Search

Highlights • Greatly improving the efficiency of the meshfree method by transforming background cell integral into boundary integration. • Directly imposing the boundary condition without any effort. • Completely avoiding the derivation of meshfree shape functions. • Improving the accuracy of the stress field in the vicinity of the crack tips. Abstract A smoothed enriched meshfree Galerkin method with two-level nesting triangular sub-domains (NSEMM) is presented for linear elastic fracture mechanics. In the present method, displacement fields are constructed by using the linear MLS approximation in linear region away from the crack tip and the enriched MLS approximation in enriched region around the crack tip respectively. To overcome the discontinuous problem of the coupling approximations and accelerate meshfree computations, two-level nesting triangular sub-domains based on the triangular background integration cells are designed and used to construct the smoothing strain. Each two-level nesting sub-domains includes the triangular background cell itself and four equal-area triangular sub-cells. The discretized system equations are created by the Generalized smoothed Galerkin (GS-Garlerkin) weak form and Richardson extrapolation method. The values of SIFs are evaluated by using the domain form of interaction integral. Numerical examples have been simulated to demonstrate the effectiveness and robustness of the present method for crack problems with complicated configurations, and very satisfactory results have been obtained. The NSEMM takes advantages of both EFGM and generalized strain smoothing technique such as lower computational cost, high accurate and easy to implementation. [ABSTRACT FROM AUTHOR]

• A coupled extended meshfree–smoothed meshfree method (CXSMM) is presented for simulating crack growth in 2D solids. • Division the analysis domain into discontinuous and continuous regions is available. • The CXSMM has the advantages of both extended meshfree method and smoothed meshfree method. • Several problems are used to evaluate the accuracy, efficiency and robustness of the CXSMM. A coupled extended meshfree–smoothed meshfree method (CXSMM) is presented for simulating crack growth in 2D solids. In terms of the relationship between the crack surface and the background integration cells, the analysis domain is easy to be divided into discontinuous and continuous regions, in which the meshfree Galerkin method and the smoothed meshfree method are employed to construct the discretized system equations, respectively. To precisely capture the singular stress field near the crack tip, higher order Gauss integration rules are used in the discontinuous region. At the same time, the general smoothed strain technique is utilized in the continuous region for efficient evaluation of the domain integration. In this work, the initiation and propagation of the crack are treated by the aid of the level set algorithm. The CXSMM has the advantages of both extended meshfree method and smoothed meshfree method and can accurately and efficiently model the linear elastic fracture. Several benchmark problems are used to evaluate the accuracy, efficiency and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

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]