Elastic cloaking theory
Abstract
The transformation theory of optics and acoustics is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to nonunique 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. (2006). 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2011
 arXiv:
 arXiv:1103.6045
 Bibcode:
 2011arXiv1103.6045N
 Keywords:

 Condensed Matter  Materials Science
 EPrint:
 24 pages