X-FEM for Three-Dimensional Dynamic Crack Growth

In this paper, the extended finite element (X-FEM) methodology is studied in the modeling and simulation of 3D crack and 3D dynamic crack growth in linear materials. And a 3D X-FEM computer code is developed. The B-bar method to modify the shape function of the 3D brick element is adopted. Stress intensify factors of 3D crack are calculated in XFEM. Several 2D and 3D crack problems are modeled by X-FEM. In the end, a 3D dynamics crack growth is simulated by using X-FEM. It is found that X-FEM is superior to the traditional FEM in the modeling and simulation of 3D dynamic crack growth.

[1]  Ted Belytschko,et al.  Smoothing, enrichment and contact in the element-free Galerkin method , 1999 .

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

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

[4]  Shaofan Li,et al.  Meshfree-Based Ductile Fracture Evaluation for Welded Aluminum Structures under Impact Loading , 2011 .

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

[6]  John A. Nairn,et al.  Calculation of J-Integral and Stress Intensity Factors using the Material Point Method , 2004 .

[7]  Edward H. Glaessgen,et al.  Recent Advances in Durability and Damage Tolerance Methodology at NASA Langley Research Center , 2007 .

[8]  T. Anderson.  Fracture Mechanics: Fundamentals and Applications, Third Edition , 1994 .

[9]  Ted Belytschko,et al.  An element-free Galerkin method for three-dimensional fracture mechanics , 1997 .

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

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

[12]  Alain Combescure,et al.  Appropriate extended functions for X-FEM simulation of plastic fracture mechanics , 2006 .

[13]  Huafeng Liu,et al.  Meshfree particle method , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[14]  Ted Belytschko,et al.  THE ELEMENT FREE GALERKIN METHOD FOR DYNAMIC PROPAGATION OF ARBITRARY 3-D CRACKS , 1999 .

[15]  Ted Belytschko,et al.  Abaqus implementation of extended finite element method using a level set representation for three-dimensional fatigue crack growth and life predictions , 2010 .

[16]  J. Brackbill,et al.  Flip: A low-dissipation, particle-in-cell method for fluid flow , 1988 .

[17]  John A. Nairn,et al.  Three-Dimensional Dynamic Fracture Analysis Using the Material Point Method , 2006 .

[18]  Shaofan Li,et al.  Meshfree Method for Ductile Fracture with Modified Gurson's Model , 2011 .

[19]  T. Belytschko,et al.  Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment , 2003 .

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

[21]  S. Rahman,et al.  Probabilistic fracture mechanics by Galerkin meshless methods – part I: rates of stress intensity factors , 2002 .

[22]  S. Rahman,et al.  Stochastic meshless analysis of elastic–plastic cracked structures , 2003 .

[23]  T. Belytschko,et al.  Fracture and crack growth by element free Galerkin methods , 1994 .

[24]  S. Rahman,et al.  An enriched meshless method for non‐linear fracture mechanics , 2004 .

[25]  Michael A. Sutton,et al.  Three-dimensional finite element simulations of mixed-mode stable tearing crack growth experiments , 2007 .

[26]  T. Belytschko,et al.  DYNAMIC FRACTURE USING ELEMENT-FREE GALERKIN METHODS , 1996 .

[27]  Ted Belytschko,et al.  AN EXTENDED FINITE ELEMENT METHOD (X-FEM) FOR TWO- AND THREE-DIMENSIONAL CRACK MODELING , 2000 .

[28]  Shaofan Li,et al.  Meshfree Simulations of Ductile Crack Propagations , 2005 .

[29]  Ted Belytschko,et al.  Cracking particles: a simplified meshfree method for arbitrary evolving cracks , 2004 .

[30]  Ted Belytschko,et al.  Modeling fracture in Mindlin–Reissner plates with the extended finite element method , 2000 .

[31]  Howard L. Schreyer,et al.  Axisymmetric form of the material point method with applications to upsetting and Taylor impact problems , 1996 .

[32]  D. Sulsky,et al.  A particle method for history-dependent materials , 1993 .

[33]  Ted Belytschko,et al.  Arbitrary Lagrangian-Eulerian formulation for element-free Galerkin method , 1998 .

[34]  Bo Cerup Simonsen,et al.  Experimental and numerical modelling of ductile crack propagation in large-scale shell structures , 2004 .

[35]  Azim Eskandarian,et al.  Meshless analysis of plasticity with application to crack growth problems , 2004 .

[36]  James C. Newman,et al.  The Merging of Fatigue and Fracture Mechanics Concepts: A Historical Perspective , 1998 .

[37]  D. Sulsky.  Erratum: Application of a particle-in-cell method to solid mechanics , 1995 .

[38]  Wen-Hwa Chen,et al.  On Three-Dimensional Fracture Mechanics Analysis by an Enriched Meshless Method , 2005 .