on SIF and �-integral value, is conducted. Visibility and diffractionmethods increase the accuracy of RKPM results and effect on the �-integral results at the crack tip. In comparing between the visibility and diffraction methods to modify the shape functions, the diffraction criterion seems to have better results for the �-integral and SIF value.



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Originally published in the Journal of Structures.



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