Smart cushioning device integrating self-folding origami honeycomb structure and inductor-capacitor passive wireless sensor

Principles of LC passive wireless sensors and SHD fabrication methods

Figure 1a shows a schematic diagram of a typical LC passive wireless sensor. The LC passive wireless sensor consists of an inductor for transmission and a capacitor for sensing, forming an LC resonant circuit. The capacitance changes in response to variations in the physical quantity being measured, and the resonant frequency changes accordingly. The relationship between capacitance and resonant frequency is expressed by Eq. (1)^28,29,30.

Here, \({f}_{s}\) is the resonant frequency, \({L}_{s}\) is the inductance, and \({C}_{s}\) is the capacitance. Figure 1b shows the corresponding equivalent circuit diagram. The communication inductor is wirelessly connected through mutual induction with a readout coil, and the resonant frequency change of the sensor is detected by monitoring the input return loss (\({S}_{11}\)) using a Vector Network Analyser (VNA) connected to the readout coil.

Figure 1c illustrates the fabrication process of SHD. SHD is created by laminating a copper LC passive wireless sensor onto a self-folded origami honeycomb structure (SHS). SHS is fabricated by cutting paper using a cutting plotter and performing inkjet printing, which causes the paper to fold autonomously³⁹. The LC passive wireless sensor is formed by cutting and shaping copper tape using a cutting plotter, and then transferred onto the cells of SHS to complete SHD.

Sensor design and performance evaluation (LC integrated design)

For the initial SHD design, we developed an integrated LC structure by embedding both the inductor and capacitor within SHS. Figure 2a illustrates the electrode pattern and the fabricated SHD. SHD consists of a capacitor that detects deformation and an inductor that transmits signals. We used SHS with a cell-wall height of 35 mm and a cell size of 618 mm², adjusting the size and shape of the electrode accordingly (\({w}_{1}\,\)= 15 mm, \({w}_{2}\) = 50 mm, \({h}_{1}\) = 30 mm, \({h}_{2}\,\)= 20 mm). Figure 2b presents a schematic illustration of SHD deformation detection mechanism, along with a conceptual graph showing the changes in the capacitance of the sensor \({C}_{s}\) and resonant frequency \({f}_{s}\). When compressed, the hinge distance of SHS decreases. As the hinge distance narrows, \({C}_{s}\) increases, and \({f}_{s}\) decreases. Therefore, the capacitor was placed at the hinges. The inductor was transferred to the upper part of the cells, where the surface is relatively flat, to maintain wireless connectivity with the readout coil.

To verify whether SHD behaves as designed, we conducted compression tests and measured the changes in inductance \({L}_{s}\) and capacitance \({C}_{s}\) before and after compression. SHD was placed in an SHD enclosure box (42 × 74 × 48 mm) to constrain the boundaries and enhance the reproducibility of the compression deformation. We fabricated three SHD and tested each to full compression. Figure 2c shows the deformation of the inductor and capacitor sections when compressed for 40 mm. It can be observed that the hinge distance decreases in response to the compression. Figure 2d presents the changes in \({L}_{s}\) and \({C}_{s}\) before and after compression. The bar graphs show the averages of three trials, with error bars indicating the standard deviation. Compression reduced the distance between hinges, resulting in an increase in \({C}_{s}\). This behaviour is consistent with the design, as the reduced distance between capacitor plates at the hinges increases \({C}_{s}\). However, the inductor deformation unexpectedly caused a decrease in \({L}_{s}\). The change in \({L}_{s}\) was greater than that in \({C}_{s}\). According to Eq. (1), the dominant change in \({L}_{s}\) caused \({f}_{s}\) to increase, deviating from the intended behaviour. While SHD deformation can be measured through changes in \({L}_{s}\), the inductor deformation lacks reproducibility, making accurate quantification challenging.

