New metamaterials with macroscopic behavior outside that of continuum elastodynamics

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.

14 pages, 4 figures

References in corpus (6)

• Optical Cloaking with Non-Magnetic Metamaterials
• Achieving transparency with plasmonic coatings
• Full-wave simulations of electromagnetic cloaking structures
• Calculation of material properties and ray tracing in transformation media
• Full-wave invisibility of active devices at all frequencies
• Three-dimensional electromagnetic metamaterials with non-Maxwellian effective fields

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• Extraordinary stiffness tunability through thermal expansion of nonlinear defect modes
• A unifying perspective on linear continuum equations prevalent in science. Part II: Canonical forms for time-harmonic equations
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• The homogenization of orthorhombic piezoelectric composites by the strong-property-fluctuation theory
• Willis elasticity from microcontinuum field theories: Asymptotics, microstructure-property relationships, and cloaking
• Discrete Transformation Elasticity: An Approach to Design Lattice-based Polar Metamaterials
• On the homogenization of orthotropic elastic composites by the strong-property-fluctuation theory
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