Bianisotropy in passive acoustic metamaterials
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Metamaterials are composite materials whose dynamic microstructure results in macroscopically observable properties beyond those available in nature. The emergence of metamaterials has enabled unprecedented control of electromagnetic, elastodynamic, and acoustic wave propagation and has led to technologies including invisibility cloaks, super- and hyper-lenses, and subwavelength bandgaps. These effects are made possible through the hidden degrees of freedom afforded by the dynamic microstructure. Analytically, the macroscopically observed parameters are the result of a dynamic homogenization procedure using weighted field averages over a representative volume element of the composite. After performing the homogenization procedure, constitutive relations reveal the dependencies between macroscopic fields and metamaterial properties. Recent research has demonstrated that dynamic homogenization results in constitutive relations that are coupled, which is not the case for most traditional materials. This general effect is well-known in electromagnetism and is known as bianisotropy, but the analogous effect in elastodynamics and acoustics was discovered more recently and is also often referred to as Willis coupling. However, most current homogenization schemes are modeled to determine macroscopic properties in the same form as traditional materials and therefore do not account for coupled constitutive relations. Additionally in the absence of embedded sources, metamaterial parameters are non-unique, which allows for macroscopic descriptions that only include traditional parameters or traditional parameters and coupling parameters. For acoustic metamaterials, the traditional properties are density and compressibility. The additional coupling parameters result in macroscopic momentum density and volume strain fields that are coupled due to both being dependent on macroscopic acoustic particle velocity and pressure fields. This dissertation explores the analogs between bianisotropy in electromagnetism, elastodynamics, and acoustics and the consequences of neglecting these effects on the physical interpretation of acoustic metamaterial parameters. The analogs are used to provide a qualitative understanding of the origin of coupling parameters, and a multiple scattering homogenization procedure is derived to demonstrate coupling due to asymmetry and nonlocal effects. Additionally, the restrictions of causality, passivity, and reciprocity on acoustic metamaterial parameters are derived, and it is demonstrated that macroscopic descriptions that neglect bianisotropy in one-dimensional acoustic metamaterials do not in general satisfy these restrictions.