Harnessing von Kármán nonlinearity for load-adaptive metadampers

Abstract

Mechanical metamaterials offer unprecedented control over wave propagation through engineered microstructures. Yet their behaviour under geometric nonlinearity and damping remains insufficiently explored. This study investigates how von Kármán nonlinearity, combined with damping, can be harnessed as a design mechanism to dynamically tune wave characteristics in periodic lattice-based metamaterials. Through nonlinear finite element simulations on regular and re-entrant hexagonal lattices subjected to distributed compressive loads, we examine changes in their band gap behaviour and deformation responses. By incorporating quadratic eigenvalue solutions, transmission losses, and iso-frequency maps, the research shows that geometric nonlinearity and damping fundamentally alter wave propagation. Under increased loading, existing band gaps diminish while new ones emerge at higher frequencies. This is accompanied by a systematic leftward and downward shift in band gap evolution due to nonlinearity and damping, respectively. Metadamping arises from the interplay between lattice geometry, nonlinearity, and damping configuration, enabling frequency-selective and load-adaptive dissipation. The study also shows that the apparent Poisson-like parameter displays nonlinear dependence on loading, reflecting microstructural deformations, and serving as an order parameter to characterise and tune auxetic behaviour in lattice metamaterials. Importantly, the applicability of Bloch’s theorem is validated in geometrically nonlinear and damped systems, extending its relevance to deformed metamaterial structures. These insights demonstrate that geometric nonlinearity and damping, rather than being limitations, can be harnessed as tunable design parameters. This work opens new directions for the development of load-adaptive metamaterials with dynamically adjustable wave-filtering and dissipation capabilities, offering broad utility in vibration control, acoustic manipulation, and impact mitigation.