Extend Finite Element Method And Level Set Method For Crack Propagation Problems

Extend finite element method is a new numerical simulation method for discontinuous problems. Comparing with the classical finite element method, there are some special differences, such as: the crack is independence on the compute mesh, needn't put the crack interface as the element boundary and set the crack tip as the element node, also, shouldn't remeshing when deal with the crack propagation problems. So, It has application to lager deformation, fracture propagation, friction contact problems. Level set method is the numerical technology for track interface and shape modeling, and the most convenient way to tracking the interface propagation paths. Then, combine the extend finite element method and level set method is the efficient way for crack propagation problems. There are some researches which restricted to the elastic material in this thesis:1. Combine with fracture mechanics, obtain the stress, displacement fields at the crack tip based on the extend finite method. Then, proposed the interaction integral method for evaluating the stress intensity factor in elastic material and write the corresponding extend finite element method program.2. Combine the extend finite element method and level set method, adopt the maximum hoop stress criterion as the crack propagation criterion, design the arithmetic for crack propagation based on extend finite element method and write the program.3. The author proposed a new method-virtual crack method, which solve the problem efficiency and doesn't affect the result. Verification the method is accurate and feasibility by some simple examples.4. First, evaluating the stress intensity factor correspond some classical fracture types.The influence of the stress intensity factor through mesh and integral domain factor are discussed, and then choose the proper parameters. The tension,shear, combine fracture pattern propagation path also simulated. The result verified that application of the extend finite element and level set method to fracture mechanics not only finite element mesh and the location of crack are mutual independent, needn't construct a mesh which conform to the crack surface and offering fine granularity partition around the crack tip and crack propagation without meshing, but also save the computation time and can obtain the quite high precision.