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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. [ABSTRACT FROM AUTHOR]

• A crack tip in the SEZ of another crack deflects the maximum von Mises stress gradient towards the latter tip. • The inclined angle of a smaller crack has a greater influence on the ESIF and plastic zone of other crack tips. • The influence of micro-cracks is concentrated around the tips of macro-cracks, whereas the influence of macro-cracks is dispersed around micro-cracks. • In the SEZ, a smaller crack inclined angle has a greater effect on promoting the mutual fusion between the plastic zones of other cracks. • The interaction range between kinked cracks with certain inclined angles can exceed the influence zone of a straight crack on a kinked crack. The influence range of crack interaction is studied using the distribution dislocation technique, and is defined as the influenced zone. For elastic materials with cracks, the equivalent stress intensity factor influenced zone is obtained, while for plastic materials with cracks, the plasticity influenced zone is determined. The interaction between multiple cracks can be analyzed by introducing the concept of the influenced zone, which simplifies the analysis. The results indicate that if a crack is located outside the influenced zone of another crack, the effect of the former on the latter can be ignored within an acceptable range of error. The influenced zone for elastic materials depends on the length and inclined angle of a crack, whereas for plastic materials, the plastic influenced zone is affected by the crack length, inclined angle, and material yield limit simultaneously. In the case of plastic materials with multiple cracks, fusion of plastic zones between two cracks may occur at certain positions under the influence of other cracks. These theoretical findings can simplify the analysis of the fatigue fracture behavior of materials with multiple cracks, whether they are elastic or plastic. [ABSTRACT FROM AUTHOR]