Recent interest in metamaterials has led to a renewed study of wave mechanics in different branches of physics. Elastodynamics involves a special intricacy, owing to a coupling between the volumetric and shear parts of the elastic waves. Through a study of in-plane waves traversing periodic laminates, we here show that this coupling can result with unusual energy transport. We find that the corresponding frequency spectrum contains modes which simultaneously attenuate and propagate, and demonstrate that these modes coalesce to purely propagating modes at exceptional points-a property that was recently reported in parity-time symmetric systems. We show that the laminate exhibits metamaterial features near these points, such as negative refraction, and beam steering and splitting. While negative refraction in laminates has been demonstrated before by considering pure shear waves impinging an interface with multiple layers, here we realize it for coupled waves impinging a simple single-layer interface. This feature, together with the appearance of exceptional points, are absent from the model problem of anti-plane shear waves which have no volumetric part, and hence from the mathematically identical electromagnetic waves. Our work further paves the way for applications such as asymmetric mode switches, by encircling exceptional points in a tangible, purely elastic apparatus.

Shmuel and Band [2016] discovered that all infinite band structures of waves at normal incidence in two-phase laminates are encapsulated in a compact universal manifold. We show that manifolds of higher dimensionality encapsulate the band structures of all multiphase laminates. We use these manifolds to determine the density of gaps in the spectrum, and prove it is invariant with respect to certain properties. We further demonstrate that these manifolds are useful for formulating optimization problems on the gaps width, for which we develop a simple bound. Using our theory, we numerically study the dependency of the gaps density and width on the impedance and number of phases. Finally, we show that in certain settings, our analysis applies to non-linear multiphase laminates, whose band diagram is tunable by finite pre-deformations. Through simple examples, we demonstrate how the universality of our representation is useful for characterizing this tunability in multiphase laminates.