Research On Plate Model Crack Propagation Based On Extended Finite Element Method

The extended finite element method (XFEM) is based on the concept of partition of unity method and within standard finite element framework. The enrichment functions typically consist of the near-tip asymptotic functions that capture the singularity around the crack tip and a discontinuous function that represents the jump in displacement across the crack surfaces. Thus, the crack surface can be presented and the crack surface is not associated with finite element model. So, the method can simulate crack propagation conveniently. Level set method (LSM) is a numerical method for track the interface propagation paths. This thesis combines extended finite element method and level set method, and simulates a series of plane crack and plate bending crack problems. The major contents are as follows:Firstly, the concepts of linear elastic fracture mechanics are introduced, and interaction energy integrals are used to compute stress intensity factor. The method for inverse isoparametric elements mapping is introduced. The theory of extend finite element is expounded detailedly. Compiled the XFEM program, the flow of implementing XFEM and the mainly parts of the program is given.Secondly, the plane crack problems are simulated by using the developed program. The factors of effecting result are discussed, including J-integral and mesh. The precision of extended finite element method is verified by simulating of single edge crack, double edge cracks, a center crack and double center cracks. Meanwhile, the quasi-static crack propagation is simulated using the maximum tangential stress criterion and the results are analyzed.Finally, Kirchhoff classical fracture theory, Reissner fracture theory and MITC element which can avoid shear locking are introduced. The method for calculate plate bending crack problem and bending stress intensity factors is introduced. Plate bending crack problem is simulated by Reissner fracture theory and MITC element respectively. The factors of effecting result are discussed, including J-integral and mesh. The phenomenon that MITC element can avoid shear locking is certified by simulating different thickness plates.The computed results of SIFs provide the reference for crack problems in engineering. The method for analytic plates with crack and the flow chart of XFEM are significant for analytic shells with crack.