Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation

By Natarajan Sukumar, Jean-Herve Prevost. 2003

438 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/e9a14008a24712d0f63084f1548dff37327377cc

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Efficient finite element methodology based on cartesian grids: application to structural shape optimization (2013, methodology): “XFEM is mainly devoted to the analysis of inclusions or cracks.”
THE NUMERICAL MANIFOLD METHOD: A REVIEW (2010, background): “The manifold element of a general shape is first partitioned into several subtriangles, same with the element partitioning in the XFEM [Sukumar and Prevost (2003)].”
Extended finite element method in computational fracture mechanics: a retrospective examination (2015, neutral): “For details into these issues, we refer the reader to discussions in Sukumar et al. (2000) and Sukumar and Prévost (2003).”
The Discontinuity‐Enriched Finite Element Method (2017, methodology): “By design, DE-FEM inherits the approximation properties of IGFEM because of the construction of the finite-dimensional approximation space (see Equation (20)).”
Extended finite element method on polygonal and quadtree meshes (2008, methodology): “A detailed description of the entries in the X-FEM discrete equations is given in Reference [ 31 ].”
Analysis of three-dimensional fracture mechanics problems: A non-intrusive approach using a generalized finite element method (2012, neutral): “If the enrichment functions La1 = 1, a = 1, . . . , N, the GFEM approximation given by (6) can be written as uhpðxÞ ¼ XN a¼1 XDL i¼1 uaiuaðxÞLaiðxÞ ¼ XN a¼1 uaðxÞ ua1 þ XDL i¼2 uaiLaiðxÞ " # ¼ XN a¼1 ua1uaðxÞ|fflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflffl} standard FEM…”
A recovery‐type error estimator for the extended finite element method based on singular+smooth stress field splitting (2008, methodology): “In recent years, the extended finite element method (XFEM) has emerged as a highly efficient numerical method for modelling inclusions and cracks [1,2].”
Cohesive and non‐cohesive fracture by higher‐order enrichment of XFEM (2012, background): “For traction-free cracks, the SIFs can be conveniently used for both purposes [29], but for a cohesive crack, the use of the SIFs excludes the effect of cohesive forces on the crack growth direction and therefore is limited to mode I dominated cohesive cracks [30].”
Strength prediction of single- and double-lap joints by standard and extended finite element modelling (2011, background): “The fundamental expression of the displacement vector u, including the displacements enrichment, is written as [43] b a , and the associated elastic asymptotic crack-tip functions, Fa(x) [45].”
Crack propagation modelling in functionally graded materials using scaled boundary polygons (2015, methodology): “The crack propagation direction θp is computed using the modified expression proposed by Sukumar and Prevost (2003) as θp = 2 tan−1 ( −2K I I (θc)/K I (θc) 1 + √1 + 8(K I I (θc)/K I (θc))2 ) , (39) where θc is the crack angle.”
hp‐Generalized FEM and crack surface representation for non‐planar 3‐D cracks (2009, methodology): “A common approach used to deal with this problem is to subdivide each computational finite element into integration sub-elements with faces fitting the crack surface and use standard quadrature rules over each sub-element [24, 37, 38, 48, 53, 54, 60].”