Sensor design and performance evaluation (LC separated design)

To accurately measure the deformation of SHD, we developed a separated LC design where an external inductor is connected to the capacitor embedded within SHS. The use of an external inductor ensures that the change in resonant frequency \({f}_{s}\) caused by SHD deformation depends solely on the change in capacitance \({C}_{s}\). Figure 3a shows the electrode patterns for LC separated design SHD. As in the integrated LC design, we adopted SHS with a cell-wall height of 35 mm and a cell size of 618 mm². Two electrodes were transferred onto the front surface of the cell-wall, measuring 15 mm in width and 35 mm in height.

The compression behaviour of SHS is shown in Supplementary Fig. 1. The central part of the cell-wall buckles first during compression. We designed and arranged the electrodes based on this behaviour, fabricating six designs of SHD with electrode gap angles of \(\theta\) = 0°, 30°, 60°, −30°, and −60°, as shown in Fig. 3a. The gap between the two electrodes was maintained at 3 mm while adjusting the electrode angles. Origami structures can be designed and controlled by pre-creasing weak points that guide their deformation behaviour⁴⁰. We expected that buckling from the weakened part with the electrode gap would increase the alignment between the two electrodes, which would raise capacitance \({C}_{s}\) and lower the resonant frequency \({f}_{s}\).

We conducted compression tests to evaluate the buckling stability of SHD. SHD was inserted into an SHD enclosure box (42 × 74 × 48 mm) to constrain the boundaries and enhance the reproducibility of compression deformation. Three SHD were fabricated for each electrode pattern and tested until fully compressed. Figure 3b shows the compressive force-displacement curve of SHS. The light blue area in the graph indicates the variability of the compression of three SHS samples. In the initial stage of compression (displacement \(x\) = 0–15 mm), the top of hinges is compressed. When \({x}\) exceeds 15 mm, the cell-walls are compressed. In this study, the range from \(x\) = 15 mm to 35 mm is defined as the plateau region, where compression and buckling of the cell-wall dominate. The standard deviation of the compression force in this region was regarded as the variation in the buckling behaviour of SHS and SHD.

For reference, the force range examined in Fig. 3b was selected with logistics applications in mind, particularly the transportation of fragile items such as fresh produce. When normalised by the enclosure footprint area (42 × 74 mm²), the forces shown in Fig. 3b correspond to a nominal compressive stress on the order of several to ~10 kPa. This stress scale is comparable to the impact stress expected from a single-fruit drop event (e.g. one apple) when the impact energy is absorbed within the plateau deformation range of the origami honeycomb structure. While the present study does not aim to optimise cushioning performance for a specific product, this comparison provides a practical reference for the relevance of the examined force range to typical small packaged goods.

Figure 3c shows the experimental results of the buckling variation with changes in the electrode angle \(\theta\). SHD with \(\theta\) = 0°, 30°, and −30° exhibited less variation than SHS, and SHD with \(\theta\) = 0° showed the smallest variation. The buckling variation of SHD with \(\theta\) = 0° was reduced by 29.2% compared to SHS. In contrast, SHD with \(\theta\)= 60° and −60° exhibited greater variation than SHS. SHD with \(\theta\) = 60° showed a 51.0% increase in variation compared to SHS. These results indicate that the placement of electrodes stabilises the buckling behaviour of the origami honeycomb structure, with the most stable buckling tendency observed when SHD with \(\theta\) = 0°.

To determine the optimal electrode gap \(g\), we fabricated SHD with electrode gaps of \(g\) = 1 mm, 3 mm, 5 mm, and 7 mm, as shown in Fig. 3d. Similar to the electrode angle selection, we evaluated the buckling stability through compression tests. Figure 3e shows the results of the buckling stability tests with changing the electrode gap \(g\). SHD with \(g\) = 3 mm, 5 mm, and 7 mm exhibited less variation than SHS. Among them, SHD with \(g\) = 5 mm exhibited the smallest variation, with a 67.6% reduction compared to SHS. In contrast, SHD with \(g\) = 1 mm exhibited the largest variation, with a 20.4% increase compared to SHS.

