Elastic cloaking theory
By Andrew N. Norris, A. Shuvalov. 2011
253 citations recorded by the source corpus.
Transformation theory is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by selection of the matrix relating displacements in the two descriptions. This gauge matrix can be chosen to make the transformed density isotropic for any transformation although the stress in the transformed material is not generally symmetric. Symmetric stress is obtained only if the gauge matrix is identical to the transformation matrix, in agreement with Milton et al. [1]. The elastic transformation theory is applied to the case of cylindrical anisotropy. The equations of motion for the transformed material with isotropic density are expressed in Stroh format, suitable for modeling cylindrical elastic cloaking. It is shown that there is a preferred approximate material with symmetric stress that could be a useful candidate for making cylindrical elastic cloaking devices.
Subfields: Atomic and Molecular Physics, and Optics, Biomedical Engineering, Oceanography
View Paper: https://www.semanticscholar.org/paper/a77012bb86a08d6c03e0f921a1f7171edd90fc3c
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In Atomic and Molecular Physics, and Optics
In Biomedical Engineering
- St'ephane Brul'e
- Stefan Enoch
- Sébastien Guenneau
- V. monchiet
- Ankit Srivastava
- Julien Yvonnet
- Nicolas Auffray
In Oceanography
Citations in the corpus
- Elastic metamaterials and dynamic homogenization: a review (2014, methodology): “This approach to designing cloaks has been applied to electromagnetic waves [12–16], acoustic waves [17], and elastic waves [18,19].”
- Computational second-order homogenization of materials with effective anisotropic strain-gradient behavior (2020, background): “Non-standard elastodynamics properties such as, for instance, the cloaking effect, are at the very beginning of the studies of what is presently known as metamaterials [43,47,41].”
- Emergence of seismic metamaterials: Current state and future perspectives (2017, background): “Localized resonant structures for elastic waves propagating within three-dimensional cubic arrays of thin coated spheres [26] and fluid filled Helmholtz resonators [27] paved the way towards acoustic analogues of electromagnetic metamaterials ([28] and [29]), including elastic cloaks ([30] to [32]).”