Flexible pressure sensors are crucial in emerging fields like epidermal electronics and biomedicine. Current commercial pressure sensors, primarily based on semiconductor and MEMS technology, lack the flexibility needed for these applications. Flexible sensors, utilizing flexible substrates, offer advantages such as large area, lightweight design, and flexibility. However, rational design for achieving specific performance characteristics, like high sensitivity, remains challenging. Various microstructures (pyramidal, porous, biomimetic, serpentine) have been explored to enhance sensitivity, but these often compromise stability and scalability. Finite element modeling is a valuable tool for predicting sensor performance, but its application to flexible piezoresistive sensors is underdeveloped. This paper introduces a finite element model incorporating the electrical constriction effect to predict the performance of a simple laminate-structured flexible pressure sensor, offering theoretical guidance for design and fabrication. The researchers fabricated a laminate-structured sensor, experimentally validating the model and demonstrating its excellent stability and durability. Finally, they developed a wearable system for real-time plantar pressure monitoring, highlighting the sensor's practicality for exercise and rehabilitation.

The introduction cites numerous studies exploring various microstructures for flexible pressure sensors to enhance sensitivity, including pyramidal microstructures for capacitive sensors (Bao et al.) and sensitivity/linearity studies on microstructured capacitive sensors (Yang et al.). Other work focused on porous, biomimetic, and serpentine structures. However, these microstructured approaches often face limitations in long-term stability and scalability. The paper emphasizes the lack of efficient models for designing flexible piezoresistive pressure sensors, highlighting the need for theoretical guidance in this area, particularly for achieving target performance in practical applications.

The researchers designed a laminate-structured flexible pressure sensor consisting of a flexible sensing layer and a flexible interdigital electrode layer separated by a ring spacer. A finite element model was developed using COMSOL Multiphysics, incorporating solid mechanics and electric currents. The model considered the Lagrangian equilibrium equations to describe mechanical deformation and introduced the electrical constriction effect to model the sensor's electrical behavior. The electrical constriction effect accounts for the non-uniform current flow due to microscale roughness at the contact interface between the sensing layer and electrode. The model uses an equation (σx = C + k ⋅ T-n) to represent the interface conductivity, where C is a constant, k is a constant related to interface roughness and material properties, T is the contact pressure, and n is a constant between 0 and 1. The model was used to simulate the sensor's response to various pressures, analyzing displacement, stress, contact pressure, and current density distributions. The simulation results were then compared to experimental data obtained from a fabricated sensor. The experimental setup involved applying various pressures to the sensor and measuring the resulting current. A wearable sensing system was constructed using arrays of these sensors for plantar pressure monitoring.

The finite element model accurately predicted the sensor's performance, validated by experimental results. The model effectively captured the electrical constriction effect, explaining the sensor's sensitivity across a broad pressure range. The sensor demonstrated excellent stability for up to three million cycles and superior durability when exposed to salt solution. Simulations showed that the detection limit of the sensor decreased linearly with decreasing Young's modulus of the flexible substrate and exponentially with decreasing thickness of the air gap or substrate. The geometry of the interdigital electrodes influenced the current flow, but not the detection limit. The current-pressure relationship showed a sharp increase at low pressures and a nearly linear increase at higher pressures. The wearable system successfully demonstrated real-time plantar pressure data collection and analysis for exercise and rehabilitation applications.

The study successfully integrated the electrical constriction effect into a finite element model for a simple laminate-structured flexible pressure sensor. This approach allows for more accurate prediction of sensor performance and facilitates rational design for specific applications. The sensor's excellent stability and durability, confirmed experimentally, highlight its suitability for wearable applications. The successful demonstration of a wearable system for plantar pressure monitoring opens up significant possibilities for exercise monitoring and rehabilitation. This work provides valuable theoretical and practical guidance for designing high-performance flexible pressure sensors suitable for a wide range of applications.

This research presented a novel finite element model incorporating the electrical constriction effect for designing laminate-structured flexible pressure sensors. The model accurately predicted sensor performance, validated by experiments demonstrating excellent stability and durability. The resulting wearable plantar pressure monitoring system showcases the practicality of this design for real-world applications. Future work could explore different materials and geometries to further optimize sensor performance and expand its applications.

The study focused on a specific laminate structure. The generalizability of the model to other sensor designs may need further investigation. The long-term stability of the sensor under extreme conditions requires further evaluation. The experimental validation was limited to a specific set of materials and environmental conditions, therefore more research is required to expand the reliability.