X-FEM, de nouvelles frontières pour les éléments finis

En 1999, une extension de la méthode des éléments finis a été proposée. Baptisée depuis X-FEM (“eXtended Finite Element Method”), cette extension permet de modéliser des surfaces de discontinuité (fissures, interfaces matériaux, bords libres, …) sur un maillage sans que ce dernier doive s'y conformer. Ce papier dresse le bilan des avancées réalisées avec X-FEM ; tout particulièrement le couplage de X-FEM avec la méthode des “level sets” qui permet une représention efficace des surfaces de discontinuité ainsi qu'un calcul robuste de leur évolution.

[1]  J. Oden,et al.  H‐p clouds—an h‐p meshless method , 1996 .

[2]  Mark A Fleming,et al.  ENRICHED ELEMENT-FREE GALERKIN METHODS FOR CRACK TIP FIELDS , 1997 .

[3]  David L. Chopp,et al.  A hybrid extended finite element/level set method for modeling phase transformations , 2002 .

[4]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[5]  D. Chopp,et al.  Extended finite element method and fast marching method for three-dimensional fatigue crack propagation , 2003 .

[6]  Ted Belytschko,et al.  Discontinuous enrichment in finite elements with a partition of unity method , 2000 .

[7]  Ted Belytschko,et al.  Modeling fracture in Mindlin–Reissner plates with the extended finite element method , 2000 .

[8]  J. Oliyer.  Continuum modelling of strong discontinuities in solid mechanics using damage models , 1995 .

[9]  O. C. Zienkiewicz,et al.  A new cloud-based hp finite element method , 1998 .

[10]  Ted Belytschko,et al.  EFG approximation with discontinuous derivatives , 1998 .

[11]  T. Belytschko,et al.  Arbitrary branched and intersecting cracks with the eXtended Finite Element Method , 2000 .

[12]  I. Babuska,et al.  The design and analysis of the Generalized Finite Element Method , 2000 .

[13]  H. Dhia.  Problèmes mécaniques multi-échelles: la méthode Arlequin , 1998 .

[14]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[15]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[16]  Ted Belytschko,et al.  An extended finite element method for modeling crack growth with frictional contact , 2001 .

[17]  Ted Belytschko,et al.  Modelling crack growth by level sets in the extended finite element method , 2001 .

[18]  T. Belytschko,et al.  MODELING HOLES AND INCLUSIONS BY LEVEL SETS IN THE EXTENDED FINITE-ELEMENT METHOD , 2001 .

[19]  T. Belytschko,et al.  Extended finite element method for cohesive crack growth , 2002 .

[20]  Ted Belytschko,et al.  The extended finite element method for rigid particles in Stokes flow , 2001 .

[21]  Ted Belytschko,et al.  THE ELEMENT FREE GALERKIN METHOD FOR DYNAMIC PROPAGATION OF ARBITRARY 3-D CRACKS , 1999 .

[22]  B. Nayroles,et al.  Generalizing the finite element method: Diffuse approximation and diffuse elements , 1992 .

[23]  T. Belytschko,et al.  A finite element with embedded localization zones , 1988 .

[24]  T. Belytschko,et al.  The extended finite element method (XFEM) for solidification problems , 2002 .

[25]  T. Belytschko,et al.  Non‐planar 3D crack growth by the extended finite element and level sets—Part I: Mechanical model , 2002 .

[26]  M. Rashid.  The arbitrary local mesh replacement method: An alternative to remeshing for crack propagation analysis , 1998 .

[27]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[28]  Milan Jirásek,et al.  Comparative study on finite elements with embedded discontinuities , 2000 .

[29]  Alex M. Andrew,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition) , 2000 .

[30]  Ted Belytschko,et al.  Arbitrary discontinuities in finite elements , 2001 .

[31]  J. Sethian,et al.  FRONTS PROPAGATING WITH CURVATURE DEPENDENT SPEED: ALGORITHMS BASED ON HAMILTON-JACOB1 FORMULATIONS , 2003 .

[32]  T. Belytschko,et al.  Extended finite element method for three-dimensional crack modelling , 2000 .

[33]  L. J. Sluys,et al.  A new method for modelling cohesive cracks using finite elements , 2001 .

[34]  T. Belytschko,et al.  Non‐planar 3D crack growth by the extended finite element and level sets—Part II: Level set update , 2002 .

[35]  Ted Belytschko,et al.  Reproducing Kernel Particle Methods for elastic and plastic problems , 1993 .