Modelling dynamic crack propagation using the scaled boundary finite element method

This study presents a novel application of the scaled boundary finite element method (SBFEM) to model dynamic crack propagation problems. Accurate dynamic stress intensity factors are extracted directly from the semi-analytical solutions of SBFEM. They are then used in the dynamic fracture criteria to determine the crack-tip position, velocity and propagation direction. A simple, yet flexible remeshing algorithm is used to accommodate crack propagation. Three dynamic crack propagation problems that include mode-I and mix-mode fracture are modelled. The results show good agreement with experimental and numerical results available in the literature. It is found that the developed method offers some advantages over conventional FEM in terms of accuracy, efficiency and ease of implementation. Copyright © 2011 John Wiley & Sons, Ltd.

[1]  De Xie,et al.  Analysis of mixed-mode dynamic crack propagation by interface element based on virtual crack closure technique , 2007 .

[2]  Z. J. Yang,et al.  Calculation of transient dynamic stress intensity factors at bimaterial interface cracks using a SBFEM-based frequency-domain approach , 2008 .

[3]  Ionel Nistor,et al.  Numerical implementation of the eXtended Finite Element Method for dynamic crack analysis , 2008, Adv. Eng. Softw..

[4]  Andrew Deeks,et al.  Determination of coefficients of crack tip asymptotic fields using the scaled boundary finite element method , 2005 .

[5]  Amir Reza Shahani,et al.  Finite element analysis of dynamic crack propagation using remeshing technique , 2009 .

[6]  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 .

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

[8]  G. Yagawa,et al.  Analysis of a rapidly propagating crack using finite elements , 1977 .

[9]  Hubert Maigre,et al.  Dynamic crack propagation under mixed-mode loading – Comparison between experiments and X-FEM simulations , 2007 .

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

[11]  D. P. Rooke,et al.  A single-region time domain BEM for dynamic crack problems , 1995 .

[12]  Andrew Deeks,et al.  Fully-automatic modelling of cohesive crack growth using a finite element-scaled boundary finite element coupled method , 2007 .

[13]  D. P. Rooke,et al.  Boundary element formulations for the dynamic analysis of cracked structures , 1996 .

[14]  Wei Gao,et al.  Transient dynamic analysis of interface cracks in anisotropic bimaterials by the scaled boundary finite-element method , 2010 .

[15]  M. F. Kanninen,et al.  Modeling of dynamic crack propagation: I. validation of one-dimensional analysis , 1979, International Journal of Fracture.

[16]  J. Wolf,et al.  A virtual work derivation of the scaled boundary finite-element method for elastostatics , 2002 .

[17]  Tatsuyuki Murakami,et al.  A laser-caustic method for the measurement of mixed-mode dynamic stress-intensity factors in fast-curving fracture tests , 1990 .

[18]  J. F. Kalthoff,et al.  Measurements of dynamic stress intensity factors for fast running and arresting cracks in double-cantilever-beam specimens , 1977 .

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

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

[21]  Hyun Moo Koh,et al.  An incremental formulation of the moving-grid finite element method for the prediction of dynamic crack propagation , 1995 .

[22]  M. F. Kanninen,et al.  A dynamic analysis of unstable crack propagation and arrest in the DCB test specimen , 1974 .

[23]  Chongmin Song,et al.  The scaled boundary finite-element method—alias consistent infinitesimal finite-element cell method—for elastodynamics , 1997 .

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

[25]  Chongmin Song,et al.  The scaled boundary finite element method in structural dynamics , 2009 .

[26]  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 .

[27]  Satya N. Atluri,et al.  On the computation of mixed-mode K-factors for a dynamically propagating crack, using path-independent integrals J'k , 1984 .

[28]  Ean Tat Ooi,et al.  Modelling multiple cohesive crack propagation using a finite element―scaled boundary finite element coupled method , 2009 .

[29]  Hong Hao,et al.  Transient dynamic fracture analysis using scaled boundary finite element method: a frequency-domain approach , 2007 .

[30]  T. Nishioka,et al.  Path-Independent Integral and Moving Isoparametric Elements for Dynamic Crack Propagation. , 1984 .

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

[32]  Masahiro Kinoshita,et al.  Dynamic fracture-path prediction in impact fracture phenomena using moving finite element method based on Delaunay automatic mesh generation , 2001 .

[33]  Toshihisa Nishioka,et al.  Computational dynamic fracture mechanics , 1997 .

[34]  P. Fedelinski,et al.  Boundary element method in dynamic analysis of structures with cracks , 2004 .

[35]  Chongmin Song,et al.  A super‐element for crack analysis in the time domain , 2004 .

[36]  A. Deeks,et al.  A p‐hierarchical adaptive procedure for the scaled boundary finite element method , 2002 .

[37]  Prasanta K. Banerjee,et al.  Two-dimensional transient wave-propagation problems by time-domain BEM , 1990 .

[38]  W. W. King,et al.  Singularity-Element Simulation of Crack Propagation , 1977 .

[39]  S. Atluri,et al.  Numerical Modeling of Dynamic Crack Propagation in Finite Bodies, by Moving Singular Elements—Part 1: Formulation , 1980 .

[40]  Satya N. Atluri,et al.  Numerical analysis of dynamic crack propagation: Generation and prediction studies , 1982 .