### Abstract

A Mode-III crack problem in a functionally graded material modeled by anisotropic strain-gradient elasticity theory is solved by the integral equation method. The gradient elasticity theory has two material characteristic lengths ℓand ℓ, which are responsible for volumetric and surface strain-gradient terms, respectively. The governing differential equation of the problem is derived assuming that the shear modulus G is a function of x, i.e., G=G(x)=G_{0}^{eβx}, where G_{0} and βare material constants. A hypersingular integro-differential equation is derived and discretized by means of the collocation method and a Chebyshev polynomial expansion. Numerical results are given in terms of the crack opening displacements, strains, and stresses with various combinations of the parameters ℓ, ℓ, and β. Formulas for the stress intensity factors, K _{III}, are derived and numerical results are provided.

Original language | English (US) |
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Pages (from-to) | 610151-6101511 |

Number of pages | 5491361 |

Journal | Journal of Applied Mechanics, Transactions ASME |

Volume | 75 |

Issue number | 6 |

DOIs | |

State | Published - Nov 1 2008 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

### Cite this

*Journal of Applied Mechanics, Transactions ASME*,

*75*(6), 610151-6101511. https://doi.org/10.1115/1.2912933