Mixed Integration Scheme for Embedded Discontinuous Interfaces by Extended Finite Element Method

The extended Finite Element Method (XFEM) is derived from the traditional finite element method for discontinuous problems. It can simulate the behavior of cracks, which significantly improves the ability of finite element methods to simulate geotechnical and geological disaster problems. The integration of discontinuous enrichment functions in weak form and the ill-conditioning of the system equations are two major challenges in employing the XFEM in engineering applications. A mixed integration scheme is proposed in this paper to solve these problems. This integration scheme has a simple form and exhibits both the accuracy of the subcell integration method and the well-conditioning of a smeared integration method. The correctness and effectiveness of the proposed scheme were verified through a series of element analyses and two typical examples. For XFEM numerical simulations with unstructured meshes and arbitrary cracks/interfaces, this method guarantees the convergence of nonlinear iterations and yields correct results.

Automated summary

This paper introduces the extended Finite Element Method (XFEM) and the challenges it faces in engineering applications, proposes a mixed integration scheme to solve these challenges, and verifies the correctness and effectiveness of the proposed scheme.