Controlling how waves slow, stop, and localize lies at the heart of modern condensed-matter and metamaterial physics. Flexoelectricity, the coupling of strain gradients and polarization that is universally present in all dielectrics, scales with structure size, thus offering a route to size-dependent electromechanics, especially in materials with nanoscale feature size. We show that a suitably designed flexoelectric medium permits a tunable landscape of band extrema where elastic and electric fields strictly co-localize, thus leading to localized vibrations, and zero-group-velocity and stationary-inflection modes that trap energy in place. The resulting defect-cavity modes exhibit dual amplification of open-circuit voltage and mass responsivity, both scaling inversely with the localization length that is determined by the curvature of the dispersion curve and frequency shift from the minimum. This framework unifies nonlocal lattice physics with continuum electromechanics, establishing a continuum route to engineer and electrically read out band-edge phenomena for ultrasensitive detection and reconfigurable energy harvesting.

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• Elastic waves
• Energy harvesting devices
• Flexoelectricity
• Metrology
• Mechanical metamaterials
• Micromechanical devices
• Solid-state detectors
• Elastic wave theory