Modelling crack growth by level sets in the extended finite element method

By M. Stolarska, David L. Chopp, Nicolas Moës, Ted Belytschko. 2001

840 citations recorded by the source corpus.

An algorithm which couples the level set method (LSM) with the extended finite element method (X‐FEM) to model crack growth is described. The level set method is used to represent the crack location, including the location of crack tips. The extended finite element method is used to compute the stress and displacement fields necessary for determining the rate of crack growth. This combined method requires no remeshing as the crack progresses, making the algorithm very efficient. The combination of these methods has a tremendous potential for a wide range of applications. Numerical examples are presented to demonstrate the accuracy of the combined methods. Copyright © 2001 John Wiley & Sons, Ltd.

Subfields: Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/425a62c360e68d325cf36964b5125d4dcc1894ea

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In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

A guided Bayesian inference approach for detection of multiple flaws in structures using the extended finite element method (2015, methodology): “Originally, the XFEM algorithm was developed to enable the modeling of crack growth without remeshing [16,43].”
XFEM fracture analysis of orthotropic functionally graded materials (2013, positive): “After successful application of original idea of XFEM for modeling 2D problems [27] [28] [29], it was soon extended to general 3D [30] [31] [32] [33] [34] [35] [36], plate [37] and shell [38] [39] [40] problems.”
A survey on level set methods for inverse problems and optimal design (2005, methodology): “In the framework of crack propagation, the representation was carried out by using two or more level set functions, a first one whose zero level set includes the crack and further ones to cut the curve at the crack tips [127].”
A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources (2006, methodology): “The X-FEM is a variation on the partition of unity method [10] and has been used for the solution of crack growth problems [11; 2; 17; 15], arbitrary fixed material interfaces and voids [16], solidification problems [5; 4], and modeling rigid particles in Stokes flow [18].”
Three‐dimensional non‐planar crack growth by a coupled extended finite element and fast marching method (2008, background): “[4, 5] for planar three-dimensional cracks, and subsequently level set algorithms for crack propagation in two dimensions [6] and for arbitrary three-dimensional non-planar cracks [7, 8] were proposed.”
Fracture modeling using meshless methods and level sets in 3D: Framework and modeling (2012, methodology): “Fracture modeling using numerical methods is well-developed following major advances in the past decade or two such as the extended finite element method (XFEM) and meshless methods [1–11].”
A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics (2017, methodology): “In a continued effort to alleviate the limitations of the finite element method, several techniques have been proposed, such as the meshfree method [32, 33, 34, 35] and the extended finite element method [36, 37, 38].”