Fracture mechanics analysis of functionally graded materials by an efficient and accurate meshless method

Abstract

In this work, an efficient and accurate meshfree method, named the two-level nesting smoothed extended meshless method (S-XMM-N), is developed for simulating the static and dynamic fracture behaviors of two-dimensional (2D) functionally graded materials (FGMs). To accurately capture the displacement discontinuity along the crack face and the stress singularities at the crack tips in FGMs, we improve the extended meshless approximation by adding the Heaviside function and four crack tip enrichment functions to the approximation of RPIM. This approximation not only inherits all the advantages of traditional extended meshless approximation but also has interpolation properties. Furthermore, to avoid the complex and expensive integration calculation when constructing the global stiffness matrix, we use the recently developed two-level nesting smoothing integration algorithm, which is based on the first and second level smoothed strains and Richardson extrapolation theory. The static and dynamic stress intensity factors (SIFs) are calculated by the interaction integral. Several static and dynamic problems of FGM thin plates with the elastic modulus varying with respect to the exponential or hyperbolic tangent functions are solved by S-XMM-N. By investigating the SIFs given by various methods, the feasibility and effectiveness of the proposed methods are validated.