Hyperelastic antiplane ground cloaking

TL;DR

This paper investigates the use of hyperelastic materials, especially Arruda-Boyce, for antiplane ground cloaking, demonstrating their potential to manipulate elastic waves and achieve cloaking effects through finite element simulations.

Contribution

It explores hyperelastic materials beyond neo-Hookean models for ground cloaking, highlighting Arruda-Boyce as a promising candidate for elastic wave manipulation.

Findings

Neo-Hookean medium achieves perfect cloaking.

Arruda-Boyce material shows excellent cloaking performance.

Mooney-Rivlin material is less effective for AGC.

Abstract

Hyperelastic materials possess the appealing property that they may be employed as elastic wave manipulation devices and cloaks by imposing pre-deformation. They provide an alternative to microstructured metamaterials and can be used in a reconfigurable manner. Previous studies indicate that exact elastodynamic invariance to pre-deformation holds only for neo-Hookean solids in the antiplane wave scenario and the semi-linear material in the in-plane compressional/shear wave context. Furthermore, although ground cloaks have been considered in the acoustic context they have not yet been discussed for elastodynamics, either by employing microstructured cloaks or hyperelastic cloaks. This work therefore aims at exploring the possibility of employing a range of hyperelastic materials for use as antiplane ground cloaks (AGCs). The use of the popular incompressible Arruda-Boyce and Mooney-Rivlin nonlinear materials is explored. The scattering problem associated with the AGC is simulated via finite element analysis where the cloaked region is formed by an indentation of the surface. Results demonstrate that the neo-Hookean medium can be used to generate a perfect hyperelastic AGC as should be expected. Furthermore, although the AGC performance of the Mooney-Rivlin material is not particularly satisfactory, it is shown that the Arruda-Boyce medium is an excellent candidate material for this purpose.