Extended Finite Element Method Program Research And Application For In-homogeneous Material With Inclusions

It is researcher's responsibility to develop composite material which is one of materials that has been developing rapidly in the 21st century. In the field of solid mechanics and material, the study of inclusion model has always been a hot issue. Some numerical methods, FEM and Meshless Method, are the main solution to this problem because of their many advantages, however, the shape function should be continuous and the material must be homogeneous in FEM which make the meshing difficult. To settle this trouble, the Meshless Method is adopted, but it still cannot solve discontinuous problem perfectly. Since 1999, Extended Finite Element Method (XFEM), which is developed based on FEM and mainly solve discontinuous problems, has provided almost perfect plan to settle the difficult of traditional FEM in discontinuous problems.XFEM inherits all the advantages of FEM, additionally, it overcomes the trouble of high density meshing and remeshing in the discontinuous field, for its mesh is independent on the geometric and physical interface. In XFEM, the geometric description of an interface is represented by the zero level set function, enrichment function referring to boundary is added in the shape function of element. This paper uses XFEM to model the in-homogeneous materials with inclusions, and the program of isotropic element with 4 nodes in the theory of XFEM is carried out. The basic theory of XFEM such as Partition of Unity Method (PUM) and Level Set Method (LSM) are introduced , as well as how to judge the intersection form and determine the intersection point of element and interface in chapter 2; in chapter 3, the related algorithm and some special treatments about program of XFEM are deduced, such as additional degree of freedom and strain transition matrix and methods of numerical integration; in chapter 4, numerical examples, hiberarchy inclusion model, one circle inclusion model, multi-circle inclusion model and elliptical inclusion, are presented, and the results are compared with that result got by other methods to demonstrate the practicability and accuracy of XFEM.