An improved numerical manifold method incorporating hybrid crack element for crack propagation simulation

The numerical manifold method (NMM) simulates continuous and discontinuous problems in a unified framework; thus NMM has advantages in analysing crack propagation. However, calculation of the stress intensity factors (SIFs) when adopting the NMM requires additional procedures, such as the J-integral and the interaction integral. In this study, a hybrid crack element (HCE) method is incorporated into the NMM to directly obtain the SIFs; the new algorithm combines the merits of both the NMM and HCE method. In the proposed algorithm, the HCE is used in the crack-tip region while the NMM is applied in the remaining region. The SIFs at the crack-tip are calculated directly from the solution of the governing equation with less computational complexity relative to existing methods. The proposed algorithm does not require any changes to the initial mesh during crack propagation. It is verified by a few examples and the results show that the simulated crack propagation paths are in good agreement with the results from existing studies while the computational efficiency is improved due to the direct calculation of the SIFs and the consistency of the mesh system in the crack propagation process.

[1]  K. Washizu.  Variational Methods in Elasticity and Plasticity , 1982 .

[2]  FRACTURE SIMULATIONS USING MANIFOLD AND SINGULAR BOUNDARY ELEMENT METHOD , 1999 .

[3]  I. Babuska,et al.  The Partition of Unity Method , 1997 .

[4]  G. Sih,et al.  Fracture mechanics applied to engineering problems-strain energy density fracture criterion , 1974 .

[5]  Louis Ngai Yuen Wong,et al.  Modeling cracking behavior of rock mass containing inclusions using the enriched numerical manifold method , 2013 .

[6]  Hussain,et al.  Strain Energy Release Rate for a Crack Under Combined Mode I and Mode II , 1974 .

[7]  Amir R. Khoei,et al.  Numerical simulation of multiple crack growth in brittle materials with adaptive remeshing , 2011 .

[8]  Louis Ngai Yuen Wong,et al.  Elastic–plastic cracking analysis for brittle–ductile rocks using manifold method , 2013, International Journal of Fracture.

[9]  Guowei Ma,et al.  THE NUMERICAL MANIFOLD METHOD: A REVIEW , 2010 .

[10]  Song Cen,et al.  A quasi-static crack propagation simulation based on shape-free hybrid stress-function finite elements with simple remeshing , 2014 .

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

[12]  Chen Yi-Zhou,et al.  General case of multiple crack problems in an infinite plate , 1984 .

[13]  F. Erdogan,et al.  On the Crack Extension in Plates Under Plane Loading and Transverse Shear , 1963 .

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

[15]  Bhushan Lal Karihaloo,et al.  Implementation of hybrid crack element on a general finite element mesh and in combination with XFEM , 2007 .

[16]  N. Sukumar,et al.  Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method , 2010 .

[17]  Bhushan Lal Karihaloo,et al.  An overview of a hybrid crack element and determination of its complete displacement field , 2007 .

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

[19]  Guowei Ma,et al.  Numerical analysis of 2-D crack propagation problems using the numerical manifold method , 2010 .

[20]  Theodore H. H. Pian,et al.  A hybrid‐element approach to crack problems in plane elasticity , 1973 .

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

[22]  Bhushan Lal Karihaloo,et al.  Accurate determination of the coefficients of elastic crack tip asymptotic field , 2001 .

[23]  M. Williams,et al.  On the Stress Distribution at the Base of a Stationary Crack , 1956 .

[24]  Yu-Min Lee,et al.  Mixed mode fracture propagation by manifold method , 2002 .

[25]  Hong Zheng,et al.  New strategies for some issues of numerical manifold method in simulation of crack propagation , 2014 .

[26]  G. Shi,et al.  Discontinuous Deformation Analysis , 1984 .

[27]  H. H. Zhang,et al.  Extract of stress intensity factors on honeycomb elements by the numerical manifold method , 2012 .

[28]  I. Babuska,et al.  The generalized finite element method , 2001 .

[29]  David R. Owen,et al.  Engineering fracture mechanics : numerical methods and applications , 1983 .

[30]  G. Ma,et al.  Fracture modeling of isotropic functionally graded materials by the numerical manifold method , 2014 .

[31]  O. C. Zienkiewicz,et al.  The Finite Element Method: Its Basis and Fundamentals , 2005 .

[32]  Louis Ngai Yuen Wong,et al.  Frictional crack initiation and propagation analysis using the numerical manifold method , 2012 .

[33]  Feng Liu,et al.  The MLS-based numerical manifold method with applications to crack analysis , 2014, International Journal of Fracture.

[34]  Jeen-Shang Lin,et al.  A mesh-based partition of unity method for discontinuity modeling , 2003 .

[35]  Y. Chiou,et al.  CRACK GROWTH PREDICTION BY MANIFOLD METHOD , 1999 .

[36]  F. Ren,et al.  Cover refinement of numerical manifold method for crack propagation simulation , 2014 .

[37]  Guowei Ma,et al.  Footwall slope stability analysis with the numerical manifold method , 2011 .

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

[39]  Guangqi Chen,et al.  DEVELOPMENT OF HIGH-ORDER MANIFOLD METHOD , 1998 .