The Extended Finite Element Method Of Dislocation And Its Application In The Interface Problems

The method of extended FEM was born in1999, it is shorted as XFEM. Although the FEM is very well, it is still very difficult when it faces the problems of discontinuous, such as crack,inclusion,void and so on. The XFEM use the shape function with a nature of discontinuous to represent the discontinuity, the discontinuous field is independent of model's boundary in the calculation, Compared to the FEM, it is the biggest advantage. Actually, dislocation is an inside discontinuous defects of material, so the problem of dislocation can also be calculated by XFEM.This paper achieved the simulation of dislocation problems by self-made XFEM Matlab code and explored the differences between the two forms of extended shape functions, we did some modifications to the extended shape functions on the basis of Belyschko and for the first time achieved dislocation simulation under the anisotropic material by XFEM. The main results are as follows:(1)Using Matlab program achieved the step shape function XFEM program, then the stress field and Peach-Koehler force calculated by program was contrasted with analytical Solutions, the contrast indicated the applicability and accuracy of XFEM on dislocation preliminary.(2)We achieved the dislocation core shape function XFEM program on the basis of step shape function XFEM program and proposed a new approach for the dislocation core shape function mixing unit, we also proposed an approach for the stress discontinuities in the calculation of oblique slip systems, it indicated the validity of the new approach after comparing the results before and after. Then we used the complete program calculated the interaction of dislocations with the inclusions and holes, etc. The results further show the accuracy of the XFEM program.(3)We obtained the dislocation core extended shape function of anisotropic material from the analytical displacement field solution of anisotropic material, then we compared the stress field calculated by Matlab program of dislocation core extended shape function under anisotropic material, the results indicated that this dislocation core extended shape function is suitable for anisotropic material, At last, we did some research on the interaction of dislocations with the inclusions and holes under anisotropic material.