High-stretchability and low-hysteresis strain sensors using origami-inspired 3D mesostructures

Stretchable strain sensors are essential for various applications such as wearable electronics, prosthetics, and soft robotics. Strain sensors with high strain range, minimal hysteresis, and fast response speed are highly desirable for accurate measurements of large and dynamic deformations of soft bodies. Current stretchable strain sensors mostly rely on deformable conducting materials, which often have difficulties in achieving these properties simultaneously. In this study, we introduce capacitive strain sensor concepts based on origami-inspired three-dimensional mesoscale electrodes formed by a mechanically guided assembly process. These sensors exhibit up to 200% stretchability with 1.2% degree of hysteresis, <22 ms response time, small sensing area (~5 mm2), and directional strain responses. To showcase potential applications, we demonstrate the use of distributed strain sensors for measuring multimodal deformations of a soft continuum arm.

Since the only unknown is , we can find the angle  given the distance between the bonding sites .

Estimation of total capacitance
Assuming that the electric field lines between the two folded electrodes have arc shapes (59), the charge per unit area on these two folded electrodes can be expressed as: Using the charge-voltage relationship, all charges can be summed up along the edges of the electrodes:

𝜎𝜎𝜃𝜃
Here,  2   1 are the arc lengths from point  to the two ends of the electrodes, which are  +  and , respectively.Since the space between the two electrodes is filled with liquid glycerol,   is used as the dielectric constant.Integrating the equation above will give: Since the electrodes are insulated by parylene C, the parylene layer's capacitance   and the glycerol capacitance   will form a series of capacitors as shown in the schematic drawing above.Therefore, the total inner capacitance   in the space between the two electrodes is: It is worth noting that the use of liquid glycerol as the dielectric medium can possibly generate electrical double layer capacitance.However, the extremely low ionic conductivity of the glycerol used in the sensors could only result in double layer capacitance that is several orders of magnitude higher than   (2-3 pF) (60).Since this possible double layer capacitor   and glycerol capacitance   are connected in series, its high capacitance will have little influence on the total capacitance   .
Modeling of the fringe capacitance is adopted from previous studies (25,26,42) that use conformal mapping to transform the non-parallel-plate capacitance to parallel-plate capacitance in complex domains.According to the geometry presented in Fig. 1A, the capacitance   is as follows: The first term represents the fringe capacitance at the top of the angled electrodes, where the electric field exists within the liquid glycerol.The second term represents the fringe capacitance at the bottom of the angled electrodes, while the third term represents the fringe capacitance generated by the two flat plates at the bonding sites.Both fringe capacitances exist mostly inside the bottom Ecoflex substrate.The expression for the fringe capacitance   is shown below, which is the capacitance generated between the edges of the angled electrodes: Since   ,   , and   are connected in parallel, the total capacitance can be estimated as: Explanation for discrepancies between models and experimental results for sensors with long electrodes In Fig. S8B, the capacitance reductions from the analytical solution and simulation are smaller than those in the experiments.These discrepancies may result from several factors.First, both the analytical solution and simulation account for the Ecoflex at the bottom of the electrodes and exclude the Ecoflex surrounding the 3D electrodes in the top cover.Under large stretching, the reduced gap between the Ecoflex cover and 3D electrodes leads to decreases in   and   due to a lower dielectric constant of Ecoflex compared to glycerol.This effect is more pronounced in sensors with longer electrode lengths than those with shorter lengths.Other factors such as slight tilting of bonding sites due to stress concentration and the presence of the slit at the center crease of the 3D electrodes (not considered in analytical modeling) can also contribute to discrepancies observed between analytical modeling, simulation, and experiments.
Supplementary Note S2: Influence of normal pressure on strain sensing.
Fig. S18 shows the capacitance responses of a representative sensor to uniaxial stretching under coexisting uniaxial stretching and normal pressure.The capacitance is normalized to the initial capacitance before stretching and without normal pressure.The error bars on each data point indicate the standard deviation of capacitance changes across 5 repeated tests.An increase in normal pressure from 0 to 30 kPa leads to partial unfolding of the 3D electrodes, resulting in a capacitance decrease.This reduction is 4.3% for unstretched sensor at 30 kPa.When the sensor is stretched under 30% strain, the strain-induced relative capacitance change is -12.1%, while the normal pressure-induced relative capacitance change is -3.2%.The influence of normal pressure on strain sensing is even smaller at 60% strain, as the 3D electrodes further unfold.The relative capacitance change contributed by stretching and normal pressure is -21.1% and -3.9%, respectively.The results suggest that the influence of normal pressure from 0 to 30 kPa on strain sensing decreases as the strain increases from 0 to 60%, and it is expected to be even smaller for large strain sensing.It should be noted that the sensor is only sensitive to normal pressure applied above its active sensing area (< 5 mm 2 ).Modification of the sensor design can further reduce its sensitivity to normal pressure, including the use of top silicone cover with larger thickness and higher modulus.

