Elastodynamic Transformation Cloaking for Non-Centrosymmetric Gradient Solids

TL;DR

This paper explores the theoretical possibility of elastodynamic cloaking in non-centrosymmetric gradient solids, analyzing the conditions under which cloaking can be achieved and identifying fundamental physical constraints.

Contribution

It extends the analysis of transformation cloaking to non-centrosymmetric gradient solids, demonstrating the persistent obstacle posed by angular momentum balance.

Findings

Cloaking in non-centrosymmetric solids faces similar angular momentum constraints as centrosymmetric cases.

The balance of angular momentum prevents perfect elastodynamic cloaking in these materials.

Theoretical analysis clarifies fundamental limitations of cloaking in complex elastic media.

Abstract

In this paper we investigate the possibility of elastodynamic transformation cloaking in bodies made of non-centrosymmetric gradient solids. The goal of transformation cloaking is to hide a hole from elastic disturbances in the sense that the mechanical response of a homogeneous and isotropic body with a hole covered by a cloak would be identical to that of the corresponding homogeneous and isotropic body outside the cloak. It is known that in the case of centrosymmetric gradient solids the balance of angular momentum is the obstruction to transformation cloaking. We will show that this is the case for non-centrosymmetric gradient solids as well.