hp-Generalized FEM and crack surface representation for non-planar 3-D cracks

J. P. Pereira, C. A. Duarte, D. Guoy, X. Jiao

Research output: Contribution to journalArticlepeer-review


A high-order generalized finite element method (GFEM) for non-planar three-dimensional crack surfaces is presented. Discontinuous p-hierarchical enrichment functions are applied to strongly graded tetrahedral meshes automatically created around crack fronts. The GFEM is able to model a crack arbitrarily located within a finite element (FE) mesh and thus the proposed method allows fully automated fracture analysis using an existing FE discretization without cracks. We also propose a crack surface representation that is independent of the underlying GFEM discretization and controlled only by the physics of the problem. The representation preserves continuity of the crack surface while being able to represent non-planar, non-smooth, crack surfaces inside of elements of any size. The proposed representation also provides support for the implementation of accurate, robust, and computationally efficient numerical integration of the weak form over elements cut by the crack surface. Numerical simulations using the proposed GFEM show high convergence rates of extracted stress intensity factors along non-planar curved crack fronts and the robustness of the method.

Original languageEnglish (US)
Pages (from-to)601-633
Number of pages33
JournalInternational Journal for Numerical Methods in Engineering
Issue number5
StatePublished - Jan 29 2009


  • Extended finite element method
  • Fracture
  • Generalized finite element method
  • High-order approximations

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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