Nonlinear pre-stress for cloaking from antiplane elastic waves

TL;DR

This paper proposes a novel cloaking method using elastic pre-stress in nonlinear elastic materials to bend waves around objects, potentially simplifying cloaking devices by avoiding complex metamaterials.

Contribution

It introduces a new cloaking approach based on pre-stress in nonlinear elastic materials, eliminating the need for inhomogeneous anisotropic metamaterials.

Findings

Pre-stress induces inhomogeneous stress fields that bend waves around objects.

The wave equation in pre-stressed media mimics that in complex metamaterials.

Adjustable pre-stress allows cloaking of objects of various sizes and shapes.

Abstract

A theory is presented showing that cloaking of objects from antiplane elastic waves can be achieved by elastic pre-stress of a neo-Hookean nonlinear elastic material. This approach would appear to eliminate the requirement of metamaterials with inhomogeneous anisotropic shear moduli and density. Waves in the pre-stressed medium are bent around the cloaked region by inducing inhomogeneous stress fields via pre-stress. The equation governing antiplane waves in the pre-stressed medium is equivalent to the antiplane equation in an unstressed medium with inhomogeneous and anisotropic shear modulus and isotropic scalar mass density. Note however that these properties are induced naturally by the pre-stress. Since the magnitude of pre-stress can be altered at will, this enables objects of varying size and shape to be cloaked by placing them inside the fluid-filled deformed cavity region.