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An inverse nano-cavity/-inhomogeneity problem with surface/interface effects in terahertz frequency range

Shodja, H. M ; Sharif University of Technology | 2023

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  1. Type of Document: Article
  2. DOI: 10.1016/j.mechmat.2023.104562
  3. Publisher: Elsevier B.V , 2023
  4. Abstract:
  5. In nondestructive evaluation, the maximum wavelength of the incident wave must be smaller than twice the perceptible obstacle size. Hence, in order to be able to detect a nanosize fiber of radius about a few nanometer, the frequency of the incident elastic wave should be in the order of 1012 Hz, i.e., in the terahertz frequency range. The present work addresses the possibility of application of elastic waves in terahertz frequency range to detect embedded circular nanosize inhomogeneity or nanocavity for which, respectively, the interface and surface effects are remarkable. Traditionally, singular sources method (SSM) and linear sampling method (LSM) have been utilized to treat inverse problems in the context of classical elasticity theory, where the surface/interface effects are not important. In the present paper these methods are extended to operate in the mathematical framework of surface/interface elasticity theory, suitable for capturing the surface/interface effects. In this framework the boundary conditions in contrast to the common Dirichlet and Neumann types involve the second derivative of the displacement field. The validity and uniqueness of the extended LSM and SSM in this framework will be established. An exact analysis emphasizing the importance of the consideration of surface/interface effects will also be given for the direct problem of SH waves scattering. In this work, the scatterer will be reconstructed solely based on data from the incident waves and the far-field pattern. Using the proposed theory, the size and location of the embedded nano-size cavity and nano-size inhomogeneity are detected. The surface effects of a nano-size cavity within a silver plate are more significant than the copper–silver interface effects in the case of a nano-size copper inhomogeneity embedded in a silver plate. © 2023 Elsevier Ltd
  6. Keywords:
  7. Inverse scattering ; Nano-size scatterer ; Non-standard boundary/interface conditions ; Surface/interface effect ; Terahertz frequency
  8. Source: Mechanics of Materials ; Volume 178 , 2023 ; 01676636 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S016766362300008X