A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries

A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries. Simone, A., Duarte, C. A., & van der Giessen, E. International Journal for Numerical Methods in Engineering, 67(8):1122--1145, 2006.
doi abstract bibtex

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 (C. Daux, N. Möes, J. Dolbow, N. Sukumar and T. Belytschko, Int. J. Numer. Meth. Engng. 48 (2000) 1741).

@article{ Simone:GFEMxtal2006,
  author = {A. Simone and C. A. Duarte and van der Giessen, E.},
  title = {A {G}eneralized {F}inite {E}lement {M}ethod for polycrystals with discontinuous grain boundaries},
  journal = {International Journal for Numerical Methods in Engineering},
  year = {2006},
  volume = {67},
  number = {8},
  pages = {1122--1145},
  kind = {journal paper (ISI)},
  doi = {http://dx.doi.org/10.1002/nme.1658},
  pdf = {J7 - A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries --
		  Simone, Duarte, Van der Giessen - ijnme - 2006.pdf},
  abstract = {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 (C.
		  Daux, N. Mö{e}s, J. Dolbow, N. Sukumar and T. Belytschko, Int. J. Numer. Meth. Engng. 48 (2000)
		  1741).}
}

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