Active acoustic metamaterials incorporate electric circuit elements that input energy into an otherwise passive medium to aptly modulate the effective material properties. Here, we propose an active acoustic metamaterial with Willis coupling to drastically extend the tunability of the effective density and bulk modulus with the accessible parameter range enlarged by at least two orders of magnitude compared to that of a non-Willis metamaterial. Traditional active metamaterial designs are based on local resonances without considering the Willis coupling that limit their accessible effective material parameter range. Our design adopts a unit cell structure with two sensor-transducer pairs coupling the acoustic response on both sides of the metamaterial by detecting incident waves and driving active signals asymmetrically superimposed onto the passive response of the material. The Willis coupling results from feedback control circuits with unequal gains. These asymmetric feedback control circuits use Willis coupling to expand the accessible range of the effective density and bulk modulus of the metamaterial. The extreme effective material parameters realizable by the metamaterials will remarkably broaden their applications in biomedical imaging, noise control, and transformation acoustics-based cloaking.

Gels are composed of crosslinked polymer networks and solvent molecules imbibed into the networks. Gels are both ubiquitous in nature and important engineering materials widely used in many applications. Due to their biocompatibility, stimuli-responsiveness, and compliance, gels gain an edge over traditional materials, such as metals and composites in many modern engineering applications. In the past, the static and kinetic properties of gels have been widely studied. However, the dynamic properties of gels, particularly their structural damping, remain largely unknown even though gels are often under dynamic conditions in various applications. The literature of soft materials is lacking both damping data for hydrogels and a standard testing method to that end. This work reports experimentally identified structural damping data for a set of hydrogel samples via resonant vibration tests for the first bending mode. Beam-shaped samples of rectangular cross-section are clamped vertically at both ends and tested under linear base excitation. An analysis of the frequency response functions based on the Euler–Bernoulli beam theory is conducted to extract Young’s modulus and structural damping values. In the experiments, polyacrylamide gels of three different compositions and polydimethylsiloxane (PDMS) elastomers of two different compositions are prepared and tested. The remarkable result is that the hydrogels have 80% less damping than PDMS, even though hydrogels are an order of magnitude softer than PDMS. The molecular origins of the damping in hydrogels and PDMS are discussed. The low damping of gels may open new avenues of research and applications of soft materials in structural dynamics and wave propagation, such as metamaterials and topological insulators, among others.

Gels are composed of cross-linked polymer network and solvent. Gels are both ubiquitous in nature and widely applied in engineering applications. In this work, we develop a physics-based dynamic theory to investigate the tunable wave propagation properties of gels. Gels are soft and can generate large deformation. The constitutive relation takes account the coupled large deformation and diffusion of gels. The dynamic governing equations take account the relative motions between the polymer network and solvent, which leads to a pressure diffusion wave similar to the “slow pressure wave” in the classical Biot’s poroelastodynamics. It is different from the pressure wave in pure solid or pure liquid. The phase velocity, group velocity and attenuation coefficient are analyzed at different frequencies and propagating directions for both pressure wave and shear wave. We show that the wave propagation properties of gels are not only related to the material properties including the crosslink density and the interaction property between solvent and polymer, but also can be tuned by different mechanical loading conditions and chemical stimuli. It is also predicted that the constrained swollen gel exhibits anisotropic wave propagation properties, which leads to the splitting of the pressure wave and shear wave propagating through it. The theory provides a general frame for fundamental understanding and quantitative characterization of the dynamic behaviors of gels.