Nearly cloaking the elastic wave fields

Guanghui Hu, Hongyu LIU*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

In this work, we develop a general mathematical framework on regularized approximate cloaking of elastic waves governed by the Lamé system via the approach of transformation elastodynamics. Our study is rather comprehensive. We first provide a rigorous justification of the transformation elastodynamics. Based on the blow-up-a-point construction, elastic material tensors for a perfect cloak are derived and shown to possess singularities. In order to avoid the singular structure, we propose to regularize the blow-up-a-point construction to be the blow-up-a-small-region construction. However, it is shown that without incorporating a suitable lossy layer, the regularized construction would fail due to resonant inclusions. In order to defeat the failure of the lossless construction, a properly designed lossy layer is introduced into the regularized cloaking construction. We derive sharp asymptotic estimates in assessing the cloaking performance. The proposed cloaking scheme is capable of nearly cloaking an arbitrary content with a high accuracy.

Original languageEnglish
Pages (from-to)1045-1074
Number of pages30
JournalJournal des Mathematiques Pures et Appliquees
Volume104
Issue number6
DOIs
Publication statusPublished - Dec 2015

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • Asymptotic estimates
  • Elastic cloaking
  • Lamé system
  • Regularization
  • Transformation elastodynamics

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