## Abstract

The asymptotic solution in the vicinity of a crack front in a three-dimensional (3-D) elastic domain is provided explicitly following the general framework in M. Costabel, M. Dauge and Z. Yosibash, 2004, SIAM Journal of Mathematical Analysis, 35(5), 1177-1202. Using it, we show analyticall y for several fully 3-D displacement fields (which are neither plane strain nor plane stress) that the pointwise path-area J_{X1}-integral in 3-D is path-independent. We then demonstrate by numerical examples, employing p-finite element methods, that good numerical approximations of the path-area J_{X1}-integral may be achieved which indeed show path independency. We also show that computation of the path part of the J_{X1} on a plane perpendicular to the crack front is path dependent. However, one may still use this path integral computed at several radii, followed by the application of Richardson's extrapolation technique (as R → 0) to obtain a good estimate for J_{X1}-integral.

Original language | English |
---|---|

Pages (from-to) | 1-36 |

Number of pages | 36 |

Journal | International Journal of Fracture |

Volume | 136 |

Issue number | 1-4 |

DOIs | |

State | Published - Nov 2005 |

Externally published | Yes |

## Keywords

- Edge stress intensity functions
- High order finite elements
- J -integral