We also measured the capacitance change ratio \({\Delta C}_{s}/{C}_{s0}\) of SHD with varying \(g\). The following equation was used to derive the capacitance change ratio.

Here, \({C}_{s0}\) denotes the initial capacitance value. Figure 3f shows the capacitance change of SHD as changing the electrode gap \(g\). The bar graphs show the average of three trials, with error bars indicating the standard deviation. SHD with \(g\) = 1 mm exhibited the smallest capacitance change ratio \({\Delta C}_{s}/{C}_{s0}=0.67\). This result suggests that the buckling behaviour was unstable, which prevented the two electrodes from aligning as expected. In contrast, SHD with \(g\) = 3 mm exhibited the largest capacitance change ratio \({\Delta C}_{s}/{C}_{s0}=2.10\). As the electrode gap increased to \(g\) = 5 mm and 7 mm, \({\Delta C}_{s}/{C}_{s0}\) decreased accordingly. This decrease was attributed to the reduction in electrode area with increasing \(g\), given that height of the cell-wall was fixed. Based on the results shown in Fig. 3e, f, we adopted SHD with \(\theta\) = 0° and \(g\) = 3 mm for the following experiments, because it exhibited the most stable buckling behaviour, and the largest capacitance change ratio.

To enhance sensor sensitivity by increasing the dielectric constant and to prevent electrical short circuits upon contact, a 1.7 mm thick PVC tape was applied to the electrode surface. The rightmost bar in Fig. 3f indicates the capacitance change ratio \({\Delta C}_{s}/{C}_{s0}\) of SHD with PVC tape. The ratio reached \({\Delta C}_{s}/{C}_{s0}=3.12\), indicating a 30.8% increase compared to SHD with \(g\) = 3 mm without PVC tape. These results suggest that using the dielectric sheet prevents unintended short circuits while improving the sensitivity of SHD.

Deformation modelling and investigation of sensing mechanisms

SHD deforms vertically under compression, while the capacitance changes result from the buckling of the cell-walls. To investigate the sensing mechanism, we modelled the relationship between the compression displacement \(x\) and the folding angle of the cell-walls \({\theta }_{c}\). Figure 4a presents the deformation model of SHD and the defined modelling parameters. The angle of the buckled cell-wall represents the buckling angle \({\theta }_{c}\). The geometric relationship between the buckling angle \({\theta }_{c}\), compression displacement \(x\), and electrode distance \({d}_{c}\) is as follows.

Here, \({l}_{0}\) is the height of cell-wall. From Eqs. (3) and (4):

Thus, Eq. (5) allows the experimentally obtained \(x\) to be converted to \({\theta }_{c}\).

Using Eq. (2), \(x\) is converted into \({\theta }_{c}\). However, because of the elastic property of the paper, SHD recovers after compression. Directly substituting \(x\) obtained from the mechanical experiment into Eq. (5) does not yield consistent results. Figure 4b illustrates the recovery process of SHD. We incorporated the recovery value into \(x\) to enhance the model accuracy. Figure 4c presents the results of the compression test along with the structure recovery. When \(x < 15\) mm, SHD remains in the elastic deformation region, where the cell-wall height does not change. Theoretically, when \(x > 15\) mm, the cell-wall height should decrease as the compression displacement increases. However, because of recovery characteristics of SHD, the experimental results deviated from the theoretical values. This difference was defined as the recovery value and incorporated into the equation derived from the deformation model.

Compression tests were conducted to verify the accuracy of the model, and the calculated \({\theta }_{c}\) values were compared with those of the actual SHD. Three SHD samples were prepared, and the buckling angle \({\theta }_{c}\) was measured for each compression displacement from \(x\) = 0 to 40 mm. Figure 4d presents a comparison between \({\theta }_{c}\) values obtained from the deformation model and those measured from actual SHD. The experimental plots show the average of three trials, with error bars indicating the standard deviation. Incorporating the recovery value enhanced accuracy of the proposed model, demonstrating agreement with the experimental results across all compression displacements. In the following experiments, \(x\) is converted into \({\theta }_{c}\) using the model for further analysis.

