An edge-based smoothed XFEM for fracture in composite materials

In this work, an edge-based smoothed extended finite element method (ES-XFEM) is extended to fracture analysis in composite materials. This method, in which the edge-based smoothing technique is married with enrichment in XFEM, shows advantages of both the extended finite element method (XFEM) and the edge-based smoothed finite element method (ES-FEM). The crack tip enrichment functions are specially derived to represent the characteristic of the displacement field around the crack tip in composite materials. Due to the strain smoothing, the necessity of integrating the singular derivatives of the crack tip enrichment functions is eliminated by transforming area integration into path integration, which is an obvious advantage compared with XFEM. Two examples are presented to testify the accuracy and convergence rate of the ES-XFEM.

[1]  D. Chopp,et al.  A combined extended finite element and level set method for biofilm growth , 2008 .

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

[3]  Jiun-Shyan Chen,et al.  A stabilized conforming nodal integration for Galerkin mesh-free methods , 2001 .

[4]  Lei Chen,et al.  A singular edge-based smoothed finite element method (ES-FEM) for bimaterial interface cracks , 2009 .

[5]  R. Barsoum.  On the use of isoparametric finite elements in linear fracture mechanics , 1976 .

[6]  G. Liu.  A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part I theory , 2010 .

[7]  Jack Chessa,et al.  An Enriched Finite Element Method for Axisymmetric Two-Phase Flow with Surface Tension' , 2013 .

[8]  Sundararajan Natarajan,et al.  On the approximation in the smoothed finite element method (SFEM) , 2010, ArXiv.

[9]  Hung Nguyen-Xuan,et al.  An alternative alpha finite element method (AαFEM) for free and forced structural vibration using triangular meshes , 2010, J. Comput. Appl. Math..

[10]  Stéphane Bordas,et al.  Numerically determined enrichment functions for the extended finite element method and applications to bi‐material anisotropic fracture and polycrystals , 2010 .

[11]  G. Liu.  A G SPACE THEORY AND WEAKENED WEAK (W 2 ) FORMULATION OF MESHFREE METHODS FOR BIOMECHANICS PROBLEMS , 2010 .

[12]  H. Nguyen-Xuan,et al.  A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates , 2010 .

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

[14]  John P. Wolf,et al.  Semi-analytical representation of stress singularities as occurring in cracks in anisotropic multi-materials with the scaled boundary finite-element method , 2002 .

[15]  Guirong Liu.  A GENERALIZED GRADIENT SMOOTHING TECHNIQUE AND THE SMOOTHED BILINEAR FORM FOR GALERKIN FORMULATION OF A WIDE CLASS OF COMPUTATIONAL METHODS , 2008 .

[16]  Ted Belytschko,et al.  The extended finite element method for rigid particles in Stokes flow , 2001 .

[17]  Hung Nguyen-Xuan,et al.  An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates , 2010 .

[18]  T. Rabczuk,et al.  A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics , 2007 .

[19]  Alireza Asadpoure,et al.  Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method , 2007 .

[20]  Guirong Liu.  Mesh Free Methods: Moving Beyond the Finite Element Method , 2002 .

[21]  Zhenjun Yang,et al.  Fully automatic modelling of mixed-mode crack propagation using scaled boundary finite element method , 2006 .

[22]  Guiyong Zhang,et al.  A novel singular node‐based smoothed finite element method (NS‐FEM) for upper bound solutions of fracture problems , 2010 .

[23]  Guirong Liu,et al.  Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC‐PIM) , 2008 .

[24]  Guirong Liu.  Meshfree Methods: Moving Beyond the Finite Element Method, Second Edition , 2009 .

[25]  Stéphane Bordas,et al.  Addressing volumetric locking and instabilities by selective integration in smoothed finite elements , 2009 .

[26]  Stéphane Bordas,et al.  On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM) , 2011 .

[27]  Guangyan Liu,et al.  An enriched element‐failure method (REFM) for delamination analysis of composite structures , 2009 .

[28]  Guirong Liu,et al.  A normed G space and weakened weak (W2) formulation of a cell-based smoothed point interpolation method , 2009 .

[29]  Stéphane Bordas,et al.  Smooth finite element methods: Convergence, accuracy and properties , 2008 .

[30]  Guirong Liu,et al.  Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth , 2012 .

[31]  Glaucio H. Paulino,et al.  Mixed-mode fracture of orthotropic functionally graded materials using finite elements and the modified crack closure method , 2002 .

[32]  P. C. Paris,et al.  On cracks in rectilinearly anisotropic bodies , 1965 .

[33]  G. Sih,et al.  Mathematical theories of brittle fracture. , 1968 .

[34]  H. Nguyen-Xuan,et al.  A simple and robust three-dimensional cracking-particle method without enrichment , 2010 .

[35]  R. Barsoum.  Triangular quarter‐point elements as elastic and perfectly‐plastic crack tip elements , 1977 .

[36]  Stéphane Bordas,et al.  A Node-Based Smoothed eXtended Finite Element Method (NS-XFEM) for Fracture Analysis , 2011 .

[37]  H. Nguyen-Xuan,et al.  A smoothed finite element method for plate analysis , 2008 .

[38]  Glaucio H. Paulino,et al.  The interaction integral for fracture of orthotropic functionally graded materials: Evaluation of stress intensity factors , 2003 .

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

[40]  Stéphane Bordas,et al.  Strain smoothing in FEM and XFEM , 2010 .

[41]  Guirong Liu.  A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part II applications to solid mechanics problems , 2010 .

[42]  G. Liu.  A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part II applications to solid mechanics problems , 2010 .

[43]  T. Belytschko,et al.  A three dimensional large deformation meshfree method for arbitrary evolving cracks , 2007 .

[44]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

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

[46]  T. Rabczuk,et al.  Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment , 2008 .

[47]  Stéphane Bordas,et al.  Crack growth calculations in solder joints based on microstructural phenomena with X-FEM , 2011 .