Department of Mathematics
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.
Asymptotic estimates, Elastic cloaking, Lamé system, Regularization, Transformation elastodynamics
Source Publication Title
Journal de Mathématiques Pures et Appliquées
Copyright © 2015 Elsevier Masson SAS. All rights reserved.
The work of G. Hu was financed by the German Research Foundation (DFG) under Grant No. HU 2111/1-2. The work of H. Liu was supported by the Hong Kong RGC General Research Fund No. 12302415, and the FRG grants of Hong Kong Baptist University, No. FRG1/14-15/009 and No. FRG2/14-15/033, and the NSFC grant No. 11371115.
Link to Publisher's Edition
Hu, G., & Liu, H. (2015). Nearly cloaking the elastic wave fields. Journal de Mathématiques Pures et Appliquées, 104 (6), 1045-1074. https://doi.org/10.1016/j.matpur.2015.07.004