Simple and effective mechanical cloaking

TL;DR

This paper presents a simple, theoretically perfect method for elastostatic mechanical cloaking of circular inclusions using three concentric isotropic layers, effective for all deformation modes and adaptable to arbitrary shapes.

Contribution

The authors introduce a universal cloaking scheme with three concentric layers that can hide any circular inclusion from all deformation modes, regardless of material stiffness.

Findings

Achieves near-perfect elastostatic cloaking with three concentric layers.

Cloaking method is effective for all deformation modes and inclusion stiffness.

Simulation confirms cloaking effectiveness and potential for composite material design.

Abstract

We show theoretically that essentially perfect elastostatic mechanical cloaking of a circular inclusion in a homogeneous surrounding medium can be achieved by means of a simple cloak comprising three concentric annuli, each formed of a homogeneous isotropic linear elastic material of prescribed shear modulus. Importantly, we find that the same combination of annuli will cloak any possible mode of imposed deformation or loading, for any randomly chosen admixture of imposed compression, pure shear and simple shear, without the need to re-design the cloak for different deformation modes. A full range of circular inclusions can be cloaked in this way, from soft to stiff. In consequence, we suggest that an inclusion of any arbitrary shape can also be cloaked, by first enveloping it in a stiff circle, then cloaking the combined structure with three annuli as described. Given that a single inclusion can be fully cloaked in this way, even at near field close to the cloaking perimeter, it also follows that multiple such neutral inclusions arranged with arbitrarily high packing fraction in a surrounding medium can also be cloaked. We confirm this by direct simulation. This indicates a possible route to fabricating composite materials with the same global mechanical response as a counterpart homogeneous material, and with uniform strain and stress fields outwith the cloaked inclusions.