A study of the representation of cracks with level sets

By Marc Duflot. 2007

188 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/6be183688bca92f4d59e389ec7847d5f75192eca

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In Civil and Structural Engineering

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

The extended finite element method in thermoelastic fracture mechanics (2008, methodology): “Only the fourth term in the right-hand side of the previous equation is a contribution of the thermal loading, the first three terms comes from the definition of the auxiliary fields in the level set co-ordinate system and vanish for straight cracks (see References [20, 22 ]).”
Three-dimensional crack growth with hp-generalized finite element and face offsetting methods (2010, methodology): “A detailed review of crack surface representation with level set methods in XFEM simulations can be found in [ 18 ].”
A simple method for crack growth in mixed mode with X-FEM (2012, background): “Duflot (2007) proposes several algorithms to retrieve level sets with good properties.”
hp‐Generalized FEM and crack surface representation for non‐planar 3‐D cracks (2009, background): “Their high order approximations are based on non-hierarchical Lagrangian shape functions.”
Derivative recovery and a posteriori error estimate for extended finite elements (2007, methodology): “MLS derivative recovery in finite elements was first proposed in Reference [44] of which this work is a generalization.”
The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “An overview of different level-set approaches for the description and update of crack geometries is given by Duflot [68].”
A review of extended/generalized finite element methods for material modeling (2009, unknown): “Other relevant papers are [39] and [58].”
Domain integral formulation for 3-D curved and non-planar cracks with the extended finite element method (2013, unknown): “Nodes that need to be enriched are the nodes which fulfill the conditions (4) where I is the set of nodes belonging to a given element [6,8]:”
A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics (2011, methodology): “The use of level sets to represent the crack has been shown to provide a useful methodology for crack propagation studies [18].”