A study of the representation of cracks with level sets

The level set method has been used for a few years to represent cracks in fracture mechanics simulations instead of an explicit description of the cracks faces geometry. This paper studies in detail the shape of the level set functions around a crack in two dimensions that is propagating with a sharp kink, obtained both with level set update methods found in the literature and with several innovative update methods developed by the author. A criterion based on the computation of a J integral of a virtual displacement field obtained with the values of the level set functions is proposed in order to assess the quality of these update methods. With the help of this criterion, two optimal approaches are identified, which predict an accurate evolution of the crack with smooth and consistent level set functions. These methods are then applied in three dimensions to the case of an initially penny‐shaped crack that propagates out of its plane. Copyright © 2006 John Wiley & Sons, Ltd.

[1]  David Galbally,et al.  International Journal for Numerical Methods in Engineering , 2009 .

[2]  Stéphane Bordas,et al.  Enriched finite elements and level sets for damage tolerance assessment of complex structures , 2006 .

[3]  M. Duflot.  A meshless method with enriched weight functions for three‐dimensional crack propagation , 2006 .

[4]  N. Moës,et al.  Improved implementation and robustness study of the X‐FEM for stress analysis around cracks , 2005 .

[5]  Michel Salaün,et al.  High‐order extended finite element method for cracked domains , 2005 .

[6]  T. Belytschko,et al.  A method for multiple crack growth in brittle materials without remeshing , 2004 .

[7]  T. Belytschko,et al.  A method for growing multiple cracks without remeshing and its application to fatigue crack growth , 2004 .

[8]  Marc Duflot,et al.  Fatigue crack growth analysis by an enriched meshless method , 2004 .

[9]  M. Duflot,et al.  A meshless method with enriched weight functions for fatigue crack growth , 2004 .

[10]  David L. Chopp,et al.  Modeling thermal fatigue cracking in integrated circuits by level sets and the extended finite element method , 2003 .

[11]  T. Belytschko,et al.  Vector level sets for description of propagating cracks in finite elements , 2003 .

[12]  Ted Belytschko,et al.  An extended finite element method with higher-order elements for curved cracks , 2003 .

[13]  Ted Belytschko,et al.  A vector level set method and new discontinuity approximations for crack growth by EFG , 2002 .

[14]  T. Belytschko,et al.  Non‐planar 3D crack growth by the extended finite element and level sets—Part II: Level set update , 2002 .

[15]  T. Belytschko,et al.  Non‐planar 3D crack growth by the extended finite element and level sets—Part I: Mechanical model , 2002 .

[16]  B. Moran,et al.  An interaction energy integral method for computation of mixed-mode stress intensity factors along non-planar crack fronts in three dimensions , 2002 .

[17]  T. Belytschko,et al.  MODELING HOLES AND INCLUSIONS BY LEVEL SETS IN THE EXTENDED FINITE-ELEMENT METHOD , 2001 .

[18]  Ted Belytschko,et al.  Modelling crack growth by level sets in the extended finite element method , 2001 .

[19]  S. Osher,et al.  Motion of curves in three spatial dimensions using a level set approach , 2001 .

[20]  T. Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[21]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[22]  J. A. Sethian,et al.  Fast Marching Methods , 1999, SIAM Rev..

[23]  J. Sethian.  Level Set Methods and Fast Marching Methods/ J. A. Sethian , 1999 .

[24]  Mark A Fleming,et al.  ENRICHED ELEMENT-FREE GALERKIN METHODS FOR CRACK TIP FIELDS , 1997 .

[25]  Mark A Fleming,et al.  Continuous meshless approximations for nonconvex bodies by diffraction and transparency , 1996 .

[26]  E. Fatemi,et al.  A level set approach for computing solutions to incompressible two- phase flow II , 1995 .

[27]  T. Belytschko,et al.  Finite element derivative recovery by moving least square interpolants , 1994 .

[28]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[29]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[30]  Shuodao Wang,et al.  A Mixed-Mode Crack Analysis of Isotropic Solids Using Conservation Laws of Elasticity , 1980 .

[31]  J. Rice.  A path-independent integral and the approximate analysis of strain , 1968 .

[32]  D. Chopp,et al.  Extended finite element method and fast marching method for three-dimensional fatigue crack propagation , 2003 .

[33]  David L. Chopp,et al.  Some Improvements of the Fast Marching Method , 2001, SIAM J. Sci. Comput..

[34]  Brian Moran,et al.  Crack tip and associated domain integrals from momentum and energy balance , 1987 .

[35]  J. D. Eshelby.  The Continuum Theory of Lattice Defects , 1956 .