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Reflection and refraction of rays in pre-stressed solids

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Abstract

Rays in viscoelastic, pre-stressed solids are considered. The eikonal equation and the transport equation are derived for both transverse and longitudinal polarizations. The analogue of the standard Snell's law is established. Then the amplitudes of reflected and transmitted rays are determined. The pre-stress is shown to affect the geometry of reflection-refraction processes and the amplitudes of the rays emanating from the interface. Pre-stress effects are also found on traction-free surfaces.

Sommario

Si considerano raggi in solidi viscoelastici soggetti ad uno stress iniziale. L'equazione dell'iconale e l'equazione del trasporto sono dedotte sia per polarizzazione trasversale, sia per polarizzazione longitudinale. Stabilita la forma appropriata della legge di Snell, si determinano le ampiezze dei raggi riflessi e trasmessi. Si mostra che lo stress iniziale interviene sia negli angoli sia nelle ampiezze dei raggi reflessi e trasmessi. Effetti dello stress iniziale si presentano persino nel caso di riflessione sulla superficie libera di un semispazio.

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Caviglia, G., Morro, A. Reflection and refraction of rays in pre-stressed solids. Meccanica 27, 47–53 (1992). https://doi.org/10.1007/BF00453002

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Key words

  • Reflection
  • Refraction
  • Rays
  • Pre-stress
  • Solids