A degenerate polar lattice for cloaking in full two-dimensional elastodynamics and statics

A lattice design of a cloak for full two-dimensional elasticity is suggested when the background continuum is isotropic with Lame parameters (lambda, mu) satisfying mu <= lambda. The lattice is polar in the sense that it elastically resists rotations; and is degenerate meaning it admits a stressless collapse mechanism. These characteristics are attained through the use of appropriately distributed restoring torques in conjunction with hinge-like spring-mass contacts. Thus, the lattice is proven to exhibit a rank-3 elasticity tensor lacking the minor symmetries. Accordingly, it rigorously adheres to the formin-variance requirements of the transformation method under the Brun-Guenneau-Movchan gauge. The cloak is numerically tested in statics and in dynamics under pressure and shear incident waves and shows satisfactory performance. Finally, a theoretical generalization extends the design to three dimensions and to arbitrarily anisotropic backgrounds so as to enable cloaking as well as other transformation-based static and dynamic field manipulation techniques in these cases.