Carpinteri, Alberto and Paggi, Marco
*Singular harmonic problems at a wedge vertex: mathematical analogies between elasticity, diffusion, electromagnetism, and fluid dynamics.*
Journal of Mechanics of Materials and Structures, 6 (1-4).
pp. 113-125.
ISSN 1559-3959
(2011)

## Abstract

Multimaterial wedges are frequently observed in composite materials. They consist of two or more sectors of dissimilar materials joined together, whose interfaces converge at the same vertex. Due to the mismatch in material properties such as Young’s modulus, thermal conductivity, dielectric permittivity, or magnetic permeability, these geometrical configurations can lead to singular fields at the junction vertex. This paper discusses mathematical analogies, focused on singular harmonic problems, between antiplane shear problem in elasticity due to mode III loading or torsion, the steady-state heat transfer problem, and the diffraction of waves in electromagnetism. In the case of a single material wedge, a mathematical analogy between elasticity and fluid dynamics is also outlined. The proposed unified mathematical formulation is particularly convenient for the identification of common types of singularities (power-law or logarithmic type), the definition of a standardized method to solve nonlinear eigenvalue problems, and the determination of common geometrical and material configurations allowing the relief or removal of different singularities.

Item Type: | Article |
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Identification Number: | 10.2140/jomms.2011.6.113 |

Uncontrolled Keywords: | Singularities, Multimaterial wedges, Elasticity, Diffusion, Electromagnetism, Fluid dynamics |

Subjects: | T Technology > TJ Mechanical engineering and machinery |

Research Area: | Computer Science and Applications |

Depositing User: | Prof Marco Paggi |

Date Deposited: | 02 Dec 2013 11:46 |

Last Modified: | 09 Oct 2014 09:20 |

URI: | http://eprints.imtlucca.it/id/eprint/1992 |

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