Flexible pressure sensors are crucial in flexible electronics, with applications in electronic skin, healthcare monitoring, and human-machine interfaces. Improving sensitivity and response speed is often achieved through microstructures like pyramids or microdomes. However, deformation saturation at high pressures due to compressibility reduction in the elastomer is a significant challenge. Passive designs using irregular microstructures with hierarchical properties offer a solution for continuous deformation, but lack rational design based on fundamental contact principles. Previous approaches utilizing Hertzian contact theory for hyperelastic materials have limitations due to constitutive model mismatch. This paper proposes a new positive design strategy based on hyperelastic mechanics to address these limitations, enabling precise control over sensitivity and linearity.

The literature review highlights existing methods for enhancing the performance of flexible pressure sensors, focusing on the use of micro-engineering strategies to control geometric and spatial designs. The limitations of passive designs based on inverting natural templates are discussed, emphasizing the lack of rational design based on fundamental contact principles. The paper also reviews previous positive design approaches, noting the limitations of using Hertzian contact theory for hyperelastic materials and the resulting lack of predictable performance. Existing models are shown to be inadequate for describing large deformations in hyperelastic materials.

The researchers propose a positive design strategy using a modified hyperelastic contact model to predict deformation parameters more accurately than previous Hertzian contact models. This model is used to pre-calculate the size and number of microdome pixels in hierarchical structures to achieve desired sensitivity and linearity. The neo-Hooken model, a simplified version of the Mooney-Rivlin model, is employed to characterize the hyperelastic properties of the conductive elastomer. Equations are derived to determine the parameters of multistage dome-like microstructures, considering the relationship between contact area, compression height, and pressure. The design process involves determining the desired working range and resolution, calculating the number and order of hierarchical microstructures, and generating a distribution diagram for the sensitive layer. Fabrication involves 3D printing a microdome-like structure template, coating with a MWCNT/PDMS conductive solution, and encapsulating with flexible electrodes and PU adhesive.

The fabricated pressure sensors demonstrated highly customizable sensitivity (0.7, 1.0, and 1.3 kPa⁻¹) and high linearity (R² = 0.99) over a pre-designed linear working range (approximately 200 kPa). The sensors exhibited a fast response/release time (12.5/37.5 ms), a low limit of detection (LOD) of 35 Pa, and good repeatability over 10,000 cycles. Experimental results closely matched the pre-designed target sensitivities, with minimal deviation. The success of the sensors demonstrates the effectiveness of the proposed hyperelasticity-based modified model for accurate prediction of deformation parameters.

The results confirm the effectiveness of the positive design strategy based on hyperelastic mechanics for creating flexible pressure sensors with highly customizable sensitivity and linearity. The use of the modified hyperelastic contact model enables more accurate prediction of deformation parameters compared to previous approaches using Hertzian contact theory, leading to improved control over sensor performance. The ability to precisely control sensitivity and linearity opens up new possibilities for designing sensors tailored to specific applications, such as physiological signal recognition and other wearable device applications. The high linearity and low sensitivity error further enhance the reliability and accuracy of the sensor.

This work introduces a novel positive design strategy for flexible pressure sensors, enabling highly customizable sensitivity and linearity. The use of a hyperelastic model for design significantly improves the predictability and accuracy of sensor performance. The demonstrated sensors show excellent characteristics, promising for applications requiring tailored sensitivity and working range. Future work may explore expanding the model to include other hyperelastic materials and explore diverse microstructure designs.

While the study demonstrates the effectiveness of the proposed methodology, further investigation is needed to evaluate the long-term stability and durability of the sensors under various environmental conditions. The current model is based on specific hyperelastic material properties; further research should investigate the applicability of the model to other materials. The fabrication process relies on 3D printing; optimization of this process could improve efficiency and reduce costs.