Analysis of transient dynamic fracture parameters of cracked functionally graded composites by improved meshfree methods

In this paper, computation and analysis for transient dynamic stress intensity factors (DSIFs) of two-dimensional fracture problems of functionally graded materials (FGMs) by extended meshfree methods are described. The extended moving Kriging based meshfree method (X-MK) is introduced and compared with recently developed extended meshfree radial point interpolation method (X-RPIM) in the dynamical fracture context of FGM models. Moreover, in the present study, the X-MK is improved by introducing three new different types of correlation function that fully eliminate the user parameter for MK shape functions. The standard basis functions are used as the enrichment for asymptotic near crack tip fields to accurately capture the singularities at the crack tip and the Heaviside function is used to enrich the displacement discontinuity along the crack faces. We apply the dynamic form of non-homogenous interaction integral in conjunction with the asymptotic near crack tip field to extract the DSIFs. The DSIFs obtained from the proposed methods are further compared with reference solutions derived from other existing methods, including analytical method, (extended-) finite element method, boundary element method, and scaled boundary finite element method.