To validate the sensing mechanism, we conducted electromagnetic capacitance simulations of SHD using the finite element method (FEM). The simulation was conducted using COMSOL Multiphysics 6.1 with AC/DC module. To replicate the deformation, we built a model with two electrodes (16 × 15 × 0.07 mm) placed on the cell-wall section (35 × 15 × 0.805 mm) and enclosed in an air domain with a radius of 15 cm. The simulations were conducted for two models: one without PVC layered on the electrodes and the other with 1.7 mm thick PVC. \({\theta }_{c}\) was varied from 180° to 20° in increments of 20° for both models.

Figure 4e presents the simulation results of the electric field distribution. As the structure buckled, the electric field intensity between the opposing electrodes increased, corresponding to the increase in capacitance. Figure 4f presents the capacitance values \({C}_{s}\) as solid lines, varying with \({\theta }_{c}\). As the cell-wall buckled and the electrodes moved closer, \({C}_{s}\) increased. \({C}_{s}\) was higher in the model with PVC than in the model without PVC. The increase in \({C}_{s}\) resulted from the application of the dielectric material, consistent with the results in Fig. 3e.

To validate the simulation results, we conducted compression tests and measured the capacitance \({C}_{s}\). Three SHD without PVC and three SHD with 1.7 mm thick PVC layered on the electrodes were fabricated. Compression was applied at 5 mm intervals from x = 0 to 40 mm, and \({C}_{s}\) was measured at each \({\theta }_{c}\). Figure 4f plots the experimental values of \({C}_{s}\) at each buckling angle \({\theta }_{c}\), connected by dashed lines. The plots show the average of three trials, with error bars indicating the standard deviation. As the SHD buckled and the electrodes moved closer, \({C}_{s}\) increased. In both cases, with and without PVC, the experimental results closely matched the simulation results. Additionally, the small error bars demonstrated high reproducibility of \({C}_{s}\) across the three experiments. This reproducibility was achieved by stabilising the buckling behaviour through adjustments to the electrode angle \(\theta\) and gap \(g\) in prior experiments. These results indicate that \({\theta }_{c}\) can be estimated from measurements of \({C}_{s}\). Furthermore, adding the PVC dielectric layer increased \({C}_{s}\), thereby improving the sensor resolution. We successfully demonstrated the measurement of SHD buckling deformation through the development of a deformation model and the use of finite element method (FEM) simulations.

Wireless deformation measurement performance and demonstration

A system was developed to wirelessly measure deformation by connecting an inductor to the electrodes of SHD. Figure 5a presents a schematic diagram of the wireless system. Rectangular loop coils made from copper tape, each cut to a size of 30 × 30 mm, were used for the wireless connection. One coil was connected in series with the capacitor electrodes of SHD, and the other coil was connected to a Vector Network Analyser (VNA). The two coils were positioned 3 mm apart, and the resonant frequency was measured using the VNA.

To verify whether SHD deformation can be measured wirelessly, resonant frequency change ratio during compression was measured. Equation (6) was used to derive the resonant frequency change ratio \(\left|{\Delta f}_{s}\right|/{f}_{s0}\).

