XLME interpolants, a seamless bridge between XFEM and enriched meshless methods

F. Amiri, C. Anitescu, M. Arroyo, S. P A Bordas, Timon Rabczuk

Research output: Contribution to journalArticle

139 Citations (Scopus)


In this paper, we develop a method based on local maximum entropy shape functions together with enrichment functions used in partition of unity methods to discretize problems in linear elastic fracture mechanics. We obtain improved accuracy relative to the standard extended finite element method at a comparable computational cost. In addition, we keep the advantages of the LME shape functions, such as smoothness and non-negativity. We show numerically that optimal convergence (same as in FEM) for energy norm and stress intensity factors can be obtained through the use of geometric (fixed area) enrichment with no special treatment of the nodes near the crack such as blending or shifting.

Original languageEnglish
Pages (from-to)45-57
Number of pages13
JournalComputational Mechanics
Issue number1
Publication statusPublished - 2014 Jan 1


  • Convex approximation
  • Extrinsic enrichment
  • Local maximum entropy
  • Meshless methods

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Mechanical Engineering
  • Ocean Engineering
  • Applied Mathematics
  • Computational Mathematics

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