13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Virtual Crack Closure Technique Based on MSIM Method Feng Su 1, 2, Jie Wu 1, 2, *, Yongchang Cai 1, 2 1 State Key Laboratory for disaster reduction in Civil Engineering, Tongji University, Shanghai, China 200092; 2 Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai, China 200092; * Corresponding author: jiee.wu@gmail.com Abstract The virtual crack closure technique is applied to the calculation of stress intensity factor (SIF) in the framework of meshless Shepard interpolation method (MSIM). In the MSIM interpolation, the Shepard shape functions are used for the partition of unity and the local cover functions are separately constructed for the nodes on the boundary and inside the domain. There are three desirable properties in the MSIM including the completeness property, the delta property which lead to easy boundary treat and the low computational expense of the shape function. In the virtual crack closure technique, the assistant finite element mesh is added beside the crack tips, and the SIFs are calculated naturally and effectively near the tips by using the MSIM. Numerical result for a star-shaped crack in a square plate is reported to demonstrate the correctness and robust of the present method. Keywords Meshless Shepard interpolation method, Partition of unity method, Virtual crack closure technique, Stress intensity factor 1. Introduction Calculating of parameters such as stress intensity factor, J integral and strain energy release rate are always highly important but not well addressed in fracture mechanics, and lots of efforts have been devoted by the researchers and engineers in recent years. Analytic solutions for some particular structural components have been proposed and expressed as functions, line graft or tables, which can be referred in some handbooks compiled for the engineers [1-3]. However, the limited number of analytic solutions is far from the satisfaction of the need in the real world. The numerical calculations for the parameters in fracture mechanics become necessary in term of the realistic when considering the dramatically development of the hardware and software of computers [4-9]. J integral was proposed by Rice in 1969 and was introduced into the element free Galerkin method by Brighenti [7]. This method is attractive for the calculation of SIF because of its completeness of theory, high accuracy and path-independent integration. But the inappropriate determination of the radius of the integration circle may degrade the accuracy of J integral when dealing with problems involving short crack segment such as broken cracks and crack tips near the boundaries. Virtual crack closure technique (VCCT) requires only 2 parameters (the nodal force and displacement near the crack tip) which can be obtained naturally in the FEM method to evaluate the SIF and, besides, the calculation results are often reliable and not effected by the small length of crack tips. Consequently, it is paid increasingly more attention by the researchers. However, at present, the VCCT is always carried out in the framework of the FEM, which is unavoidably encountered with the mesh refinement. More details about VCCT can refer to [10]. To alleviate this drawback, the meshless Shepard interpolation method (MSIM) [11] is used to model the discontinuous stress field near the crack and stress singularity near the crack tips and then, the stress and displacement results are used by the VCCT to evaluate the SIF. The time consuming remeshing process is unnecessary in this method and makes the simulation much more reliable and possessing high accuracy. Details of meshless simulation of discontinuous model and the determination of the SIF are provided. In the end, the method described here is used to analyze a square plate with a star-shape crack. The results obtained by the present method are compared with
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