Computational Mechanics

, Volume 59, Issue 5, pp 831–842 | Cite as

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

  • E. Martínez-PañedaEmail author
  • S. Natarajan
  • S. Bordas
Original Paper


Strain gradient plasticity theories are being widely used for fracture assessment, as they provide a richer description of crack tip fields by incorporating the influence of geometrically necessary dislocations. Characterizing the behavior at the small scales involved in crack tip deformation requires, however, the use of a very refined mesh within microns to the crack. In this work a novel and efficient gradient-enhanced numerical framework is developed by means of the extended finite element method (X-FEM). A mechanism-based gradient plasticity model is employed and the approximation of the displacement field is enriched with the stress singularity of the gradient-dominated solution. Results reveal that the proposed numerical methodology largely outperforms the standard finite element approach. The present work could have important implications on the use of microstructurally-motivated models in large scale applications. The non-linear X-FEM code developed in MATLAB can be downloaded from


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



The authors gratefully acknowledge financial support from the European Research Council (ERC Starting Grant Agreement No. 279578). E. Martínez-Pañeda also acknowledges financial support from the Ministry of Economy and Competitiveness of Spain through Grant MAT2014-58738-C3-1, and the University of Oviedo through Grant UNOV-13-PF.

Supplementary material

466_2017_1375_MOESM1_ESM.pdf (195 kb)
Supplementary material 1 (pdf 194 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Solid MechanicsTechnical University of DenmarkKgs. LyngbyDenmark
  2. 2.Department of Mechanical EngineeringIndian Institute of Technology, MadrasChennaiIndia
  3. 3.Faculté des Sciences, de la Technologie et de la CommunicationUniversity of LuxembourgLuxembourg-KirchbergLuxembourg
  4. 4.School of EngineeringCardiff UniversityCardiffWales, UK

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