Experimental evidence of Willis coupling in a one-dimensional effective material element

Abstract

The primary objective of acoustic metamaterial research is to design subwavelength systems that behave as effective materials with novel acoustical properties. One such property couples the stress–strain and the momentum–velocity relations. This response is analogous to bianisotropy in electromagnetism, is absent from common materials, and is often referred to as Willis coupling after J.R., Willis, who first described it in the context of the dynamic response of heterogeneous elastic media. This work presents two principal results: first, experimental and theoretical demonstrations, illustrating that Willis properties are required to obtain physically meaningful effective material properties resulting solely from local behaviour of an asymmetric one-dimensional isolated element and, second, an experimental procedure to extract the effective material properties from a one-dimensional isolated element. The measured material properties are in very good agreement with theoretical predictions and thus provide improved understanding of the physical mechanisms leading to Willis coupling in acoustic metamaterials.

Symmetry breaking creates electro-momentum coupling in piezoelectric metamaterials

“…Therefore, they capture a new mechanism that can be employed for rectifying mechanical waves by modulation of external stimuli. We expect that future studies will show that extraordinary wave response such as asymmetric reflections and unidirectional transmission are modeled by the new couplings [42], analogously to Willis coupling [28,[32][33][34]. These kind of results are to be guided by theoretical analyses based upon proper homogenization schemes [25].…”

“…A series of theoretical studies were carried out to characterize Willis coupling and understand its physical origins [18][19][20][21][22][23][24][25][26]. Guided by accompanying predictions that Willis coupling is connected with unusual phenomena such as asymmetric reflections and unidirectional transmission, recent experimental realizations of Willis metamaterials that demonstrate these phenomena were reported [27][28][29][30][31][32][33][34][35]. To date, these investigations were limited to metamaterials that are deformable only by mechanical forces.…”

Origins of Willis coupling and acoustic bianisotropy in acoustic metamaterials through source-driven homogenization

“…Their demonstrations provide the first experimental evidence of acoustic bianisotropy and were inspired by the analogs to bianisotropy in electromagnetism. The experimental demonstrations were recently explained in terms of Willis coupling by Muhlestein et al 50 who provided detailed theoretical and experimental evidence of Willis coupling in a small asymmetric metamaterial sample. Also independently, Shui et al 32 demonstrated nonreciprocal coupling for elastic waves using a layered medium with time-varying properties, which appears to be analogous to nonreciprocal coupling κ nr in electromagnetism, though it was not described in this manner.…”

“…Therefore, the parameters determined using transmission line techniques and reflection/transmission measurements are not effective or equivalent parameters, as defined in this work, but are Bloch parameters relating the fields at the boundary of a unit cell defined by a transmission matrix 64 or measurement sample. 50,65 As Bloch parameters do not relate effective fields but instead microscopic fields at a point, they cannot account for nonlocal effects, and will not generally satisfy restrictions based on causality, Eq. (7).…”

Experimental Realization of Acoustic Bianisotropic Gratings

“…Bianisotropic properties were observed in electromagnetism where a coupling tensor that relates electric and magnetic fields with monopolar and dipolar moments in the scattered waves [22]. Acoustic bianisotropic materials couple the pressure and local particle velocity fields with monopole and dipole scattering resulting in asymmetric wave propagations [23][24][25][26][27][28][29][30]. The bianisotropic material was used as an effective sound barrier [31].…”