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

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 fromwww.empaneda.com/codes.