A two-level nesting smoothed extended meshfree method for dynamic fracture analysis

Abstract

A two-level nesting smoothed extended meshfree method (S-XMM-N) is presented for modeling dynamic fracture behaviors in two-dimensional linear elastic solids. The extended meshfree method based on the partition of unity allows for arbitrary discontinuities, but with low computational efficiency needs improvement. Meanwhile, directly introducing the generalized smoothed strain technique into the extended meshfree method can save more computational times, and with low accuracy also improvement. The proposed method combined the best feature of both the recently developed two-level nesting smoothing meshfree method and the extended radial point interpolation method (XRPIM). On the one hand, the S-XMM-N saves much more computational time than XRPIM by using the proposed two-level nesting triangular sub-domains smoothing integration, where only fewer integration points are employed and the derivatives of shape functions do not need to be calculated for constructing the stiffness matrix. On the other hand, the computational accuracy can be ensured due to the employment of Richardson extrapolation method. The results for the static and dynamic SIFs are compared with the analytical and other numerical solutions by several benchmark fracture problems.