### Abstract

The main objective of this work is to prove that, with the Dugdale model, the small size defects, comparatively to the material characteristic length, are practically without influence on the limit load of structures. For that, we treat the case of a crack in a semi-infinite plane under anti-plane shear loading. Using integral transforms, the elasticity equations are converted analytically into a singular integral equation. The singular integral equation is solved numerically using Chebychev polynomials. Special care is needed to take into account the presence of jump discontinuities in the loading distribution along the crack lips.

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

Pages (from-to) | 41-55 |

Number of pages | 15 |

Journal | Continuum Mechanics and Thermodynamics |

Volume | 21 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jun 2009 |

Externally published | Yes |

### Fingerprint

### Keywords

- Chebychev polynomials
- Dugdale's model
- Fracture
- Singular integral equation
- Size effects

### ASJC Scopus subject areas

- Mechanics of Materials
- Materials Science(all)
- Physics and Astronomy(all)

### Cite this

*Continuum Mechanics and Thermodynamics*,

*21*(1), 41-55. https://doi.org/10.1007/s00161-009-0098-0

**Study of size effects in the Dugdale model through the case of a crack in a semi-infinite plane under anti-plane shear loading.** / Ferdjani, H.; Abdelmoula, R.; Marigo, J. J.; El-Borgi, Sami.

Research output: Contribution to journal › Article

*Continuum Mechanics and Thermodynamics*, vol. 21, no. 1, pp. 41-55. https://doi.org/10.1007/s00161-009-0098-0

}

TY - JOUR

T1 - Study of size effects in the Dugdale model through the case of a crack in a semi-infinite plane under anti-plane shear loading

AU - Ferdjani, H.

AU - Abdelmoula, R.

AU - Marigo, J. J.

AU - El-Borgi, Sami

PY - 2009/6

Y1 - 2009/6

N2 - The main objective of this work is to prove that, with the Dugdale model, the small size defects, comparatively to the material characteristic length, are practically without influence on the limit load of structures. For that, we treat the case of a crack in a semi-infinite plane under anti-plane shear loading. Using integral transforms, the elasticity equations are converted analytically into a singular integral equation. The singular integral equation is solved numerically using Chebychev polynomials. Special care is needed to take into account the presence of jump discontinuities in the loading distribution along the crack lips.

AB - The main objective of this work is to prove that, with the Dugdale model, the small size defects, comparatively to the material characteristic length, are practically without influence on the limit load of structures. For that, we treat the case of a crack in a semi-infinite plane under anti-plane shear loading. Using integral transforms, the elasticity equations are converted analytically into a singular integral equation. The singular integral equation is solved numerically using Chebychev polynomials. Special care is needed to take into account the presence of jump discontinuities in the loading distribution along the crack lips.

KW - Chebychev polynomials

KW - Dugdale's model

KW - Fracture

KW - Singular integral equation

KW - Size effects

UR - http://www.scopus.com/inward/record.url?scp=67650427390&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67650427390&partnerID=8YFLogxK

U2 - 10.1007/s00161-009-0098-0

DO - 10.1007/s00161-009-0098-0

M3 - Article

AN - SCOPUS:67650427390

VL - 21

SP - 41

EP - 55

JO - Continuum Mechanics and Thermodynamics

JF - Continuum Mechanics and Thermodynamics

SN - 0935-1175

IS - 1

ER -