Non‐planar 3D crack growth by the extended finite element and level sets—Part I: Mechanical model

By Nicolas Moës, Anthony Gravouil, Ted Belytschko. 2002

714 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/51860008361d0da0614f3bca16eac2d31efe3abc

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In Mechanics of Materials

Citations in the corpus

Analysis of three‐dimensional fracture mechanics problems: A two‐scale approach using coarse‐generalized FEM meshes (2010, methodology): “[12, 19, 20, 35, 51 , 57, 58, 66, 67] and the references therein, for details on the selection of these functions for the case 3-D linear elastic fracture mechanic s problems like those considered in this paper.”
An extended finite element method with higher-order elements for curved cracks (2003, methodology): “Non-planar quasi-static crack growth in three dimensions was considered in Moe ¨s et al. [ 20 ] and Gravouil et al. [16] with an orthogonal pair of level set functions to represent the crack.”
Improved conditioning and accuracy of GFEM/XFEM for three-dimensional fracture mechanics (2015, background): “Another important extension of the work presented here is the case of non-planar cracks with curved fronts, like those considered in [20, 23, 36, 42, 43].”
Stress analysis around crack tips in finite strain problems using the eXtended finite element method (2005, methodology): “The Heaviside function is computed using the level set representation of the crack [20, 8].”
Modeling three‐dimensional crack propagation—A comparison of crack path tracking strategies (2008, neutral): “[19, 22, 24–39].”
The extended finite element method in thermoelastic fracture mechanics (2008, background): “where e1 is a local axis perpendicular to the gradient of the normal level set function and ! is the intensity of the virtual velocity field varyng from 0 to 1 inside the external layer of elements of the chosen set of elements around the crack tip and equal to 1 inside this layer (see again Referen”
Improved implementation and robustness study of the X‐FEM for stress analysis around cracks (2005, methodology): “Enrichment functions The X-FEM method, based on the local PUM [4, 5, 11], uses elementary displacement fields obtained from an infinite cracked body.”
Domain integral formulation for 3-D curved and non-planar cracks with the extended finite element method (2013, positive): “The general local basis is defined using the normalized gradients of the level set functions (5) as in [6].”
Three-dimensional crack growth with hp-generalized finite element and face offsetting methods (2010, methodology): “solution are commonly used as enrichment functions for three-dimensional cracks in finite size domains [13,14, 39 , 71].”
Derivative recovery and a posteriori error estimate for extended finite elements (2007, methodology): “We believe that using the enhanced strain and stress fields to compute the interaction integrals commonly used to obtain the stress intensity factors, the oscillations in the soobtained SIFs, reported in various papers [30, 21, 13, 40, 42] will be reduced.”