## Abstract

The solution to the elasticity problem in three-dimensional polyhedral domains in the vicinity of an edge around which the material properties depend on the angular angle is addressed. This asymptotic solution involves a family of eigenpairs and their shadows which are being computed by means of p-finite element methods. In particular the examples we give explicitly provide the asymptotic solution for cracks and V-notch edges and explore the eigenvalues as a function of the change in material properties in the angular direction. We demonstrate that the singular exponents may change considerably by changing the material properties variation in the angular direction. These eigenpairs are necessary to allow the extraction of the edge stress intensity functions.

Original language | English |
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Pages (from-to) | 2288-2308 |

Number of pages | 21 |

Journal | Mathematics and Mechanics of Solids |

Volume | 22 |

Issue number | 12 |

DOIs | |

State | Published - 1 Dec 2017 |

Externally published | Yes |

## Keywords

- Edge stress intensity functions
- composite materials
- elasticity
- fracture mechanics
- high order finite elements