A note on enrichment functions for modelling crack nucleation

By J. Bellec, John Dolbow. 2003

53 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/494cfcc9497130753c667d4dc237e4df8e7671ef

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

A multiscale projection method for macro/microcrack simulations (2007, methodology): “The methods of Bellec and Dolbow [28] are used for very short cracks.”
A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics (2007, background): “For instance, in finite elements, it is very difficult or impossible to close the crack front within a single element, see Bellec and Dolbow [6].”
Extended finite element method in computational fracture mechanics: a retrospective examination (2015, unknown): “But here too, there are limits to the basic extended ﬁnite element approximation (4a) as discussed in Bellec and Dolbow (2003).”
An extended finite element method for hydraulic fracture problems (2009, methodology): “In this paper, we investigate the use of the extended finite element method (X-FEM) [7–11] for the solution of hydraulic fracture problems in order to avoid re-meshing.”
Extended finite element method on polygonal and quadtree meshes (2008, methodology): “Suitable enrichment functions to model intraelement cracks within the X-FEM have been developed [44]; the modeling of discontinuities on quadtree meshes is an alternative approach to represent and capture the growth of very small cracks without incurring significant additional costs.”
On three-dimensional modelling of crack growth using partition of unity methods (2010, background): “If the two crack tips of the same crack lie within the domain of influence of one node, then the crack cannot be described accurately by a partition of unity method any more [7] (Fig.”
Coarse‐graining of multiscale crack propagation (2010, methodology): “They use blending methods to combine two sets of the branch functions given in [33].”
Analysis of three‐dimensional fracture mechanics problems: A two‐scale approach using coarse‐generalized FEM meshes (2010, background): “Even when analytical enrichments are able to approximate well the solution, as is the case in many 2-D fracture mechanics problems, the minimum crack size which can be modeled is controlled by the element size in the mesh [ 7 ].”
A method for multiple crack growth in brittle materials without remeshing (2004, unknown): “Bellec and Dolbow [ 52 ] have given an enrichment for shorter cracks but this was not used here. procedure Therefore the to set a mesh is as follows.”