Here, \({f}_{s0}\) denotes the initial capacitance value. Three SHD without PVC and three SHD with PVC were prepared. Each SHD was compressed at 5 mm intervals from 0 to 40 mm, and the resonant frequency at each compression displacement was measured. The compression displacement \(x\) was converted to the buckling angle \({\theta }_{c}\) based on the constructed model. Figure 5b presents the relationship between \({\theta }_{c}\) and the resonant frequency change ratio \(\left|{\Delta f}_{s}\right|/{f}_{s0}\). Supplementary Fig. 2 shows the relationship between \({\theta }_{c}\), \({C}_{s}\), and \({f}_{s}\). The plots represent the average of three trials, with error bars defined as the standard deviation. As shown in Supplementary Fig. 2, \({f}_{s}\) decreases as \({C}_{s}\) increases and follows an inverse square root relationship. This result is consistent with Eq. (1), indicating that SHD exhibited the expected behaviour as designed. SHD with PVC increased \(\left|{\Delta f}_{s}\right|/{f}_{s0}\) compared to SHD without PVC. A comparison of \(\left|{\Delta f}_{s}\right|/{f}_{s0}\) showed an average increase of 124%, indicating that dielectric material contributes to improving the sensitivity of the wireless sensor performance.

Two demonstrations were conducted to verify whether the fabricated SHD can contribute to improve logistics and enhance transport traceability. The first demonstration involved measuring the weight of load. Weight monitoring ensures appropriate load management, helping to prevent overloading and uneven loading. Figure 5c presents a schematic diagram of the wireless weight measurement system. The cell-walls must buckle in response to the applied load to measure the weight. As shown in Fig. 3b, a force peak of SHD exists, which constrains the buckling of the cell-walls when objects are placed on. SHD was pre-strained to eliminate the force peak to address the force peak issue, allowing the cell-walls to deform according to the applied load. This method removes force peaks that could potentially damage protected objects while maintaining 90% of the energy absorption performance³⁹.

The pre-strained SHD was sandwiched between two acrylic plates (90 × 150 mm) to form a honeycomb sandwich structure and connected in series with a rectangular loop coil (3 × 3 mm). Weights ranging from 100 to 500 g were placed on the honeycomb sandwich, and the resonant frequency peaks for each weight were measured using the VNA. Figure 5d presents the wireless measurement results. As the load increased, the buckling angle \({\theta }_{c}\) decreased, causing the resonant frequency peak to shift to the left. A comparison between 0 and 500 g loads revealed a decrease of 16 MHz in the resonant frequency \({f}_{s}\). Additionally, \({f}_{s}\) was found to decrease by approximately 1 MHz for every 31 g increase in weight.

The second demonstration involved detecting SHD damage by the fallen object. Monitoring the condition of the cushioning material in real time allows instant identification of the time, location, and situation of damage during transportation. Identifying damage causes and taking action are easier, improving logistics and traceability in transportation. Figure 5e presents a schematic of damage detection system for SHD with the fallen object. A 3 × 3-cell SHD was sandwiched between acrylic plates (120 × 200 mm) to form a honeycomb sandwich structure. Water was added to a spherical PET bottle with a 50 mm radius until it weighed 500 g, then it was dropped from a height of 300 mm to SHD sandwich structure. Two SHD samples were prepared for drops at the edge and centre, with jumper wires connected to each cell to measure \({f}_{s}\) before and after the drop. Figure 5f shows the distribution of resonant frequency shifts before and after dropping the object. The \({f}_{s}\) changed according to the drop location, enabling successful detection of the damage state. Electrodes were attached to all cells in the demonstration, however SHD detection resolution can be adjusted by varying the electrode placement depending on the application. Changing the number of turns in the coils connected to each cell allows the formation of a matrix and stacking of multiple layers, enabling simultaneous measurement of damage of the multiple cells⁴¹.

In this study, we have developed the wireless smart cushioning material, SHD, by designing electrodes and arranging them according to the compression behaviour of SHS. Laminating sheets with different rigidities enhanced deformation stability and enabled wireless measurement of SHD deformation. The simulations conducted with FEM software confirmed that the capacitance changes due to deformation aligned with the expected electrostatic mechanism. We demonstrated the functionality of SHD as the smart cushioning material in two tests: measuring the weight of load and detecting damage caused by the falling object. We are confident that our developed SHD will contribute to logistics improvements and enhance transport traceability, acting as a pioneering example for the future adoption of the wireless smart cushioning materials.