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

Abstract

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 www.empaneda.com/codes.

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Acknowledgements

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.

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Correspondence to E. Martínez-Pañeda.

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Martínez-Pañeda, E., Natarajan, S. & Bordas, S. Gradient plasticity crack tip characterization by means of the extended finite element method. Comput Mech 59, 831–842 (2017). https://doi.org/10.1007/s00466-017-1375-6

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Keywords

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