Time domain analysis of locally resonant elastic metamaterials under impact*

Impact mitigation using metamaterials (MM) requires low-frequency stopbands for wave attenuation. Conventional low-frequency MM solutions often rely on complex, heavy, multi-material unit cells. Most MM studies analyze infinite periodic domains through Frequency Domain (FD) simulations, a practice that limits applicability to realistic impact scenarios. The present study employs Time Domain (TD) finite element analysis to investigate the dynamic response of single-material, locally resonant ceramic MMs under impact loading. This design achieves a low-frequency stopband while minimizing the mass and fabrication complexity associated with multi-material systems. TD results are contrasted with FD predictions to highlight the advantages of TD analysis for finite-sized structures subjected to impact, blast, and other boundary conditions. MM slabs are benchmarked against conventional monolithic and alternative microstructured slabs, with performance assessed in terms of stress-wave attenuation, peak-load retardation, energy transfer, and dissipation by material damping. Resonance within the MM amplifies dissipation within the assumed mass-proportional Rayleigh damping model. A graded slab further enhances energy mitigation by broadening the attenuation band relative to uniform MM slabs. Overall, the proposed MM design slows and redistributes stress waves, and the TD analysis framework provides a robust, efficient tool for such structures.