Transformation acoustics and elastodynamics.

Abstract

The properties associated with acoustic metamaterials are usually related to the idea of spatial transformation. The acoustic magnifying hyperlens [Li et al. (2009)] and the acoustic cloak are two notable examples. The basic premise is that spatial deformation can be accommodated by changes in the material properties. This is fine as long as the material properties are mapped into new ones that are physically realistic. Often, however, the transformed material no longer lies within the original class of constitutive relations of linear acoustics. This talk will describe how acoustics and elastodynamics transform to produce new material behavior. The transformed acoustic material is not unique and can be, at one extreme, an anisotropic inertial fluid and, at the other, a pentamode material. Transformed elastic materials are even more general in their constitutive behavior. However, for SH waves in elasticity, the transformation implies another elastic material—in this case, just an orthotropic material. These ideas will be illustrated by application to cloaking of acoustic and elastic waves.