13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- the stain energy release rate of the crack could be calculated by B a F v G y I 2 1 3,4 （26a） B a F u G x II 2 1 3,4 （26b） where, 1xF and 1yF are the node forces (X direction, Y direction, respectively) belonging to node 1. 3,4 v and 3,4 u are the Y direction displacement and X direction displacement between node 3 and 4, respectively. Figure 2. Illustration of calculating the strain energy release rate by the VCCT Due to the fact that the virtual crack closure technique is always implemented in the framework of FEM, the remeshing during the simulation of crack propagation are unavoidably encountered. To solve this problem, the virtual crack closure technique will be introduced into MSIM in this section. Both the advantages of the two methods will be maintained to make the evaluation of the SIFs much more efficient. The progress will be carried out mainly in the following steps: 1) Construction of meshless numerical model; 2) Calculation of the displacement of the nodes based on the MSIM; 3) Setting the assistant mesh near the crack tip in order to calculate the nodal force 4) Constructing the global stiffness matrix of the assistant mesh and calculating the displacement of the node in the assistant mesh based on the MSIM. 5) Getting the nodal force near the crack tip by e e eF K a , where eF is the assistant nodal force, eK is the global stiffness matrix of the assistant mesh, ea is the displacement vector of the assistant nodes. Figure 3. The assistant mesh employed in the MSIM to evaluate the nodal force 4. A case study on a finite plate with star-shaped crack In this section, a star-shaped crack in a square plate subjected to bi-axial tension as shown in Fig.4 will be examined. The analysis is treated as plate strain problem, and the plate size is taken to be W = 2.0, and the bi-axial tension to be unity. The material constants are the Young’s modulus
RkJQdWJsaXNoZXIy MjM0NDE=