While piezoelectricity in bulk crystals is strictly confined by lattice symmetry, architected metamaterials overcome these limits, unlocking previously forbidden electromechanical couplings via mesoscale geometry. However, a comprehensive framework relating metamaterial topology to the full piezoelectric tensor remains absent, particularly in the dynamic regime where structural resonances render responses highly frequency dependent. Furthermore, current AI-driven design methods focus on static properties or natural crystals, leaving dynamic tensor discovery largely out of reach.
Here, we establish a dynamic, explicitly tensorial framework for piezoelectric metamaterials. First, we formalize how deliberate symmetry-breaking yields novel non-crystallographic tensors. Second, we quantify the frequency-dependent evolution of effective couplings in resonant 3D lattices, revealing the rotation and amplification of principal axes near resonances. Third, we introduce a frequency-conditioned, symmetry-aware graph neural network that predicts the full dynamic piezoelectric tensor directly from 3D unit-cell graphs, enabling rapid discovery of extreme properties. Finally, we experimentally validate this framework by demonstrating direction-selective active vibration damping and Multi-Modal Actuation. Ultimately, this work recasts metamaterial piezoelectricity as a designable, frequency-dependent tensor field, unlocking programmable routes for advanced sensing, energy transduction, and vibration control.
Project currently funded by: Federal