Structural Optimization Design of Intelligent Flexible Sensors Based on Analytical Methods

Intelligent flexible sensors have demonstrated significant potential for applications in wearable electronics, electronic skins, and intelligent robotics due to their high sensitivity, wide operational range, and mechanical flexibility. This study systematically investigates the material-elasticity model of gel-based intelligent flexible sensors, focusing on its theoretical construction and mathematical derivation. While classical Hertzian contact theory accurately describes sensor behavior under low pressures, it fails to capture nonlinear elastic effects and microstructural collapse at higher pressures. To address these limitations, a multistage correction approach incorporating a saturation function for contact area and a strain-dependent elastic modulus was proposed. Furthermore, the model considers the influence of the electric double-layer capacitance series effect. The revised model demonstrates excellent agreement with experimental results across a wide pressure range, significantly improving predictive accuracy, particularly in the medium-to-high pressure regime. These findings provide a theoretical foundation for the optimization and design of next-generation flexible capacitive sensors.