I. Abstract of the Paper’s Core Research

• A dual-electrode configuration enables both positive and negative capacitance responses, with a sensitivity coefficient of 5.2.

When the interdigitated electrodes are oriented perpendicular to the stretching direction, the applied load increases and the electrode gap widens, leading to a decrease in capacitance; in contrast, when the electrodes are arranged parallel to the stretching direction, the capacitance rises. Devices at the nF level exhibit a maximum strain‑sensitivity coefficient of 5.2, while those at the pF level offer superior stability, allowing for tailored matching to meet specific monitoring‑accuracy requirements.

• Under large-strain conditions, the hysteresis is significantly superior to that of conventional resistance strain gauges.

A peak load of 18.7 kN (rated at 70%) was maintained statically for 65 minutes, during which the aerosol capacitance sensor exhibited negligible signal drift; in contrast, the commercial resistive‑film sensor showed pronounced irreversible hysteresis, with significant baseline shifts after multiple cycling cycles, rendering it incapable of long-term stable monitoring.

• Dynamic / Cyclic loading is stable and reliable, suitable for repeated deployment and retrieval in aerospace applications.

5.3–10.7 kN tensile cycling; excellent repeatability of the capacitance‑strain curve; significant discrepancies between the initial and subsequent cyclic responses of the resistive strain gauge, with erratic resistance‑strain behavior at high strains.

• All‑flexible, integrated maskless printing, compatible with irregularly shaped fabric substrates.

Aerosol‑free, non‑contact forming enables the thin Kapton sensing film to adhere securely to Kevlar’s woven texture, stretching in tandem with the fabric without constraining structural deformation.

• Digitally and rapidly iterate the dimensions of the interdigital array to accommodate varying fabric bandwidths.

CAD enables direct modification of interdigitated logarithmic structures and electrode spacing, eliminating the need for photolithographic masks and facilitating rapid prototyping and validation of small‑batch aerospace sensor samples.

II. Complete Process Flow for the Preparation of Aerosol-Sprayed Strain Gauges and Their Core Advantages

(1) Complete Preparation Procedure for Capacitive Strain Gauges

• 125 μm Kapton film undergoes ultrasonic cleaning and plasma activation to enhance the adhesion of the silver coating.
• AJ200 pneumatic atomization silver nano‑ink, printed with a 200 μm nozzle to form 50 interdigitated electrodes, followed by isothermal curing at 300 °C for 30 minutes.
• Spin-coat a PMMA dielectric/protective layer to isolate from air and improve the capacitance baseline.
• Silver epoxy is used to bond the copper leads, completing the encapsulation of the sensing unit.
• A specialized chloroprene rubber adhesive is used to bond Kevlar webbing, and a MTS universal materials testing machine is employed for multi‑load calibration.

(II) Five Key Advantages of Aerosol-Based Processes (Comparison with Lithography, Screen Printing, and Commercial Die Attach)

• Ultra-thin, flexible in-situ molding that conforms closely to knitted fabrics.

The printing substrate is only 125 μm thick, and the overall structure is lightweight and free of a rigid base, enabling it to stretch in tandem with Kevlar’s large deformations without compromising the fabric’s mechanical properties.

• Maskless Digital Customization of Interdigital Array

Finger‑type logarithmic structures, electrode spacing, and device dimensions can all be adjusted with a single click, enabling compatibility with space‑grade ribbons of varying widths and significantly shortening the R&D iteration cycle.

• Micrometer-scale precision interdigitated electrode fabrication, with a controllable sensing area.

Stable printing with a 71 μm electrode width and a 78 μm inter-electrode spacing, featuring uniform interdigitated electrode arrays and high capacitance baseline consistency.

• A single device can complete the fabrication of the functional layer using only silver ink.

No multilayer metal lamination is required, simplifying the process and reducing material costs compared to vacuum evaporation and photolithography.

• Conformal Printing Potential for Curved and Woven Surfaces

A safe spray distance of 3–5 mm allows direct inkjet printing of sensor arrays onto flexible fabric surfaces, eliminating the need for film‑lamination and adhesive‑bonding steps.

III. Five Core Technological Innovations of This Study

Innovation 1: All‑printable aerosol‑based interdigitated capacitive strain sensor tailored for aerospace‑grade large‑strain fabrics.

