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Abstract In solid state physics, a bandgap (BG) refers to a range of energies where no electronic states can exist. This concept was extended to classical waves, spawning the entire fields of photonic and phononic crystals where BGs are frequency (or wavelength) intervals where wave propagation is prohibited. For elastic waves, BGs are found in periodically alternating mechanical properties (i.e., stiffness and density). This gives birth to phononic crystals and later elastic metamaterials that have enabled unprecedented functionalities for a wide range of applications. Planar metamaterials are built for vibration shielding, while a myriad of works focus on integrating phononic crystals in microsystems for filtering, waveguiding, and dynamical strain energy confinement in optomechanical systems. Furthermore, the past decade has witnessed the rise of topological insulators, which leads to the creation of elastodynamic analogs of topological insulators for robust manipulation of mechanical waves. Meanwhile, additive manufacturing has enabled the realization of 3D architected elastic metamaterials, which extends their functionalities. This review aims to comprehensively delineate the rich physical background and the state‐of‐the art in elastic metamaterials and phononic crystals that possess engineered BGs for different functionalities and applications, and to provide a roadmap for future directions of these manmade materials. 

Advances in data-driven design and additive manufacturing have substantially accelerated the development of truss metamaterials—three-dimensional truss networks—offering exceptional mechanical properties at a fraction of the weight of conventional solids. While existing design approaches can generate metamaterials with target linear properties, such as elasticity, they struggle to capture complex nonlinear behaviours and to incorporate geometric and manufacturing constraints—including defects—crucial for engineering applications. Here we present GraphMetaMat, an autoregressive graph-based framework capable of designing three-dimensional truss metamaterials with programmable nonlinear responses, originating from hard-to-capture physics such as buckling, frictional contact and wave propagation, along with arbitrary geometric constraints and defect tolerance. Integrating graph neural networks, physics biases, imitation learning, reinforcement learning and tree search, we show that GraphMetaMat can target stress–strain curves across four orders of magnitude and vibration transmission responses with varying attenuation gaps, unattainable by previous methods. We further demonstrate the use of GraphMetaMat for the inverse design of novel material topologies with tailorable high-energy absorption and vibration damping that outperform existing polymeric foams and phononic crystals, potentially suitable for protective equipment and electric vehicles. This work sets the stage for the automatic design of manufacturable, defect-tolerant materials with on-demand functionalities. 

Architected metamaterials have emerged as a central topic in materials science and mechanics, thanks to the rapid development of additive manufacturing techniques, which have enabled artificial materials with outstanding mechanical properties. This Letter seeks to investigate the elastodynamic behavior of octet truss lattices as an important type of architected metamaterials for high effective strength and vibration shielding. We design, fabricate, and experimentally characterize three types of octet truss structures, including two homogenous structures with either thin or thick struts and one hybrid structure with alternating strut thickness. High elastic wave transmission rate is observed for the lattice with thick struts, while strong vibration mitigation is captured from the homogenous octet truss structure with thin struts as well as the hybrid octet truss lattice, though the underlying mechanisms for attenuation are fundamentally different (viscoelasticity induced dampening vs bandgaps). Compressional tests are also conducted to evaluate the effective stiffness of the three lattices. This study could open an avenue toward multifunctional architected metamaterials for vibration shielding with high mechanical strength.