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Elastic Invisibility in Three Dimensions: Neutral Inclusions and Low Frequency Transparency.

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Title: Elastic Invisibility in Three Dimensions: Neutral Inclusions and Low Frequency Transparency.
Authors: Charlton, Charlotte (AUTHOR), Parnell, William J1 (AUTHOR)
Source: Quarterly Journal of Mechanics & Applied Mathematics. May2026, Vol. 79 Issue 2, p1-22. 22p.
Subjects: Invisibility, Surface coatings, Scattering (Mathematics), Anisotropic crystals
Abstract: We address the topic of elastostatic invisibility, or cloaking, in three dimensions, where an inclusion is coated with some medium to ensure that it is invisible to imposed forces in the far-field. Typically this effect requires the coating to be an inhomogeneous and anisotropic material, with examples generated via transformation elastostatics, and often with unphysical properties. Such complex designs have limited applicability to the manufacture of real-world materials. In materials science and engineering, the neutral inclusion concept offers the more realistic aim of ensuring that coated inclusions are invisible to specified loading states. Here we demonstrate that it is possible to make a spherical inclusion invisible to any linear combination of hydrostatic and shear deformation by surrounding it with an appropriate spherically transversely isotropic coating. It is additionally shown that two isotropic layers can have an equivalent neutralising effect. Finally, we demonstrate the links with low frequency transparency by considering the dynamic analogue to the neutral inclusion setup at low frequency. In particular, it is shown that low frequency transparency, achieved by eliminating the leading order scattering coefficients, may fail to neutralise the leading order perturbed field local to the obstacle. [ABSTRACT FROM AUTHOR]
Copyright of Quarterly Journal of Mechanics & Applied Mathematics is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Elastic Invisibility in Three Dimensions: Neutral Inclusions and Low Frequency Transparency.
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  Data: <searchLink fieldCode="AR" term="%22Charlton%2C+Charlotte%22">Charlton, Charlotte</searchLink> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Parnell%2C+William+J%22">Parnell, William J</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Quarterly+Journal+of+Mechanics+%26+Applied+Mathematics%22">Quarterly Journal of Mechanics & Applied Mathematics</searchLink>. May2026, Vol. 79 Issue 2, p1-22. 22p.
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  Data: <searchLink fieldCode="DE" term="%22Invisibility%22">Invisibility</searchLink><br /><searchLink fieldCode="DE" term="%22Surface+coatings%22">Surface coatings</searchLink><br /><searchLink fieldCode="DE" term="%22Scattering+%28Mathematics%29%22">Scattering (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Anisotropic+crystals%22">Anisotropic crystals</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We address the topic of elastostatic invisibility, or cloaking, in three dimensions, where an inclusion is coated with some medium to ensure that it is invisible to imposed forces in the far-field. Typically this effect requires the coating to be an inhomogeneous and anisotropic material, with examples generated via transformation elastostatics, and often with unphysical properties. Such complex designs have limited applicability to the manufacture of real-world materials. In materials science and engineering, the neutral inclusion concept offers the more realistic aim of ensuring that coated inclusions are invisible to specified loading states. Here we demonstrate that it is possible to make a spherical inclusion invisible to any linear combination of hydrostatic and shear deformation by surrounding it with an appropriate spherically transversely isotropic coating. It is additionally shown that two isotropic layers can have an equivalent neutralising effect. Finally, we demonstrate the links with low frequency transparency by considering the dynamic analogue to the neutral inclusion setup at low frequency. In particular, it is shown that low frequency transparency, achieved by eliminating the leading order scattering coefficients, may fail to neutralise the leading order perturbed field local to the obstacle. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Quarterly Journal of Mechanics & Applied Mathematics is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1093/qjmam/hbag007
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 22
        StartPage: 1
    Subjects:
      – SubjectFull: Invisibility
        Type: general
      – SubjectFull: Surface coatings
        Type: general
      – SubjectFull: Scattering (Mathematics)
        Type: general
      – SubjectFull: Anisotropic crystals
        Type: general
    Titles:
      – TitleFull: Elastic Invisibility in Three Dimensions: Neutral Inclusions and Low Frequency Transparency.
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            NameFull: Charlton, Charlotte
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            NameFull: Parnell, William J
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              M: 05
              Text: May2026
              Type: published
              Y: 2026
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              Value: 79
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            – TitleFull: Quarterly Journal of Mechanics & Applied Mathematics
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