On Near-cloaking for Linear Elasticity

Richard Craster (1) , André Diatta (2) , Sébastien Guenneau (3) , Harsha Hutridurga (4)

1 Department of Mathematics [Imperial College London]
2 EPSILON - EPSILON
3 Abraham de Moivre
4 IIT Bombay - Indian Institute of Technology Bombay

We make precise some results on the cloaking of displacement fields in linear elasticity. In the spirit of transformation media theory, the transformed governing equations in Cosserat and Willis frameworks are shown to be equivalent to certain high contrast small defect problems for the usual Navier equations. We discuss near-cloaking for elasticity systems via a regularised transform and perform numerical experiments to illustrate our near-cloaking results. We also study the sharpness of the estimates from [H. Ammari, H. Kang, K. Kim and H. Lee, J. Diff. Eq. 254, 4446-4464 (2013)], wherein the convergence of the solutions to the transmission problems is investigated, when the Lamé parameters in the inclusion tend to extreme values. Both soft and hard inclusion limits are studied and we also touch upon the finite frequency case. Finally, we propose an approximate isotropic cloak algorithm for a symmetrized Cosserat cloak.

Domaines: Optique [physics.optics]

Richard Craster, André Diatta, Sébastien Guenneau, Harsha Hutridurga. On Near-cloaking for Linear Elasticity. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2021, 19 (2), pp.633-664. ⟨10.1137/20M1333201⟩. ⟨hal-03431816⟩