A Bilayer Liquid–Metal Interdigitated Capacitive Sensor for Omnidirectional Strain Decoupling in Wearable Motion Monitoring

Abstract

Soft and stretchable strain sensors are important for human–machine interfaces, soft robotics, and electronic skins. However, most existing sensors cannot simultaneously resolve strain magnitude and direction and are easily affected by normal pressure under multidirectional deformation. To solve this problem, we present a bilayer liquid–metal interdigitated capacitive omnidirectional flexible strain sensor. The device employs liquid–metal interdigitated electrodes encapsulated in Ecoflex and is fabricated as a five-layer sandwich structure via a low-cost mask-assisted laser patterning process. By integrating two capacitive sensing units, C₁ (lower sensing layer) and C₂ (upper sensing layer), with distinct orientations in a 30° cross-stacked architecture, the device can detect in-plane strain with different directional responses. Single-layer interdigitated electrodes show different capacitive responses when stretched parallel or perpendicular to the electrode direction, whereas the bilayer structure generates distinguishable dual-channel outputs over tensile directions from 0° to 180°. Simulations and experiments confirm a linear, repeatable, and direction-dependent response under multidirectional stretching. Leave-one-angle-out cross-validation yielded a mean absolute angular error of 3.12°, an angular root-mean-square error of 3.70°, and a maximum absolute angular error of 6.05°. Under normal loads of 10–17.5 N, the capacitance signals of both channels remain nearly unchanged, indicating low sensitivity to normal pressure. On-body tests further showed that the sensor records stable and reproducible direction-dependent strain signals during periodic wrist, knee, and waist motions. This work provides a design strategy for flexible capacitive strain sensors in wearable direction-resolved strain monitoring, health sensing, and electronic skin.