Two-dimensional crack analysis using the extended finite element method with polynomial enrichment technique

Abstract

Extended Finite Element Method / General Finite Element Method is one of the most commonly used methods for crack analysis. This method does not require re-meshing as the crack propagates by enriching the displacement field by the partition of unity method. However, the mesh refinement process near the crack tip is still necessary to obtain a satisfactory solution. Recently, research was proposed to solve the linear dependence problem using the 2-D 4-node quadrilateral elements and to improve the solution through polynomial enrichment technique. In this thesis, a polynomial enrichment technique that resolves the linear dependence problem is applied to the Extended Finite Element Method using the 2-D 4-node quadrilateral elements. As a result, a method that does not require a mesh refinement process is proposed. In addition, an efficient adaptive local enrichment technique is proposed through the Zienkiewicz-Zhu error estimator in terms of degrees of freedom. Verification of the proposed method is performed through several fracture mechanics numerical examples.