Topology‐Optimized Stretchable Piezoelectric Sensors With Tailored Liquid‐Metal Circuits for Anisotropic Stress‐Adaptive Motion Monitoring

ABSTRACT The design of high‐sensitivity stretchable piezoelectric sensors remains challenging due to the inherent trade‐off between the ability to achieve high levels of mechanical deformation while maintaining efficient stress transduction. Here, we propose a new topology‐optimization strategy to construct stretchable piezoelectric sensors that efficiently utilize the spatial stress distribution and are able to adapt to a range of anisotropic mechanical stress states. By exploiting computer‐aided topology optimization, the distribution of piezoelectric ceramic units within the sensor was tailored to maximize the degree of stress transfer, resulting in an increase of 103.5% and 59.7% in the maximum piezoelectric potential when subject to tension and torsion, respectively. To ensure structural stretchability and adaptability of the topology optimized sensors when subject to complex loading environments, a direct ink writing process was developed to create stretchable eutectic gallium‐indium liquid alloy (EGaIn) electrodes. Based on a shear‐driven mechanism of printing, new predictive theoretical equations governing printing performance were developed that could predict the printed state (with 94.7% accuracy) and enable trace width control (relative error < 15%). The final optimized sensor exhibited excellent sensitivity, achieving 14.0 V per strain and 0.10 V per degree when subject to tensile and torsional loads, exceeding the unoptimized device by 59.2% and 92.4%, respectively. Finally, inspired by the morphological characteristics of butterflies and guided by the topology‐optimized layout, a multi‐channel sensor was constructed to accurately identify the pattern and amplitude of a complex range of neck movements, demonstrating the significant potential of the new design and manufacturing approach for wearable electronics.