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

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.