A Stable Generalized/eXtended p-hierarchical FEM for three-dimensional linear elastic fracture mechanics

A. G. Sanchez-Rivadeneira, N. Shauer, B. Mazurowski, C. A. Duarte

Research output: Contribution to journalArticlepeer-review


In this paper, the quadratic Stable Generalized Finite Element Method (SGFEM) proposed in Sanchez-Rivadeneira and Duarte (2019) is extended to 3-D fracture problems with non-planar crack surfaces and curved crack fronts. This SGFEM is based on p-hierarchical FEM enrichments and its approximation space is the same as in its GFEM counterpart. Singular enrichments are modified using a discontinuous finite element interpolant for conditioning control. This leads, with the proper choice of enrichments, to stiffness matrices with a scaled condition number of O(h−2) — the same order as in the standard FEM. The robustness of the method with respect to the position of a crack relative to the mesh is demonstrated. A scalar implementation of singular enrichments that can exactly reproduce the first term of the Mode I, II, and III of the asymptotic expansion of the elasticity solution is presented. Improved approximations of signed distance functions based on integration sub-elements are also presented. Convergence studies of a fully 3-D fracture problem with a non-planar crack surface and a curved crack front are presented. They show that the convergence rate of the proposed method on a sequence of uniform meshes is three times higher than quadratic quarter-point finite elements.

Original languageEnglish (US)
Article number112970
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Jun 1 2020


  • Conditioning
  • Fracture
  • GFEM
  • XFEM
  • p-FEM

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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