Modeling crack in orthotropic media using a coupled finite element and partition of unity methods

The problem of crack modeling in 2D orthotropic media is considered. The extended finite element method has been adopted for modeling and analyzing a crack and its domain numerically. In this method, first the finite element model without any discontinuities is created and then the two-dimensional asymptotic crack-tip displacement fields with a discontinuous function are added to enrich the finite element approximation using the framework of partition of unity. The main advantage is the ability of the method in taking into consideration a crack without any explicit meshing of the crack surfaces, and the growth of crack can readily be applied without any remeshing. Mixed-mode stress intensity factors (SIFs) are evaluated to determine the fracture properties of domain. The results of proposed method are compared with other available numerical or (semi-) analytical methods. The SIFs are obtained by means of the interaction integral (M-integral).

[1]  Christian Carloni,et al.  Fracture analysis for orthotropic cracked plates , 2005 .

[2]  G. Tupholme.  A study of cracks in orthotropic crystals using dislocation layers , 1974 .

[3]  J. Prévost,et al.  Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation , 2003 .

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

[5]  T. Cruse.  Boundary Element Analysis in Computational Fracture Mechanics , 1988 .

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

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

[8]  T. Belytschko,et al.  Extended finite element method for three-dimensional crack modelling , 2000 .

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

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

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

[12]  Oden,et al.  An h-p adaptive method using clouds , 1996 .

[13]  H. T. Corten,et al.  A mixed-mode crack analysis of rectilinear anisotropic solids using conservation laws of elasticity , 1980 .

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

[15]  Alireza Asadpoure,et al.  Crack analysis in orthotropic media using the extended finite element method , 2006 .

[16]  E. Viola,et al.  Crack propagation in an orthotropic medium under general loading , 1989 .

[17]  Bhavani V. Sankar,et al.  Biaxial load effects on crack extension in anisotropic solids , 2001 .

[18]  Anthony R. Ingraffea,et al.  Modeling mixed-mode dynamic crack propagation nsing finite elements: Theory and applications , 1988 .

[19]  S. Atluri,et al.  A finite-element program for fracture mechanics analysis of composite material , 1975 .

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