A meshless sub-region radial point interpolation method for accurate calculation of crack tip fields

A new meshless sub-region radial point interpolation method (MS-RPIM) is proposed for linear elastic fracture mechanics. The Williams expansions of stress field for mode I/II crack is used as the trial functions in crack tip region, the meshless radial point interpolation is used for the rest of domain, and a mixed variational principle is used for discretisation. In contrast to existing meshless formulations, the present MS-RPIM requires only very few nodes around the crack tip to obtain smooth stress and accurate results and the SIFs can be directly obtained as part of the solution and no additional effort via post-processing.