A generalized finite element method for the simulation of three-dimensional dynamic crack propagation

By Carlos Armando Duarte, O. Hamzeh, T. Liszka, W. Tworzydlo. 2001

421 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/e9e4ebbebf9108758a6edb0776f677f95812dbf6

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Cohesive and non‐cohesive fracture by higher‐order enrichment of XFEM (2012, background): “Some few examples are [5, 6] for threedimensional cracks, [7–9] for cohesive crack growth, [10,11] for considering dynamic fracture, and [12–15] for treating the blending and integration issues.”
Numerical simulation of dynamic fracture using finite elements with embedded discontinuities (2009, background): “We can quote Gao and Klein (1999), Falk et al. (2001), Duarte et al. (2001) , Klein et al. (2001), Li et al. (2002), Belytschko et al. (2003), Areias and Belytschko (2006), Song et al. (2006), Huespe et al. (2006),Medyanik et al.(2007), Remmers et al. (2008), or Rabczuk and Samaniego (2008), beside”
Bridging multiple structural scales with a generalized finite element method (2015, methodology): “The GFEM has been applied successfully to the simulation of fracture mechanics [49], polycrystalline and fiber-reinforced microstructures [50], heat transfer with sharp temperature gradients [51], and several other examples where closed-form, analytical enrichment functions are available.”
A two-scale approach for the analysis of propagating three-dimensional fractures (2012, methodology): “Representative methods for three-dimensional crack growth simulations include the standard finite element method (FEM) with remeshing [60], the boundary element method (BEM) [36] [11], and the extended [38] [25] [57] [1] [8] [58] or generalized FEM [18] [48].”
ANALYSIS OF THE FINITE ELEMENT METHOD FOR TRANSMISSION/MIXED BOUNDARY VALUE PROBLEMS ON GENERAL POLYGONAL DOMAINS ∗ (2010, background): “Cracks are important in Engineering applications, see [33] and the references therein.”
Element‐local level set method for three‐dimensional dynamic crack growth (2009, neutral): “[25, 26].”
A note on enrichment functions for modelling crack nucleation (2003, methodology): “These include the eXtended nite-element method (X-FEM) [1, 2] and the generalized nite-element method [3, 4].”
A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries (2006, neutral): “Other procedures are described in [24–26].”
A review of extended/generalized finite element methods for material modeling (2009, methodology): “[35] a least squares fit of the GFEM stresses to the asymptotic crack tip fields was used to extract stress intensity factors.”
The Discontinuity‐Enriched Finite Element Method (2017, background): “The solution of the corresponding boundary value problem yields the displacement at the free end expressed as the sum of the elastic deformation contributions of the parts and the spring: u(L) = PwL EIA + P k + P(1 − w)L EIIA , (1)”
hp‐Generalized FEM and crack surface representation for non‐planar 3‐D cracks (2009, neutral): “Early works on the XFEM for 3-”