Analyses of Plane Crack Propagations by the Extended Finite Element Method

Abstract: The extended finite element method(X-FEM) is a new numerical method for modeling discontinuity problems. It was first introduced by Professor Belytschko and his coworkers at Northwest University in 1999. As the method is established in a standard finite element framework, and remeshing is not necessary during the growth of discontinuous faces, it has become one of the hot research topics in Engineering Mechanics in recent years. Till now, there are many articles about the basic principles and a variety of formulations of X-FEM, but few of them are written in details on the implementations. Therefore, in this thesis, some details and physical concepts within the procedure of modeling cohesive crack growth in 2-D using X-FEM are first discussed thorouthly. Secondly, rectangular extended finite element formulations and discretized equations for analysis of cohesive crack growth are derived based on the newly proposed discontinuous displacement field by Zi and Belytschko. Instead of the Newton-Raphson method, a direct iteration algorithm is proposed for solving the non-linear finite element equations. Details are given for both displacement and load control loadings. A FORTRAN program is written to analyze the fracture of a three-point bending beam. The obtained results agree well with existing data in the literature, thus, prove the correctness of the proposed method, derived formulations and the written program. Finally, some conclusions are drawn based on the results reported herein, and some future research problems are suggested…
Key words: extended finite element method; cohesive crack growth; direct iteration algorithm; displacement control loading; load control loading; three-point bending beam

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