## Abstract

We consider Casal's strain gradient elasticity with two material lengths l, l′ associated with volumetric and surface energies, respectively. For a Mode III finite crack we formulate a hypersingular integrodifferential equation for the crack slope supplemented with the natural cracktip conditions. The full-field solution is then expressed in terms of the crack profile and the Green function, which is obtained explicitly. For l′ = 0, we obtain a closed form solution for the crack profile. The case of small l′ is shown to be a regular perturbation. The question of convergence, as l, l′ → 0, is studied in detail both analytically and numerically.

Original language | English (US) |
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Pages (from-to) | 1066-1091 |

Number of pages | 26 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 62 |

Issue number | 3 |

DOIs | |

State | Published - 2002 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Applied Mathematics

## Keywords

- Hypersingular integral equation
- Strain-gradient elasticity