Abstract
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 diffraction methods 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.
Highlights
In fracture mechanic problems, the finite element formulations have been well developed and several amounts of research has been accomplished
The major difference between finite element methods is that the domain of interest is discretized only with nodes, often called particles
Much research has been done on mesh-free methods for solving differential equation problems including crack and obtained satisfactory results
Summary
The finite element formulations have been well developed and several amounts of research has been accomplished. Much research has been done on mesh-free methods for solving differential equation problems including crack and obtained satisfactory results. Among these methods reproducing kernel particle method (RKPM) has been used increasingly in fracture mechanic problems. Boundary value problems (BVPs) often have essential boundary conditions (EBCs) that involve derivatives, for example, in beams and plates, where slopes are commonly enforced at the boundaries Such problems are solved numerically using mesh-free techniques like the RKPM and the EFGM. A visibility criterion has been developed by Belytschko et al in 1994 [4] to modify the shape function of the particles near to discontinuities or nonconvex parts such as cracks. A diffraction criterion has been developed by Belytschko et al in 1996 [5] to modify the shape function of the particles in the vicinity of the discontinuities such as cracks
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