Design and optimization of a mechanical metamaterial featuring dual tunability in auxeticity and bandgap modulation

Abstract

This study introduces an optimized nested sinusoidal re-entrant (oNSR) mechanical metamaterial that achieves dynamically tunable auxeticity and bandgaps under applied strain. To enhance the metamaterial’s vibration-blocking capabilities (relative bandgap width) and auxetic behavior (effective Poisson’s ratio), support vector machine regression was utilized to model the nonlinear relationships between geometric parameters and performance indexes, followed by a genetic algorithm based multi-objective optimization. Furthermore, Sobol sensitivity analysis identified the influence of the parameters, thereby guiding the optimization process. The mechanical behavior of the optimized structure was evaluated through numerical simulations and experimental tests, revealing a notable auxetic effect with a minimum effective Poisson’s ratio of −0.25 and a tunable bandgap around 210 Hz. Compression-induced tuning further generated new bandgaps near 155 Hz, enhancing wave suppression across multiple frequencies. Group velocity analysis confirmed directional energy propagation, while frequency response validation demonstrated consistent bandgap performance under varied strain. These findings underline the oNSR’s potential in adaptive engineering applications, offering enhanced structural stability, stress management, and elastic wave manipulation capability.