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Numerically determined enrichment functions for the extended finite element method and applications to bi‐material anisotropic fracture and polycrystals
Author(s) -
Menk Alexander,
Bordas Stéphane P. A.
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2858
Subject(s) - finite element method , singularity , gravitational singularity , mathematical analysis , mathematics , extended finite element method , convergence (economics) , mixed finite element method , elasticity (physics) , linear elasticity , hp fem , numerical analysis , smoothed finite element method , anisotropy , boundary element method , finite element limit analysis , boundary knot method , structural engineering , materials science , physics , engineering , composite material , quantum mechanics , economics , economic growth
Strain singularities appear in many linear elasticity problems. A very fine mesh has to be used in the vicinity of the singularity in order to obtain acceptable numerical solutions with the finite element method (FEM). Special enrichment functions describing this singular behavior can be used in the extended finite element method (X‐FEM) to circumvent this problem. These functions have to be known in advance, but their analytical form is unknown in many cases. Li et al . described a method to calculate singular strain fields at the tip of a notch numerically. A slight modification of this approach makes it possible to calculate singular fields also in the interior of the structural domain. We will show in numerical experiments that convergence rates can be significantly enhanced by using these approximations in the X‐FEM. The convergence rates have been compared with the ones obtained by the FEM. This was done for a series of problems including a polycrystalline structure. Copyright © 2010 John Wiley & Sons, Ltd.