Spectral analysis of the Neumann-Poincaré operator and characterization of the stress concentration in anti-plane elasticity

Giulio Ciraolo, Kihyun Yun, Habib Ammari, Hyeonbae Kang, Hyundae Lee

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43 Citazioni (Scopus)

Abstract

When holes or hard elastic inclusions are closely located, stress which is the gradient of the solution to the anti-plane elasticity equation can be arbitrarily large as the distance between two inclusions tends to zero. It is important to precisely characterize the blow-up of the gradient of such equation. In this paper we show that the blow-up of the gradient can be characterized by a singular function defined by the single layer potential of an eigenfunction corresponding to the eigenvalue 1/2 of a Neumann-Poincaré type operator defined on the boundaries of the inclusions. Bycomparing the singular function with the one corresponding to two disks osculatingto the inclusions, we quantitatively characterize the blow-up of the gradient in termsof explicit functions. In electrostatics, our results apply to the electric field, which is the gradient of the solution to the conductivity equation, in the case where perfectly conducting or insulating inclusions are closely located.
Lingua originaleEnglish
pagine (da-a)275-304
Numero di pagine30
RivistaArchive for Rational Mechanics and Analysis
Volume208
Stato di pubblicazionePublished - 2013

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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