MODELING HOLES AND INCLUSIONS BY LEVEL SETS IN THE EXTENDED FINITE-ELEMENT METHOD

By Natarajan Sukumar, David L. Chopp, Nicolas Moës, Ted Belytschko. 2001

1,242 citations recorded by the source corpus.

A methodology to model arbitrary holes and material interfaces (inclusions) without meshing the internal boundaries is proposed. The numerical method couples the level set method (S. Osher, J.A. Sethian, J. Comput. Phys. 79 (1) (1988) 12) to the extended finite-element method (X-FEM) (N. Moes, J. Dolbow, T. Belytschko, Int. J. Numer. Methods Engrg. 46 (1) (1999) 131). In the X-FEM, the finite-element approximation is enriched by additional functions through the notion of partition of unity. The level set method is used for representing the location of holes and material interfaces, and in addition, the level set function is used to develop the local enrichment for material interfaces. Numerical examples in two-dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/70937f01cb2da6c2aec515d628e7af41abb0f1c0

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Derivative recovery and a posteriori error estimate for extended finite elements (2007, background): “To handle discontinuities in the dual unknown (multi-materials [41], solidification [16], biofilms [35], multi-phase flow [15], Stokes flow [47]), functions with discontinuous derivatives enhance the standard basis.”
X-FEM explicit dynamics for constant strain elements to alleviate mesh constraints on internal or external boundaries (2008, background): “The determination of these nodes can be made with the help of a level set representation of the surface [17].”
Mass lumping strategies for X‐FEM explicit dynamics: Application to crack propagation (2008, background): “This level set representation of cracks was also found to be extremely convenient to handle crack growth [7–9] (without any remeshing).”
Stress concentration minimization of 2D filets using X-FEM and level set description (2007, methodology): “The modeling of material-void interfaces with X-FEM (see Sukumar et al. (2001) ) differs only marginally from”
Towards the algorithmic treatment of 3D strong discontinuities (2006, neutral): “[3, 4].”
Imposing Dirichlet boundary conditions in the extended finite element method (2006, background): “The discontinuities may be related to cracks [7, 8], material interfaces [9, 10] or voids [11].”
Three-dimensional crack growth with hp-generalized finite element and face offsetting methods (2010, methodology): “It is an alternative to the level set method [63] that has been broadly used in the extended finite element method context [26,54, 68 ].”
Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation (2003, methodology): “The interface of the X-FEM with level set techniques to model weak discontinuities such as material interfaces (bimaterials) was introduced in Sukumar et al. (2001), whereas the representation of tangential discontinuities was presented in Belytschko et al. (2001).”
Transient thermal shock fracture analysis of functionally graded piezoelectric materials by the extended finite element method (2014, background): “In the past decades, there are a great number of studies concerning the improvement or applications of the X-FEM for various discontinuous problems (Belytschko et al., 2003; Samaniego and Belytschko, 2005; Gerstenberger and Wall, 2008; Zhang et al., 2012; Groß and Reusken, 2007; Sukumar et al., 2001”
Extended finite element method and fast marching method for three-dimensional fatigue crack propagation (2003, methodology): “Other works that have used the level set method for material interfaces within the context of a mesh-independent Galerkin formulation can be found in [24] [32].”