partition of unity; enrichment function; level sets; signed distance function; fast marching method; stress intensity factor; crack propagation
Abstract :
[en] A numerical technique for non-planar three-dimensional linear elastic crack growth simulations is proposed. This technique couples the extended finite element method (X-FEM) and the fast marching method (FMM). In crack modeling using X-FEM, the framework of partition of unity is used to enrich the standard finite element approximation by a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields. The initial crack geometry is represented by two level set functions, and Subsequently signed distance functions are used to maintain the location of the crack and to compute the enrichment functions that appear in the displacement approximation. Crack modeling is performed without the need to mesh the crack, and crack propagation is simulated without remeshing. Crack growth is conducted using FMM; unlike a level set formulation for interface capturing, no iterations nor any time step restrictions are imposed in the FMM. Planar and non-planar quasi-static crack growth simulations are presented to demonstrate the robustness and versatility of the proposed technique. Copyright (C) 2008 John Wiley & Sons, Ltd.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others Mathematics
Author, co-author :
Sukumar, N.; Department of Civil and Environmental Engineering, University of California, Davis, CA 95616, U.S.
Chopp, D. L.; Department of Engineering Sciences & Applied Mathematics, Northwestern University, Evanston, IL 60208, U.S.A.
Béchet, Eric ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Conception géométrique assistée par ordinateur
Moes, N.; Laboratoire de Mécanique et Matériaux, Ecole Centrale de Nantes, 1 Rue de la No´e, 44321 Nantes, France
Language :
English
Title :
Three-dimensional non-planar crack growth by a coupled extended finite element and fast marching method
Publication date :
2008
Journal title :
International Journal for Numerical Methods in Engineering
ISSN :
0029-5981
eISSN :
1097-0207
Publisher :
John Wiley & Sons, Inc, Chichester, United Kingdom
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