hp‐Generalized FEM and crack surface representation for non‐planar 3‐D cracks

By J. Pereira, Carlos Armando Duarte, Damrong Guoy, Xiangmin Jiao. 2009

122 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/898b525b822cb221b608f7725ea009a90882e71a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Improved conditioning and accuracy of GFEM/XFEM for three-dimensional fracture mechanics (2015, background): “Another important extension of the work presented here is the case of non-planar cracks with curved fronts, like those considered in [20, 23, 36, 42, 43].”
Analysis of three-dimensional fracture mechanics problems: A non-intrusive approach using a generalized finite element method (2012, methodology): “The GFEM denotes a PUM with the partition of unity provided by Lagrangian finite element shape functions.”
Integration of singular enrichment functions in the generalized/extended finite element method for three‐dimensional problems (2009, methodology): “A review of general singular integration techniques can be found in References [9, 11].”
Three-dimensional crack growth with hp-generalized finite element and face offsetting methods (2010, methodology): “4.3. The numerical examples are solved using the hp-GFEM with the refinement and enrichment recommendations as well as the crack surface representation presented in [ 50 ,51].”
The finite element method enriched by interpolation covers (2013, background): “Melenk and Babuška [14,15] presented the partition of unity finite element formulation to include Ansatz spaces containing the local properties of solutions, and Strouboulis et al. [16,17] used special handbook functions.”
A new generalized finite element method for two‐scale simulations of propagating cohesive fractures in 3‐D (2015, background): “x / is a vector normal to the surface coh, high-order Heaviside functions, as proposed in [72, 73], are used at nodes whose support ! ̨ are intersected by the crack surface coh.”
A two-scale approach for the analysis of propagating three-dimensional fractures (2012, background): “…\(∂ Ω k L ∩∂ Ω σ ) u u u k L · v v v k L ds = ∂ Ω k L ∩∂ Ω σ ¯ t t t · v v v k L ds + η ∂ Ω k L ∩∂ Ω u ¯ u u u · v v v k L ds + η ∂ Ω k L \(∂ Ω k L ∩∂ Ω) u u u k G · v v v k L ds (10) where X X X k L (Ω k L ) is a discretization of H 1 (Ω k L ) using the GFEM shape functions presented in [46] [47].”
Studied X-FEM enrichment to handle material interfaces with higher order finite element (2010, methodology): “This idea was also developed in hp Generalized FEM [24]: representation of crack surfaces is controlled by a Delaunay tetrahedralization of elements cut by the discontinuity.”
Analysis of three‐dimensional fracture mechanics problems: A two‐scale approach using coarse‐generalized FEM meshes (2010, methodology): “Discontinuous and singular analytical enrichment functions presented in [ 57 ] are automatically assigned to local nodes in order to model the crack.”
Element‐local level set method for three‐dimensional dynamic crack growth (2009, methodology): “[24] have used triangular facet representations of cracks in three dimensions in conjunction with the generalized finite element method of Duarte et al.”
A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics (2013, background): “These functions, and their higher-order counterparts, were first proposed in Section 3 of [30] for arbitrary 3-D cracks and in Section 2 of [18] for 3-D branching cracks that are planar in one direction.”