A polygonal XFEM with new numerical integration for linear elastic fracture mechanics

Hai Dong Huynh, Minh Ngoc Nguyen, Gianluca Cusatis, Satoyuki Tanaka, Tinh Quoc Bui*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


The extended finite element method (XFEM) has become a powerful and effective technique for modeling fracture problems without remeshing. In this paper, we introduce a novel and effective computational approach that is based on polygonal XFEM (named as PolyXFEM) for the analysis of two-dimensional (2D) linear elastic fracture mechanics problems. The PolyXFEM is equipped with a new numerical integration technique that uses the concept of Cartesian transformation method (CTM) over polygonal domains. The underlying idea of the CTM is to transform a domain integral into a boundary integral and a one-dimensional integral. This is computationally more efficient compared to the two-level mapping integration commonly used on polygons. Furthermore, the PolyXFEM is effective in modeling crack problems due to the local enrichment based on the partition of unity method. Our numerical results show that improvements in accuracy are reached thanks to the higher-order of the polygonal shape functions of the PolyXFEM. In addition, efficiency in computational time is achieved because of the usage of the CTM integration scheme, which appears to be quite suitable for polygonal domains. To demonstrate the accuracy and performance of the developed PolyXFEM approach, several numerical examples for 2D linear elastic fracture problems are considered, in which static stress intensity factors and crack propagation are investigated and compared with reference solutions. The convergence and mesh independence of the PolyXFEM for crack analysis is also analyzed.

Original languageEnglish (US)
Pages (from-to)241-263
Number of pages23
JournalEngineering Fracture Mechanics
StatePublished - May 15 2019


  • Cartesian transformation
  • Fracture
  • Polygonal elements
  • Stress intensity factors
  • XFEM

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering


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