Supplementary Note S3: Characterization of sensors' mechanical robustness against collisions and abrasions.
Mechanical robustness against collisions and abrasions is crucial for strain sensors used in wearable applications.Movie S2 shows the sensor's mechanical robustness tests.To characterize the sensor performance against collisions, dynamic compression tests are performed utilizing a fast-actuating press head that moves at 20 mm/s to apply normal pressure at the sensor's sensing region (Fig. 19A).The sensor performance is evaluated by measuring the sensor capacitance before and after compression.Fig. S19B shows that the sensor can still be stretched to 100% strain after compression with 240 kPa peak pressure above the sensing area.The degree of hysteresis remains mostly around 2% for all applied pressure levels.No significant changes on 3D electrodes are observed until applying a compression with 240 kPa peak pressure, where the 3D electrodes significantly tilt to one side (Fig. S19C).The gauge factor changes from -0.22 at the initial state to -0.26 after 240 kPa normal pressure, which may be explained by the gradual tilting of the electrodes after repeated compression tests.Further increasing the pressure (~360 kPa) snaps the serpentine interconnects and breaks the 3D electrodes within the Ecoflex compartment.Modifications including a more damped, pressure-resistant cover may better attenuate the dynamic normal pressure from collisions.
To characterize the sensor performance against abrasions, both longitudinal and transverse shear stresses are applied on two sensors.Fig. S19D shows that the sensor can function after an applied shear stress of 46 kPa along the sensor's longitudinal direction, despite misalignment in the serpentine interconnects (Fig. S19E).Similar misalignment in the serpentine interconnects also occurs when the sensor is under 40 kPa shear stress in the transverse direction (Fig. S19G).Shear in the transverse direction can also undermine the bonding strength at the 3D electrodes' bonding sites, resulting in increased hysteresis (Fig. S19F).Overall, the sensors can maintain their performance at 22~23 kPa shear stress in both the longitudinal and transverse directions without obvious degradation.Larger shear stresses can cause damage to the serpentine interconnects and lead to the delamination of the 3D electrodes from the bonded surface.Shear-resistant designs of liquid channels and serpentine structures may help increase the sensor's resistance to shear damage.

Supplementary Note S4: Machine learning for classifying deformation modes.
To classify single deformation modes for the continuum arm, 1,119 sets of relative capacitance changes are collected during multiple trials of 9 deformation modes, including bending (4 directions), twisting (2 directions), elongation, compression, and no deformation.Each data point includes the capacitance changes from the 6 sensors attached on the arm.After each data point is labeled with its corresponding deformation, the entire dataset is randomly split, with 70% used for training and 30% for testing.K-nearest neighbor (KNN), Linear Support Vector Classifier (SVC), and Random Forest Classifier (RFC) with default parameters from Scikit-Learn 1.2.2 are chosen as the machine learning algorithms for deformation prediction.The accuracies for classifying deformation modes using the trained KNN, SVC, and RFC classification models on the test dataset are 99.7%, 99.1%, and 99.7%, respectively.The high accuracies are explained by the highly distinguishable features of the 9 different deformation modes (Fig. S26).More datasets and other machine learning algorithms including deep learning may be needed for recognition of more complex deformations such as various hybrid deformations.S3.Comparison of our origami-inspired capacitive strain sensor with other resistive and capacitive stretchable strain sensors on the strain range, degree of hysteresis, and response time.

Fig. S1 .
Fig. S1.Layouts of the 2D precursor of the basic origami-inspired capacitive strain sensor design.(A) Overview of the stacked 2D precursor layouts.(B) Layout of the Cr/Au metal layer.(C) Layout of the parylene C layer.(D) Layout of the SU-8 stiffener layer.(E) Layout of the bonding sites on the backside of the 2D precursor.

Fig. S2 .
Fig. S2.Optical images of 3D printed molds and the corresponding molded silicone top encapsulation covers for two sensor designs with different electrical interconnect lengths.Scale bar, 1 cm.

Fig. S4 .
Fig. S4.Optical images of the sensor with long serpentine interconnects.(A) Before encapsulation of the electrodes and (B) after encapsulation filled with liquid glycerol.Scale bars, 1 cm.

Fig. S6 .
Fig. S6.Sideview optical images and the corresponding simulated profiles of the origamiinspired 3D non-parallel-plate capacitor with different prestrain.(A) 0.5 mm electrode length and (B) 1 mm electrode length.Scale bars, 250 μm in A and 500 μm in B.

Fig. S7 .
Fig. S7.Characterization of structural changes of the 3D electrodes over a week.(A) Sideview images of two 3D electrodes on day 1, day 3, and day 7 after the mechanically guided assembly process.(B) Distances between the two bonding sites measured from day 1 to day 7. Scale bars, 500 μm.

