New metamaterials with macroscopic behavior outside that of continuum elastodynamics

TL;DR

This paper introduces novel metamaterials exhibiting macroscopic behaviors that deviate from traditional continuum elastodynamics, with potential applications in elastic cloaking.

Contribution

It presents a new class of metamaterials where momentum density and stress have tailored dependencies, including symmetric stress and rotation-independent momentum.

Findings

Metamaterials with frequency-dependent properties

Symmetric stress and rotation-independent momentum density

Potential for elastic cloaking applications

Abstract

Metamaterials are constructed such that, for a narrow range of frequencies, the momentum density depends on the local displacement gradient, and the stress depends on the local velocity. In these models the momentum density generally depends not only on the strain, but also on the local rotation, and the stress is generally not symmetric. A variant is constructed for which, at a fixed frequency, the momentum density is independent of the local rotation (but still depends on the strain) and the stress is symmetric (but still depends on the velocity). Generalizations of these metamaterials may be useful in the design of elastic cloaking devices.