Proper

Abstract

The extended finite element method (XFEM) is widely applied in various computational areas to deal with discontinuity problems. The idea is the use of enrichment functions to add to the finite element approximation space. Furthermore, the XFEM is associated with the level set method to track and define the geometrical representation of discontinuities. This makes it convenient to model structures containing material interfaces. This paper implements the linear modeling for two types of shapes of inclusions by using the XFEM analysis on quadrilateral elements. In particular, we consider the way to construct a new level set function that is used to develop the enrichment function for the corresponding interfaces. Several numerical examples shows results of various shapes of interfaces in practical benchmarks and stress distributions.