One emerging research area within the fields of acoustic and elastic metamaterials involves designing subwavelength structures that display elastic instabilities in order to generate an effective medium response that is strongly nonlinear. To capture the overall frequency-dependent and dispersive macroscopic response of such heterogeneous media with subwavelength heterogeneities, a theoretical framework is developed that accounts for higher-order stiffnesses of a resonant, nonlinear inclusion that varies with a macroscopic pre-strain, and the inherent inertia associated with an inclusion embedded in a nearly incompressible elastic matrix material. Such a model can be used to study varying macroscopic material properties as a function of both frequency and pre-strain and the activation of such microscale instabilities due to an external, macroscopic loading, as demonstrated with a buckling metamaterial inclusion that is of interest due to its tunable and tailorable nature. The dynamic results obtained are consistent with similar static behavior reported in the literature for structures with elastic instabilities.

Efficient control over elastic wave transmission is often critical in the design of architected materials. In this work, lattices that achieve buckling induced band gaps are designed with spatially varying material properties to leverage both effects for enhanced wave control. Each unit cell exhibits a large shape change when subjected to an external activation. Unit cells with discrete material properties are then arranged in different spatial configurations. Numerical simulations for transmission through the example structures demonstrate both bandgap widening due to different material properties in adjacent unit cells and switching at different deformation states.

In this work, we explore switchable acoustic scattering from underwater particles via instability-induced internal pattern transformation in the 50 kHz–80 kHz frequency range. Our wavelength scale aqueous scatterer is designed based on modeling using the finite element method for a square lattice of air-filled voids within a shape memory polymer and is directly 3D printed. The structure undergoes a buckling transformation when subjected to an external deformation while simultaneously being heated. Through computational and experimental results, we demonstrate that the deformation state change leads to programmable acoustic transparency, or opacity, for the scattering particle. Underwater propagation experiments resolved in the near field illustrate that the switchable acoustic characteristics are frozen in the structure with rapid cooling after compression, and the initial acoustic state can be automatically recovered through reheating.

Additive manufacturing has expanded greatly in recent years with the promise of being able to create complex and custom structures at will. Enhanced control over the microstructure properties, such as percent porosity, is valuable to the acoustic design of materials. In this work, aluminum foams are fabricated using a modified powder bed fusion method, which enables voxel-by-voxel printing of structures ranging from fully dense to approximately 50% porosity. To understand the acoustic response, samples are measured in an acoustic impedance tube and characterized with the Johnson–Champoux–Allard–Lafarge model for rigid-frame foams. Bayesian statistical inversion of the model parameters is performed to assess the applicability of commonly employed measurement and modeling methods for traditional foams to the additively manufactured, low porosity aluminum foams. This preliminary characterization provides insights into how emerging voxel-by-voxel additive manufacturing approaches could be used to fabricate acoustic metal foams and what could be learned about the microstructure using traditional measurement and analysis techniques.

Non-periodic arrangements of inclusions with incremental linear negative stiffness embedded within a host material offer the ability to achieve unique and useful material properties on the macroscale. In an effort to study such types of inclusions, the present work develops a time-*