Premium
Three‐dimensional non‐planar crack growth by a coupled extended finite element and fast marching method
Author(s) -
Sukumar N.,
Chopp D. L.,
Béchet E.,
Moës N.
Publication year - 2008
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.2344
Subject(s) - finite element method , partition of unity , planar , extended finite element method , displacement (psychology) , robustness (evolution) , fast marching method , fracture mechanics , signed distance function , crack tip opening displacement , mathematics , structural engineering , mathematical analysis , geometry , computer science , algorithm , stress intensity factor , engineering , gene , psychology , biochemistry , chemistry , computer graphics (images) , psychotherapist
Abstract 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 © 2008 John Wiley & Sons, Ltd.