A review of extended/generalized finite element methods for material modeling

By Ted Belytschko, R. Gracie, Giulio Ventura. 2009

897 citations recorded by the source corpus.

The extended and generalized finite element methods are reviewed with an emphasis on their applications to problems in material science: (1) fracture, (2) dislocations, (3) grain boundaries and (4) phases interfaces. These methods facilitate the modeling of complicated geometries and the evolution of such geometries, particularly when combined with level set methods, as for example in the simulation growing cracks or moving phase interfaces. The state of the art for these problems is described along with the history of developments.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/9f267904f7e36571f7001813eef4e5fffd5ef993

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Fracture modeling using meshless methods and level sets in 3D: Framework and modeling (2012, methodology): “The XFEM is probably the dominant method at present because it is feasible to implement within any existing finite element analysis (FEA) program as has been shown in a recent survey [12].”
Local enrichment of the finite cell method for problems with material interfaces (2013, methodology): “Concerning the accurate integration on the cut cells, other approaches such as the estimation of the discontinuous integrands with the continuous functions [35–37], or local mesh generation are also applicable [38–40].”
Extended finite element method in computational fracture mechanics: a retrospective examination (2015, neutral): “In this paper, our intent is not to provide an exhaustive overview of the X-FEM; many such reviews are already available in the literature (Belytschko et al. 2009; Fries and Belytschko 2010).”
A new generalized finite element method for two‐scale simulations of propagating cohesive fractures in 3‐D (2015, background): “A brief history of the development of GFEMs/XFEMs can be found in [22].”
A gradient-based shape optimization scheme using an interface-enriched generalized FEM (2015, neutral): “This contrasts with conventional G/XFEM where the generalized dofs are associated with duplicated nodes of the non-conforming elements [39,40].”
A two-scale approach for the analysis of propagating three-dimensional fractures (2012, background): “Recent reviews of generalized/extended FEMs along with a brief history on their development can be found in [6] [23].”