Fig. S8 .
Fig. S8.Characterization of a strain sensor with 1 mm electrode length.(A) Optical images of a sensor under uniaxial stretching at 0%, 50%, 100%, 150%, and 200%, with insets showing close-up views of the 3D electrodes.(B) Simulation, analytical, and experimental results for the relative change of bonding site distance and the corresponding relative capacitance change.The sensor has an electrode length of  = 1 mm and width of  = 1 mm. 0 corresponds to the capacitance with a bonding site distance of S0 = 403 µm.(C) Relative change in capacitance of the sensor, with different prestrain, during loading and unloading at applied strains of 50%, 100%, 150%, and 200%.Scale bars, 1 cm in A (500 μm in insets).

Fig. S10 .
Fig. S10.Design and characterization of a 3D capacitive strain sensor with electrode size of L = 250 µm and W = 550 µm.(A) 2D layout of the electrode design.The regions encircled by red dashed lines represent bonding sites (area: 250 µm × 250 µm).(B) Optical images of the front and angled view of the 3D electrodes formed by compressive buckling with 300% prestrain.(C) Relative capacitance change of the sensor during uniaxial loading and unloading at 50%, 100%, and 150% applied strain.(D) Capacitance change during cyclic 50% uniaxial loading and unloading.Scale bars, 200 μm in B.

Fig. S11 .
Fig. S11.Layouts of the 2D precursor of the five-crease, origami-inspired capacitive strain sensor design.(A) Overview of the stacked 2D precursor layouts.(B) Layout of the Cr/Au metal layer.(C) Layout of the parylene C layer.(D) Layout of the SU-8 stiffener layer.(E) Layout of the bonding sites on the backside of the 2D precursor.

Fig. S13 .
Fig. S13.Measurement of the sensor response and recovery time.(A) Experimental setup for measuring the sensor response and recovery time.(B) Capacitance responses from a representative sensor (L = 0.5 mm) subjected to 100% stretching and release for multiple cycles at fast speeds.

Fig. S14 .
Fig. S14.Capacitance response of a representative sensor ( = 1 mm) subjected to a series of step-up strain of 50% to a maximum of 200% followed by step-down strain to the initial state.The stretching and releasing rates are (A) 2 mm/s (strain rate: 8.3% s -1 ) and (B) 5 mm/s (strain rate: 20.8% s -1 ), respectively.

Fig. S18 .
Fig. S18.Sensor responses to normal pressure.(A) Optical images of a sensor before and during a static, persistent normal pressure.(B) Capacitance response of a sensor stretched to different levels (0%, 30%, and 60%) under different static, persistent normal pressures.Scale bars, 1 cm.

Fig. S20 .
Fig. S20.Design and performance of strain sensors with electromagnetic shielding.(A) Optical image (cross-sectional view) of a sensor with two electromagnetic shielding layers on the top and bottom.(B) Kirigami-inspired cut design in the electromagnetic shielding layers.(C) Comparison of sensor responses without and with electromagnetic shielding layers to proximity to human finger and pressing under different stretching conditions.(D) Comparison of noise levels for a sensor with and without the electromagnetic shielding layers.Scale bar, 1 mm.

Fig. S21 .
Fig. S21.Optical images of the directional strain sensing test.The sensor is attached to a silicone slab at (A) 0°, (B) 45°, and (C) 90° angles with respect to the longitudinal direction of the silicone slab.For each direction, the slab is stretched from 0% (left) to 70% strain (right).Scale bars, 2 cm for the top row and 250 µm for the bottom row.

Fig. S22 .
Fig. S22.Changes in the 3D electrodes, serpentine interconnects, and capacitance of the sensor under compressive strain.(A) Side view (top row) and top-down view (bottom row) of the sensor under compressive strain of 0%, -20%, and -45%.(B) The relative capacitance change of the sensor under different compressive strain.Scale bars, 1 mm for the top row and 5 mm for the bottom row in A.

Fig. S23 .
Fig. S23.FEA of sensor stretching at θ = 45° direction.The sensor is attached to a silicone slab at 45° angle with respect to the longitudinal direction of the silicone slab.(A) Experimental images and simulated electric potential field for the sensor at 0% strain.(B) Experimental images and simulated electric potential field for the sensor being stretched to 70% nominal strain.(C) Capacitance change from experiment and simulation.Scale bars, 500 μm in A and B.

Fig. S24 .
Fig. S24.Comparison of local strain in a deformed soft continuum arm from FEA and experimental measurements using sensors attached to the arm.FEA simulation results show the maximum principal strain distributions of the soft continuum arm under (A) 18.6% uniaxial stretching and (B) 12.6% uniaxial compressing.The measured local directional strain ε from the distributed sensors based on capacitance responses (data lines:  1 to  6 ) are compared with the simulated local strain from FEA (solid dots:  θ=0°,  θ=45°,  θ=90°) when the arm is under (C) stretching and (D) compression.

Fig. S25 .
Fig. S25.Additional results of sensing deformations of a soft continuum arm using the distributed sensors under (A) twisting and (B) hybrid deformations.Scale bars, 5 cm.

Table S2 . Comparison of the gauge factor, linearity, hysteresis, and baseline capacitance values of sensors (under 100% strain) with different electrode designs.
The values listed are the average measured values with standard deviation when more than 2 sensors are tested.