Extended finite element method for three-dimensional crack modelling

By Natarajan Sukumar, Nicolas Moës, B. Moran, Ted Belytschko, W. P. Murphy. 2000

433 citations recorded by the source corpus.

An extended finite element method (X-FEM) for three-dimensional crack modelling is described. A discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces. Computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed. Stress intensity factors (SIFs) for planar three-dimensional cracks are presented, which are found to be in good agreement with benchmark solutions. Copyright © 2000 John Wiley & Sons, Ltd.

Subfields: Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/2a1ce053c55f555e4fa81b8aac138cd0db734bf1

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In Mechanics of Materials

Citations in the corpus

Enriched finite elements and level sets for damage tolerance assessment of complex structures (2006, methodology): “The level set method and the extended finite element method were first used to model crack growth in two dimensions [16], and in three dimensions [17–19,12,13].”
A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM (2010, positive): “Another case where not all the generalized coordinates correspond to material points is the extended finite element method (X-FEM) [18, 19, 20, 21].”
Brittle fracture in polycrystalline microstructures with the extended finite element method (2003, methodology): “This technique provides an accurate and robust numerical method that removes the need to mesh the crack geometry in both two-dimensional [35, 36] and three-dimensional crack modelling [ 40 ].”
Three-dimensional crack growth with hp-generalized finite element and face offsetting methods (2010, methodology): “FEM (GFEM) [14] and the eXtended FEM (XFEM) [ 71 ] are promising techniques to overcome the shortcomings of the standard FEM in crack growth simulations.”
Domain integral formulation for 3-D curved and non-planar cracks with the extended finite element method (2013, positive): “The extended finite element method (XFEM) is a technique that enables an efficient numerical modeling of crack problems [1,2].”
Integration of singular enrichment functions in the generalized/extended finite element method for three‐dimensional problems (2009, methodology): “…of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 North Mathews Ave., Urbana, IL 61801, U.S.A. SUMMARY A mapping method is developed to integrate weak singularities, which result from enrichment functions in the generalized/extended finite element method.”