Multiscale electro-mechanical behaviours of TPMS piezoelectric metamaterials

Conventional bulk piezoelectric materials face intrinsic performance bottlenecks in simultaneously achieving high electromechanical sensitivity and low acoustic impedance. TPMS metamaterials, owing to their unique bi-continuous structure and superior mechanical properties, stand out as ideal candidates. However, existing research lacks a systematic investigation into their configurational mechanisms and cross-scale electro-mechanical behaviors. This study investigates the multiscale electromechanical behavior of TPMS structures as piezoelectric functional layers. At the microscale, the influences of TPMS configurations, material composition, and volume fractions on homogenized electromechanical coefficients were investigated through numerical homogenization theory and analysis of stress and electric displacement field distributions, with performance quantified via figures of merit (FOM). The results demonstrate that Primitive exhibits superior dielectric and piezoelectric responses, and Diamond achieves exceptionally high hydrostatic FOM. At the macroscale, a finite element model based on Reissner-Mindlin theory was developed to comprehensively assess actuation, sensing, and control behaviors in smart sandwich plates. The simulation revealed that the Primitive delivers optimal overall performance. This work systematically elucidates the cross-scale mapping from microscale topology for homogenized properties to macroscale responses, establishing a theoretical foundation for integrated material-structure–function design of piezoelectric metamaterials in smart devices.