Architecture tradeoffs of integrating a mesh generator to partition of unity enriched object-oriented finite element software

We explore the tradeoffs of using an internal mesher in a XFEM code. We show that it allows an efficient enrichement detection scheme, while retaining the ability to have welladapted meshes. We provide benchmarks highlighting the considerable gains which can be expected from a well designed architecture. The efficiency of the proposed algorithm is shown by solving fracture mechanics problems of densely micro-cracked bodies including adaptive mesh refinement.

[1]  T. Belytschko,et al.  Analysis of three‐dimensional crack initiation and propagation using the extended finite element method , 2005 .

[2]  Brian Moran,et al.  Energy release rate along a three-dimensional crack front in a thermally stressed body , 1986, International Journal of Fracture.

[3]  N. Kikuchi,et al.  A homogenization method for shape and topology optimization , 1991 .

[4]  Stéphane Poyet.  Étude de la dégradation des ouvrages en béton atteints par la réaction alcali-silice : approche expérimentale et modélisation numérique multi-échelles des dégradations dans un environnement hydro-chemo-mécanique variable , 2003 .

[5]  Marc Alexander Schweitzer,et al.  Partition of Unity Method , 2003 .

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

[7]  Jean-François Remacle,et al.  An algorithm oriented mesh database , 2003, IMR.

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

[9]  E. Verron,et al.  Stress analysis around crack tips in finite strain problems using the eXtended finite element method , 2005 .

[10]  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 .

[11]  Jaroslav Mackerle,et al.  Object-oriented techniques in FEM and BEM: a bibliography (1996-1999) , 2000 .

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

[13]  I. Babuska,et al.  The Partition of Unity Method , 1997 .

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

[15]  T. Strouboulis,et al.  The generalized finite element method: an example of its implementation and illustration of its performance , 2000 .

[16]  Ted Belytschko,et al.  Dislocations by partition of unity , 2005 .

[17]  Greg N. Frederickson,et al.  Optimal algorithms for tree partitioning , 1991, SODA '91.

[18]  Brian Moran,et al.  Crack tip and associated domain integrals from momentum and energy balance , 1987 .

[19]  S. Atluri,et al.  CALCULATION OF FRACTURE MECHANICS PARAMETERS FOR AN ARBITRARY THREE-DIMENSIONAL CRACK, BY THE ‘EQUIVALENT DOMAIN INTEGRAL’ METHOD , 1987 .

[20]  Thomas Zimmermann,et al.  Object-oriented finite element programming: I: Governing principles , 1992 .

[21]  D. Chopp,et al.  A combined extended finite element and level set method for biofilm growth , 2008 .

[22]  Hiroaki Chiyokura,et al.  Design of solids with free-form surfaces , 1983, SIGGRAPH.

[23]  Michel Salaün,et al.  High‐order extended finite element method for cracked domains , 2005 .

[24]  J. Prévost,et al.  Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation , 2003 .

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

[26]  S. Bordas,et al.  A posteriori error estimation for extended finite elements by an extended global recovery , 2008 .

[27]  Stéphane Bordas,et al.  An extended finite element library , 2007 .

[28]  Olivier Devillers,et al.  Fully Dynamic Delaunay Triangulation in Logarithmic Expected Time Per Operation , 1992, Comput. Geom..