Innovation: A dual-row sensor array design enables bidirectional capacitive signal modulation.

Innovative 3 PMMA Integrated Dielectric Protective Layer Composite Solution

Innovation: A Comprehensive Load Evaluation System for Aerospace-Grade Fabrics

Innovative 5‑Low-Hysteresis Capacitive Flexible Sensing Manufacturing Paradigm

IV. Existing Process Challenges and Corresponding Solutions for Overcoming Them

Challenge 1: Commercial strain gauges have high stiffness, and strains exceeding 5% result in irreversible hysteresis.

Challenge 2: Lithography can only be applied to planar rigid substrates and cannot accommodate woven flexible fabrics.

Challenge 3: In the printing of interdigitated electrodes, excessive droplet overspray often occurs, leading to an excessive edge width on the electrode.

Challenge 4: The baseline of single-layer silver‑film capacitors is low, resulting in small signal variations.

Challenge 5: Flexible fabrics are prone to delamination upon bonding, and the sensing film tends to peel off under tensile strain.

V. Future Diversified Industrial Application Scenarios

• Structural Health Monitoring of Space Inflatable Modules and Deceleration Parachutes

• Aircraft parachute and cushioning fabric ground fatigue testing

• Soft-Robotics Flexible Skin Deformation Sensing

• Real-Time Stress Monitoring of the Flexible Envelope of High-Altitude Airships

• Flexible Structural Mechanics Sensing R&D Platform for Universities

Figure 1. Schematic design of a printed flexible interdigital‑electrode capacitive strain sensor: a, schematic of the sensor configuration incorporating a 50‑pair interdigital electrode structure; b, optical image of the capacitive strain sensor mounted on a polyimide substrate fixed to a Kevlar strap (scale bar = 1 cm).

Figure 2. Micrographs showing the morphology of silver lines deposited by aerosol jet printing: a and b are optical microscopy images of silver strain gauges on a polyimide substrate (scale bar = 250 µm); c shows the optical profilometry results for AJP‑deposited silver electrodes on the polyimide surface. The cross‑sectional scanning electron microscopy characterization is as follows: d depicts a representative silver electrode of an AJP‑deposited strain gauge (scale bar = 50 µm); e shows the thickness of the PMMA dielectric layer (scale bar = 10 µm); f illustrates the thickness of the printed silver layer (scale bar = 2.5 µm).

Figure 3. Device design parameters for the printed CSG interdigitated electrode structure: (a) a schematic illustrating the variables required for calculating the theoretical capacitance; (b) the corresponding numerical values, with dimensional parameters expressed as mean values and accompanied by standard deviations representing the measurement results for the entire device.

Table 1. Experimental Summary

Figure 4 shows the results of strain gauges based on printed capacitors under dynamic, static, and cyclic tensile testing. The figure presents the relative change in capacitance (%) of the printed CSG devices when subjected to dynamic testing (devices a–e), static testing (devices a–e), or cyclic testing (devices f and g), using a total of seven distinct device configurations (see Table 1). The dynamic test results indicate that, at a target load of 18.7 kN, devices with electrode a oriented perpendicular to the strain direction (devices a–c) and those with electrode b oriented parallel to the strain direction (devices d–e) exhibit distinct performance characteristics. In the static tests, under identical loading conditions, the data correspond to devices with electrode c perpendicular to the strain direction (devices a–c) and those with electrode d parallel to the strain direction (devices d–e). Finally, the cyclic test results pertain to devices with both electrodes oriented perpendicular to the strain direction (devices f and g). Error bars represent the estimated experimental uncertainty (see the Supplementary Discussion for details). All scale bars in the figures correspond to 1.0 cm.

Figure 5. Strain response curves of commercial resistive strain gauges. The figure shows the strain responses of commercial RSGs under three test conditions: a) dynamic testing at a ramp rate of 44.5 N/s with electrodes arranged parallel to the direction of strain; b) static testing under a load of 18.7 kN; and c) cyclic testing using loads of 5.3 kN and 10.7 kN. Error bars indicate the estimated experimental uncertainty (see the Supplementary Discussion for details). The scale bar represents 4.0 mm.