Theoretical modeling and tailored design of mechanoelectrical behavior in flexible piezoelectric metamaterials

Flexible piezoelectric metamaterials offer transformative opportunities for sensing, energy transduction, and bioinspired electronics, yet their development is constrained by limited geometric tunability and the lack of unified models capable of describing complex 3D architectures under large deformations. Inspired by the hierarchical helical motifs found in collagen fibers, this study proposes a spindle-shaped helical microstructure as the fundamental unit of a flexible piezoelectric metamaterial and establishes a comprehensive theoretical framework to characterize its nonlinear mechanoelectrical behavior. By integrating Kirchhoff rod theory with piezoelectric constitutive relations, the proposed model explicitly incorporates helical geometric parameters and provides a direct quantitative relationship between mechanical strain and electrical response. Finite element simulations and targeted experiments validate the predictive accuracy of the theoretical model across a wide range of loading conditions. Systematic parametric analyses reveal that the normalized width R/d₀ governs critical strain, stiffness evolution, and strain-dependent electrical output, while also influencing global buckling and the relative importance of flexoelectric effects. Leveraging these structure–property relationships, we demonstrate that the metamaterial can reproduce nonlinear and anisotropic mechanical behaviors characteristic of biological tissues and generate physiologically relevant electrical signals. The framework further enables the rational design of topological architectures with programmable mechanical adaptability and tunable sensing performance. Overall, this work provides a unified theoretical and computational foundation for the design of flexible piezoelectric metamaterials with complex 3D geometries and nonlinear deformation characteristics. The proposed materials exhibit high structural programmability, robust sensing capabilities, and significant potential for next-generation wearable electronics, biomedical interfaces, and intelligent soft systems.