A two-scale approach for the analysis of propagating three-dimensional fractures

J. P.A. Pereira, D. J. Kim, C. A. Duarte

Research output: Contribution to journalArticlepeer-review


This paper presents a generalized finite element method (GFEM) for crack growth simulations based on a two-scale decomposition of the solution-a smooth coarse-scale component and a singular fine-scale component. The smooth component is approximated by discretizations defined on coarse finite element meshes. The fine-scale component is approximated by the solution of local problems defined in neighborhoods of cracks. Boundary conditions for the local problems are provided by the available solution at a crack growth step. The methodology enables accurate modeling of 3-D propagating cracks on meshes with elements that are orders of magnitude larger than those required by the FEM. The coarse-scale mesh remains unchanged during the simulation. This, combined with the hierarchical nature of GFEM shape functions, allows the recycling of the factorization of the global stiffness matrix during a crack growth simulation. Numerical examples demonstrating the approximating properties of the proposed enrichment functions and the computational performance of the methodology are presented.

Original languageEnglish (US)
Pages (from-to)99-121
Number of pages23
JournalComputational Mechanics
Issue number1
StatePublished - Jan 2012


  • Crack growth
  • Extended FEM
  • Fatigue
  • Fracture
  • Generalized FEM
  • Global-local analysis
  • Multi-scale

ASJC Scopus subject areas

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


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