Willis Coupling in Acoustic Metamaterials

date October 7, 2016
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Friday, October 7, 2016
4:00 p.m. in ETC 4.150

Michael B. Muhlestein
Applied Research Laboratories
The University of Texas at Austin

Acoustic metamaterials (AMM) are deeply subwavelength acoustic structures which have been engineered to exhibit specific, often exotic, material properties. Material properties are related to field variables through constitutive equations, such as Hooke’s law, where the pressure and strain are related through a material property, the bulk modulus. Another common constitutive equation is the definition of momentum density in terms of the particle velocity and the material property of mass density. While the behavior of most AMM structures may be fully described by homogenizing the effect of subwavelength heterogeneities using effective bulk modulus and mass density, this is not always the case. Specifically, Willis (Wave Motion, 1981) showed that in a general heterogeneous elastic medium there is an additional material property which couples the constitutive relations for the momentum density and stress fields. This talk first discusses the physical origin of Willis coupling in one-dimensional materials based on asymmetric microstructure. An examination of the physical behavior leads to a method for predicting Willis material properties for a known one-dimensional microstructure. A method for determining Willis material properties from an experiment based on a plane-wave impedance tube is also presented, and results from in-air tests are compared with theoretical predictions and shown to be in strong agreement. This experiment represents the first known experimental evidence of Willis coupling. Finally, with an eye toward future applications, a homogenization method accounting for coupled inclusions in an elastic matrix is presented.