Vector level sets for description of propagating cracks in finite elements

By Giulio Ventura, Elisa Budyn, Ted Belytschko. 2003

225 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/fa04eaf4f64908fd12a2a183c5786f19e21e5065

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

A well‐conditioned and optimally convergent XFEM for 3D linear elastic fracture (2016, background): “Consequently, any of the available possibilities can be used such as level sets [16, 17, 48], vector level sets [49], or a hybrid explicit implicit representation [50].”
The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “[192, 189] in the context of enriched methods and two-dimensional applications.”
Hydro‐mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method (2013, methodology): “The technique has been applied in crack problems, including crack growth with frictional contact [23], cohesive crack growth [24, 25], stationary and growing cracks [26], three-dimensional crack propagation [27] and dynamic cohesive crack propagation [28].”
Dynamic crack propagation analysis of orthotropic media by the extended finite element method (2009, methodology): “They have been successfully implemented in the XFEM codes and can be used for quasi-static or dynamic crack evolution problems (Ventura et al. 2003).”
Thermo-hydro-mechanical modeling of impermeable discontinuity in saturated porous media with X-FEM technique (2012, methodology): “The X-FEM was originally applied in mesh-independent crack propagation problems, including: the crack growth with frictional contact [33], cohesive crack propagation [34–36], stationary and growing cracks [37] and three-dimensional crack propagation [38].”
Spatially adaptive techniques for level set methods and incompressible flow (2006, background): “In particular, several attempts have been made at extending the method to handle objects of higher codimension [9, 48, 17], there has been interesting work on inverse problems [10], and a few authors have combined level sets with finite element methods in order to accurately describe cracks and frac”
Extended Voronoi cell finite element model for multiple cohesive crack propagation in brittle materials (2006, methodology): “behind tip. A vector level set method has been developed in References [48, 49 ] to freeze the crack surface in accordance with geometric updating.”
Extended meshfree methods without branch enrichment for cohesive cracks (2007, methodology): “The recently developed XFEM has been proven to be an efficient tool for fracture problems.”
A simple method for crack growth in mixed mode with X-FEM (2012, methodology): “This technique has been reused and adapted later (Guidault et al., 2008; Ventura et al., 2003).”
A review of extended/generalized finite element methods for material modeling (2009, background): “The effects of the size of the crack tip enrichment domain has been studied by Ventura et al. [109], Laborde et al. [64] and Béchet et al. [8].”
Enhanced blending elements for XFEM applied to linear elastic fracture mechanics (2009, methodology): “A common way of selecting the nodes that have to be enriched for modelling the crack is to apply the level set method (LSM) [4, 5].”