A global-local approach for the construction of enrichment functions for the generalized FEM and its application to three-dimensional cracks

Carlos Armando Duarte, Dae Jin Kim, Ivo Babuška

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Existing generalized or extended finite element methods for modeling cracks in three-dimensions require the use of a sufficiently refined mesh around the crack front. This offsets some of the advantages of these methods specially in the case of propagating threedimensional cracks. In this paper, a strategy to overcome this limitation is investigated. The approach involves the development of enrichment functions that are computed using a new global-local approach. This strategy allows the use of a fixed global mesh around the crack front and is specially appealing for non-linear or time dependent problems since it avoids mapping of solutions between meshes. The resulting technique enjoys the same flexibility of the so-called meshfree methods for this class of problem while being more computationally efficient. The proposed generalized FEM with global-local functions, by numerically constructing the enrichment functions, brings the benefits of existing generalized FEMto a broader class of problems. The procedure is applied to the solution of three-dimensional linear elastic fracture mechanics problems. Numerical experiments demonstrating the computational efficiency and accuracy of the method are presented.

Original languageEnglish (US)
Title of host publicationAdvances in Meshfree Techniques
EditorsC. Armando Duarte, V.M.A. Leitao, Carlos J.S. Alves
PublisherSpringer Netherland
Number of pages26
ISBN (Print)9781402060946
StatePublished - Jan 1 2007
EventEcommas Thematic Conference on Meshless Methods, 2005 - Lisbon, Portugal
Duration: Jul 11 2005Jul 14 2005

Publication series

NameComputational Methods in Applied Sciences
ISSN (Print)1871-3033


OtherEcommas Thematic Conference on Meshless Methods, 2005



  • Extended finite element method
  • Fracture mechanics
  • Generalized finite element method
  • Global-local method
  • Meshfree method

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Modeling and Simulation
  • Biomedical Engineering
  • Computer Science Applications
  • Fluid Flow and Transfer Processes
  • Computational Mathematics
  • Electrical and Electronic Engineering

Cite this

Duarte, C. A., Kim, D. J., & Babuška, I. (2007). A global-local approach for the construction of enrichment functions for the generalized FEM and its application to three-dimensional cracks. In C. A. Duarte, V. M. A. Leitao, & C. J. S. Alves (Eds.), Advances in Meshfree Techniques (pp. 1-26). (Computational Methods in Applied Sciences; Vol. 5). Springer Netherland.