Extended finite element method and fast marching method for three-dimensional fatigue crack propagation

By Natarajan Sukumar, David L. Chopp, Brian Moran. 2003

331 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a9237d232411ece2596e26f4976b545c110f6566

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Derivative recovery and a posteriori error estimate for extended finite elements (2007, methodology): “We believe that using the enhanced strain and stress fields to compute the interaction integrals commonly used to obtain the stress intensity factors, the oscillations in the soobtained SIFs, reported in various papers [30, 21, 13, 40, 42] will be reduced.”
Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation (2003, methodology): “…et al. (2000), where C++ was used as the programming language and the tools developed within that framework were ideally-suited for the incorporation of many different applications within one code (Dolbow, 1999; Sukumar et al., 2001; Wagner et al., 2001; Sukumar et al., 2003a; Ji et al., 2002 ).”
Analysis of three-dimensional fracture mechanics problems: A non-intrusive approach using a generalized finite element method (2012, methodology): “We refer to [8,14,15,27,39,44,45,56,57] and the references therein, for details on the selection of these functions for the case 3-D linear elastic fracture mechanics problems like those considered in this paper.”
A study of the representation of cracks with level sets (2007, methodology): “For instance, this update can be obtained using the Fast Marching Method as in Reference [35] in the case of a crack propagating in a plane.”
A review of extended/generalized finite element methods for material modeling (2009, methodology): “[99] a fast marching method was developed for updating the level sets of cracks in three dimensions.”
Extended finite element method in computational fracture mechanics: a retrospective examination (2015, neutral): “The FMM was ﬁrst adopted for crack propagation simulations of planar cracks in Sukumar et al. (2003) and subsequently extended for nonplanar cracks in Sukumar et al. (2008).”
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].”
Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth (2017, methodology): “We propagate 10 steps and make a comparison with the exact result and the result from the XFEM + level set method [123] (Fig.”
On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM) (2011, methodology): “Enrichment scheme for LEFM For the case of LEFM, two sets of functions are used: a Heaviside jump function to capture the jump across the crack faces and asymptotic branch functions that span the two-dimensional asymptotic crack tip fields (three-dimensional methods have been proposed in [32] and ap”
XFEM fracture analysis of orthotropic functionally graded materials (2013, positive): “After successful application of original idea of XFEM for modeling 2D problems [27] [28] [29], it was soon extended to general 3D [30] [31] [32] [33] [34] [35] [36], plate [37] and shell [38] [39] [40] problems.”
MODELING HOLES AND INCLUSIONS BY LEVEL SETS IN THE EXTENDED FINITE-ELEMENT METHOD (2001, background): “For a few applications in the above spirit, see [3] [8] for crack modeling in two dimensions, and [16] [17] for threedimensional elastostatics and fatigue crack growth modeling.”
hp‐Generalized FEM and crack surface representation for non‐planar 3‐D cracks (2009, methodology): “Thus, refinement of the volume GFEM mesh or a background mesh [9, 45, 52] are not needed in order to improve the representation of the crack surface, as is the case with implicit representations based on, for example, level set methods.”
Brittle fracture in polycrystalline microstructures with the extended finite element method (2003, background): “In addition, recent studies have explored the use of fast marching and level sets for evolving crack discontinuities in three-dimensions within the X-FEM framework: growth of multiple planar cracks are handled using the fast marching method [ 44 , 45], whereas non-planar crack growth is carried out ”