Gradient plasticity crack tip characterization by means of the extended finite element method

Emilio Martínez Pañeda, S. Natarajan, S. Bordas

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Strain gradient plasticity theories are being widelyused for fracture assessment, as they provide a richerdescription of crack tip fields by incorporating the influenceof geometrically necessary dislocations. Characterizingthe behavior at the small scales involved in crack tip deformationrequires, however, the use of a very refined meshwithin microns to the crack. In this work a novel andefficient gradient-enhanced numerical framework is developedby means of the extended finite element method(X-FEM). A mechanism-based gradient plasticity modelis employed and the approximation of the displacementfield is enriched with the stress singularity of the gradientdominatedsolution. Results reveal that the proposed numericalmethodology largely outperforms the standard finiteelement approach. The present work could have importantimplications on the use of microstructurally-motivatedmodels in large scale applications. The non-linear X-FEMcode developed in MATLAB can be downloaded
Original languageEnglish
JournalComputational Mechanics
Issue number5
Pages (from-to)831–842
Publication statusPublished - 2017


  • Strain gradient plasticity
  • Extended finite element method
  • Crack tip fields
  • Material length scale

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