Linear and Nonlinear Time Domain Analysis of Resonant Metamaterials under Impact Loading

Metamaterials are artificial structures with unique overall properties not found in naturally occurring materials. Unusual properties of metamaterials can be tuned beyond the Bragg limit using local resonance. In this study, we used the Finite Element Method (FEM) to analyze the time domain response of a low-frequency resonant ceramic metamaterial under impact loading conditions. We compared the performance of the metamaterial to that of monolithic slabs and other microstructured designs in terms of stress wave mitigation, peak load retardation, and energy transfer. Our results revealed that the metamaterial system had better performance in delaying and reducing the peak of the stress wave compared to the other designs. Additionally, we found that the wave anisotropy of the metamaterial design further improved its performance in terms of stress wave mitigation. The unique directional properties of the metamaterial sample allowed for more efficient energy transfer, resulting in overall enhanced performance compared to the other designs. Moreover, we expanded the comparison to the nonlinear regime by considering material failure. We utilized the Johnson-Holmquist constitutive model for ceramics to capture material failure and found that the favorable properties of the metamaterial design did not change considerably even when the material failure was considered. Protective layers for the metamaterial cells improved the fracture response and allowed for efficient engagement with the projectile energy. The computational workload is improved significantly while maintaining accuracy by utilizing a reduced order model (ROM). Overall, our study demonstrates the potential of resonant ceramic metamaterial structures as a promising new class of materials with unique and tunable properties that can be harnessed for a variety of protective and structural applications.