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A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries
Author(s) -
Simone A.,
Duarte C. A.,
Van der Giessen E.
Publication year - 2006
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.1658
Subject(s) - finite element method , extended finite element method , partition of unity , discontinuity (linguistics) , finite element limit analysis , mixed finite element method , grain boundary , displacement (psychology) , mathematics , partition (number theory) , geometry , smoothed finite element method , mathematical analysis , structural engineering , boundary knot method , engineering , materials science , boundary element method , combinatorics , microstructure , composite material , psychology , psychotherapist
We present a Generalized Finite Element Method for the analysis of polycrystals with explicit treatment of grain boundaries. Grain boundaries and junctions, understood as loci of possible displacement discontinuity, are inserted into finite elements by exploiting the partition of unity property of finite element shape functions. Consequently, the finite element mesh does not need to conform to the polycrystal topology. The formulation is outlined and a numerical example is presented to demonstrate the potential and accuracy of the approach. The proposed methodology can also be used for branched and intersecting cohesive cracks, and comparisons are made to a related approach ( Int. J. Numer. Meth. Engng. 2000; 48 :1741). Copyright © 2006 John Wiley & Sons, Ltd.