Enriched finite elements and level sets for damage tolerance assessment of complex structures

By Stéphane P.A. Bordas, Brian Moran. 2006

194 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/787c1c32e5c898a8b3a15e8b555c73331c888c40

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

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].”
Three-dimensional crack growth with hp-generalized finite element and face offsetting methods (2010, background): “These results also show that there is no need to a priori refine the mesh in the region of potential crack growth, as proposed in [ 7 ].”
Simulations of instability in dynamic fracture by the cracking particles method (2009, unknown): “[14]; recent developments are given in [15–23].”
Analysis of three-dimensional fracture mechanics problems: A non-intrusive approach using a generalized finite element method (2012, background): “A comparison between the performance of this element and standard ten-node quadratic tetrahedral elements (TET10) is presented in [14].”
A simple method for crack growth in mixed mode with X-FEM (2012, methodology): “This algorithm has been used widely since, for example for crack propagation in industrial structures (Bordas and Moran, 2006).”
A posteriori error estimation for extended finite elements by an extended global recovery (2008, methodology): “Remarkably, extended finite elements have been employed in industrial settings [17, 18], and open-source software is now available on the internet to promote further development of XFEMs [19, 20].”
Strain smoothing in FEM and XFEM (2010, methodology): “XFEM is quite a robust and popular method which is now used for industrial problems [18,19,105,104,103,102] and under implementation by leading computational software companies.”
Extended finite element method with global enrichment (2015, background): “• Furthermore, the crack front considered is curved which is the case in practical applications ([18,19,20,21,22]).”
Extended isogeometric analysis based on PHT‐splines for crack propagation near inclusions (2017, unknown): “i=1 Ri (ξ, η)Pi ; Ri = Ni (ξ, η)wi ∑n ζ̄=1 Nζ̄ (ξ, η)wζ̄ , (7)”
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”
A robust preconditioning technique for the extended finite element method (2011, background): “Due to its flexibility X-FEM is applied to an increasing number of industrial problems [5].”
Derivative recovery and a posteriori error estimate for extended finite elements (2007, methodology): “For problems with discontinuities in the primal dependent variable (cracks [29, 28, 13], fluid-structure interaction [26]), discontinuous functions are added.”
Meshless methods: A review and computer implementation aspects (2008, methodology): “The extended finite element method (XFEM) [6] [79] [24] [45] [23] [22] [24] enriches the approximation space so that weak 27 and strong discontinuities can be captured.”