Inverse Designing Reconfigurable Piezoelectric Tensors via Architectural and Modal Programming

Piezoelectricity arises from the coupling between electric polarization and mechanical deformation, described by a third-rank tensor whose coefficients are constrained by crystal symmetry. In natural crystals, atomic periodicity and energetic stability restrict accessible symmetries, limited to 20 distinct anisotropies that can exist. Here we establish a general framework, based on graph representation, for controlling the full effective piezoelectric tensor through architecture by resolving how macroscopic symmetry, local polarization and deformation of structural elements act together. This enables each coefficient to be traced to the members that reinforce or cancel it and be controlled through targeted geometric changes. We further uncover frequency-selective tensor reconfiguration, in which excitation frequency switches the dominant piezoelectric coefficients of a single architecture. These principles open a broader class of applications in which a single piezoelectric architecture can deliver programmable sensing, actuation and mode conversion across multiple directions and deformation states. We realize a multi-degree-of-freedom actuator that integrates distinct actuation modes in one block and reduces volume by 90% relative to conventional multi-stack assemblies.