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Static elastic cloaking, low-frequency elastic wave transparency and neutral inclusions
New connections between static elastic cloaking, low-frequency elastic wave scattering and neutral inclusions (NIs) are established in the context of two-dimensional elasticity. A cylindrical core surrounded by a cylindrical shell is embedded in a uniform elastic matrix. Given the core and matrix pr...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Royal Society Publishing
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7482203/ https://www.ncbi.nlm.nih.gov/pubmed/32922148 http://dx.doi.org/10.1098/rspa.2019.0725 |
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author | Norris, Andrew N. Parnell, William J. |
author_facet | Norris, Andrew N. Parnell, William J. |
author_sort | Norris, Andrew N. |
collection | PubMed |
description | New connections between static elastic cloaking, low-frequency elastic wave scattering and neutral inclusions (NIs) are established in the context of two-dimensional elasticity. A cylindrical core surrounded by a cylindrical shell is embedded in a uniform elastic matrix. Given the core and matrix properties, we answer the questions of how to select the shell material such that (i) it acts as a static elastic cloak, and (ii) it eliminates low-frequency scattering of incident elastic waves. It is shown that static cloaking (i) requires an anisotropic shell, whereas scattering reduction (ii) can be satisfied more simply with isotropic materials. Implicit solutions for the shell material are obtained by considering the core–shell composite cylinder as a neutral elastic inclusion. Two types of NI are distinguished, weak and strong with the former equivalent to low-frequency transparency and the classical Christensen and Lo generalized self-consistent result for in-plane shear from 1979. Our introduction of the strong NI is an important extension of this result in that we show that standard anisotropic shells can act as perfect static cloaks, contrasting previous work that has employed ‘unphysical’ materials. The relationships between low-frequency transparency, static cloaking and NIs provide the material designer with options for achieving elastic cloaking in the quasi-static limit. |
format | Online Article Text |
id | pubmed-7482203 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | The Royal Society Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-74822032020-09-11 Static elastic cloaking, low-frequency elastic wave transparency and neutral inclusions Norris, Andrew N. Parnell, William J. Proc Math Phys Eng Sci Research Article New connections between static elastic cloaking, low-frequency elastic wave scattering and neutral inclusions (NIs) are established in the context of two-dimensional elasticity. A cylindrical core surrounded by a cylindrical shell is embedded in a uniform elastic matrix. Given the core and matrix properties, we answer the questions of how to select the shell material such that (i) it acts as a static elastic cloak, and (ii) it eliminates low-frequency scattering of incident elastic waves. It is shown that static cloaking (i) requires an anisotropic shell, whereas scattering reduction (ii) can be satisfied more simply with isotropic materials. Implicit solutions for the shell material are obtained by considering the core–shell composite cylinder as a neutral elastic inclusion. Two types of NI are distinguished, weak and strong with the former equivalent to low-frequency transparency and the classical Christensen and Lo generalized self-consistent result for in-plane shear from 1979. Our introduction of the strong NI is an important extension of this result in that we show that standard anisotropic shells can act as perfect static cloaks, contrasting previous work that has employed ‘unphysical’ materials. The relationships between low-frequency transparency, static cloaking and NIs provide the material designer with options for achieving elastic cloaking in the quasi-static limit. The Royal Society Publishing 2020-08 2020-08-05 /pmc/articles/PMC7482203/ /pubmed/32922148 http://dx.doi.org/10.1098/rspa.2019.0725 Text en © 2020 The Authors. http://creativecommons.org/licenses/by/4.0/ http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
spellingShingle | Research Article Norris, Andrew N. Parnell, William J. Static elastic cloaking, low-frequency elastic wave transparency and neutral inclusions |
title | Static elastic cloaking, low-frequency elastic wave transparency and neutral inclusions |
title_full | Static elastic cloaking, low-frequency elastic wave transparency and neutral inclusions |
title_fullStr | Static elastic cloaking, low-frequency elastic wave transparency and neutral inclusions |
title_full_unstemmed | Static elastic cloaking, low-frequency elastic wave transparency and neutral inclusions |
title_short | Static elastic cloaking, low-frequency elastic wave transparency and neutral inclusions |
title_sort | static elastic cloaking, low-frequency elastic wave transparency and neutral inclusions |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7482203/ https://www.ncbi.nlm.nih.gov/pubmed/32922148 http://dx.doi.org/10.1098/rspa.2019.0725 |
work_keys_str_mv | AT norrisandrewn staticelasticcloakinglowfrequencyelasticwavetransparencyandneutralinclusions AT parnellwilliamj staticelasticcloakinglowfrequencyelasticwavetransparencyandneutralinclusions |