Crack growth modeling in elastic solids by the extended meshfree Galerkin radial point interpolation method

Nguyen, Nha Thanh; Bui, Tinh Quoc; Zhang, Chuanzeng; Truong, Thanh-Dat

doi:10.1016/j.enganabound.2014.04.021

Cited by 119 publications

(25 citation statements)

References 22 publications

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“…These methods do not require any discretization of the problem domain, and therefore, the approximate solution of the problem is obtained using a set of scattered nodes. One of the attractions of the meshless methods may be devoted to their flexibility in dealing with discontinuities (such as cracks) [20][21][22][23][24]. The FFEM was firstly developed to calculate the SIFs for cracked domains [25,26].…”

Section: Introductionmentioning

confidence: 99%

Development of a new semi-analytical method in fracture mechanics problems based on the energy release rate

2016

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The existence of crack and notch is a considerable and serious subject in the failure study of solids and structures. As most of cracked domain problems do not have closed-form solutions, numerical methods are dominant approaches dealing with fracture mechanics problems. In fracture mechanics and failure analysis, cracked media energy and consequently stress intensity factors (SIFs) play a crucial and significant role. Based on linear elastic fracture mechanics, the SIFs may be estimated using the energy release rate, as an indirect approach. This study presents the development of a new semi-analytical method to model cracked media. In this method, only the boundaries of problems are discretized using specific higher-order subparametric elements and higher-order Chebyshev mapping functions. Implementing the weighted residual method and using Clenshaw-Curtis quadrature yield diagonal Euler's differential equations. Therefore, when the local coordinate origin is located at the crack tip, the geometry of crack problems is implemented directly without further processing. In order to present crack boundary conditions, a modified form of nodal force function is presented. Validity and accuracy of the proposed method is fully illustrated by four benchmark problems, whose results agree very well with those of other numerical and/or analytical solutions existing in the literature.

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Section: Introductionmentioning

confidence: 99%

Development of a new semi-analytical method in fracture mechanics problems based on the energy release rate

2016

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“…Unlike the FEM, meshfree method uses a set of scattered nodes to model the domain and approximate the field variables. Because no finite element or mesh is required in the approximation, meshfree methods are very suitable for modeling crack growth problems [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Extended meshless moving Kriging method for crack propagation analyzing in orthotropic media

et al. 2019

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Orthotropic composite material is the particular type of anisotropic materials and their products have been extensively used in a wide range of engineering applications. Study on mechanical behaviors of such materials under working conditions is very essential. In this study, an extended meshfree moving Kriging interpolation method (namely as X- MK) is presented for crack analyzing in 2D orthotropic materials models. The Gaussian function is used for constructing the moving Kriging shape functions. Typical advantages of the MK shape function are the high-order continuity and the satisfaction of the Kronecker’s delta property. To calculate the stress intensity factors (SIFs), interaction integral method is used with orthotropic auxiliary fields. Several numerical tests including static SIFs calculating and crack propagation predicting are performed to verify the accuracy of the present approach. The obtained results are compared with available refered results and they have shown a very good performance of the present method.

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“…The main property of these methods may be devoted to their efficiency in handling moving boundaries and discontinuities (eg, cracks), as well as their ability of elaborating the crack tip by employment of enriched basis functions according to the asymptotic displacement field in their vicinity. In mesh‐free methods, it is needed to perform remeshing for the movement of nodes surrounding the tip of the crack as the crack propagates . Unlike the high accuracy of mesh‐free methods, their time‐consuming and more computational cost techniques may be considered as their main disadvantages …”

Section: Introductionmentioning

confidence: 99%

Development of a new semianalytical approach for 2D analysis of crack propagation problems

Yazdani

Khaji

2018

Fatigue Fract Eng Mat Struct

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This study offers novel progresses for a semianalytical method to simulate 2D propagation of cracks based on linear elastic fracture mechanics. For this purpose, a new algorithm is proposed on the basis of the linear elastic fracture mechanics for crack propagation in single‐mode and mixed mode. Herein, discretization is only performed on the boundaries of the problem by using specific subparametric elements and higher‐order Chebyshev polynomials as mapping functions. Implementing the weighted residual method and by taking Clenshaw‐Curtis numerical quadrature, diagonal Euler's differential equations are obtained. Consequently, once the local coordinate origin is assumed at the tip of the crack, the stress intensity factors can be derived directly. In accordance with the rate of maximum energy release as a propagation criterion and by proposing a new quasi‐automatic remeshing procedure based on domain division, the crack propagation is applied here. Based on the new presented algorithm, application of the new semianalytical method to crack propagation analysis is more flexible and efficient. By taking this advantage, relatively coarse and simple discretization compared with other computational methods may be used. By modelling 4 benchmark problems with a few numbers of degrees of freedom, the validity and accuracy of the current method is illustrated. Results show that the presented algorithm is applicable for efficient and precise prediction of crack trajectories.

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Crack growth modeling in elastic solids by the extended meshfree Galerkin radial point interpolation method

Cited by 119 publications

References 22 publications

Development of a new semi-analytical method in fracture mechanics problems based on the energy release rate

Development of a new semi-analytical method in fracture mechanics problems based on the energy release rate

Extended meshless moving Kriging method for crack propagation analyzing in orthotropic media

Development of a new semianalytical approach for 2D analysis of crack propagation problems

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