Elastic cloaking theory

• Published in: Wave motion 2011-09, Vol.48 (6), p.525-538
• Main Authors: Norris, A.N., Shuvalov, A.L.
• Format: Article
• Language: English
• Subjects: Acoustics; Cloaking; Cosserat elasticity; Density; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Gages; Gauges; Materials selection; Mathematical analysis; Mathematical models; Physics; Solid mechanics; Static elasticity (thermoelasticity...); Stresses; Structural acoustics and vibration; Structural and continuum mechanics; Transformation theory; Transformations; Willis equations
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2011.03.002

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. ► It is shown that the equations of linear anisotropic elasticity can be transformed into either material equations with symmetric or nonsymmetric stress. ► Symmetric stress is obtained only if a quantity relating displacement before and after transformation, the gauge matrix, is chosen to be equal to the transformation matrix. ► It is also shown that there is a preferred approximate material with symmetric stress that could be a useful candidate for making cylindrical elastic cloaking devices.