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Local microstructural heterogeneities of elastic metamaterials give rise to non-local macroscopic cross-coupling between stress-strain and momentum-velocity, known as Willis coupling. Recent advances have revealed that symmetry breaking in…
Bianisotropy is common in electromagnetics whenever a cross-coupling between electric and magnetic responses exists. However, the analogous concept for elastic waves in solids, termed as Willis coupling, is more challenging to observe. It…
Acoustic metamaterials are structures with exotic acoustic properties, having promising applications in acoustic beam steering, focusing, impedance matching, absorption and isolation. Recent work has shown that the efficiency of many…
Willis dynamic homogenization theory revealed that the effective linear momentum of elastic composites is coupled to their effective strain. % This result, which is partially due to asymmetry at the subwavelength scale, implies that…
Electromagnetic bi-anisotropy finds an analogy in acoustic metamaterial science as Willis coupling. Its impact and emergence in the field of elastodynamic metamaterials is not as well understood however, given the coupling between…
Analogous to electromagnetic bianisotropy, engineered piezoelectric metamaterials can possess electro-momentum coupling between the macroscopic momentum and electric stimuli. This indicates the applicability of piezoelectric metamaterials…
Willis materials are complex media characterized by four macroscopic material parameters, the conventional mass density, and bulk modulus and two additional Willis coupling terms, which have been shown to enable unsurpassed control over the…
Asymmetric piezoelectric composites exhibit coupling between their macroscopic linear momentum and electric field, a coupling that does not appear at the microscopic scale. This electromomentum coupling constitutes an additional knob to…
Electro-momentum coupling in piezoelectric metamaterials with broken inversion symmetry enables asymmetric elastic wave transport by linking macroscopic electric fields to momentum, an effect analogous to Willis coupling in elastic media. A…
Acoustic meta-atoms serve as the building blocks of metamaterials, with linear properties designed to achieve functions such as beam steering, cloaking and focusing. They have also been used to shape the characteristics of incident acoustic…
Acoustic bianisotropy, also known as the Willis parameter, expands the field of acoustics by providing nonconventional couplings between momentum and strain in constitutive relations. Sharing the common ground with electromagnetics, the…
Recent developments in the engineering of metamaterials have brought forth a myriad of mesmerizing mechanical properties that do not exist in ordinary solids. Among these, twisting metamaterials, acoustical chirality, or Willis coupling are…
In this paper we review the recent advances which have taken place in the understanding and applications of acoustic/elastic metamaterials. Metamaterials are artificially created composite materials which exhibit unusual properties which…
Piezoelectric materials have wide sensing and energy transduction applications due to their inherent coupling of mechanical deformation and electric field. Recent discoveries have revealed that asymmetric or heterogeneous microstructures of…
Metamaterials whose momentum is constitutively coupled with their strain show promise in wave manipulation for engineering purposes and are called Willis materials. They were discovered using an effective medium theory which shows that…
Metamaterials are artificial composite structures designed for controlling waves or fields, and exhibit interaction phenomena that are unexpected on the basis of their chemical constituents. These phenomena are encoded in effective material…
Willis coupling in acoustic materials defines the cross-coupling between strain and velocity, analogous to bianisotropic phenomena in electromagnetics. While these effects have been garnering significant attention in recent years, to date…
In an effective medium description of acoustic metamaterials, the Willis coupling plays the same role as the bianisotropy in electromagnetism. Willis media can be described by a constitutive matrix composed of the classical effective bulk…
Mechanical motion can break the symmetry in which sound travels in a medium, but significant non-reciprocity is typically achieved only for very large motion speeds. Here we combine moving media with zero-index acoustic propagation,…
We propose and verify experimentally a new concept for achieving strong nonlinear coupling between the electromagnetic and elastic properties in metamaterials. This coupling is provided through a novel degree of freedom in metamaterial…