Anomalous wave polarization through a 3D periodic auxetic lattice

Abstract

Solid media supports both longitudinal and shear wave polarizations, providing a rich platform for designing phononic materials with prescribed wave filtering, engineered mode conversions, negative refraction, and other unique properties. While longitudinal waves almost always propagate at a faster velocity than shear waves in natural materials, tailoring the polarization of the faster wave velocity could enable unique control over wave propagation properties. Here, we present a three-dimensional periodic “bowtie” lattice that exhibits a shift in the faster wave polarization from the quasi-longitudinal to quasi-transverse wave in an anisotropic plane. We observe that this shift, termed “anomalous wave polarization”, is possible when the lattice behaves auxetically. Using the finite element method, we show that the wave polarizations in the bowtie lattice depend on certain geometric parameters and the wave propagation direction. We use wave velocity information to evaluate the lattice effective properties using the Bloch-wave homogenization approach and confirm the required elastic condition for the polarization anomaly in an anisotropic plane. We also emphasize the importance of identifying the wave polarization along with the wave velocity classification for lattice effective property evaluation. This lattice behavior will be useful for designing mode-converting metamaterials that have potential application in non-destructive testing and bio-medical ultrasounds.Solid media supports both longitudinal and shear wave polarizations, providing a rich platform for designing phononic materials with prescribed wave filtering, engineered mode conversions, negative refraction, and other unique properties. While longitudinal waves almost always propagate at a faster velocity than shear waves in natural materials, tailoring the polarization of the faster wave velocity could enable unique control over wave propagation properties. Here, we present a three-dimensional periodic “bowtie” lattice that exhibits a shift in the faster wave polarization from the quasi-longitudinal to quasi-transverse wave in an anisotropic plane. We observe that this shift, termed “anomalous wave polarization”, is possible when the lattice behaves auxetically. Using the finite element method, we show that the wave polarizations in the bowtie lattice depend on certain geometric parameters and the wave propagation direction. We use wave velocity information to evaluate the lattice effective properties ...