## Abstract

In this paper, the scattering of harmonic anti-plane shear waves by a finite crack in infinitely long strip is studied using the non-local theory. The Fourier transform is applied and a mixed boundary value problem is formulated. Then a set of dual integral equations is solved using the Schmidt method instead of the first or the second integral equation method. A one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress occurring at the crack tips. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the width of the strip and the lattice parameter.

Original language | English |
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Pages (from-to) | 328-336 |

Number of pages | 9 |

Journal | Acta Mechanica Solida Sinica |

Volume | 13 |

Issue number | 4 |

Publication status | Published - 2000 |

Externally published | Yes |

## Keywords

- Dual integral equation
- Elastic wave
- Non-local theory
- Schmidt method