Conclusion
In this study, we developed an SCS that self-folds into high-strength structures from a single sheet of paper by inkjet printing. The concept of the SCS is based on the properties of the origami technique for enhancing structural strength. The SCS has the following design parameters: printing line width L and number of printing lines n. By changing these parameters, we fabricated an SCS with various amplitudes d and half-wavelengths w. Specifically, with an increase in the linewidth, the amplitude increased, and the half-wavelength decreased. Additionally, with an increase in the number of lines, the amplitude decreased, and half-wavelength changed with respect to L. This relationship was validated by measuring d and w for a total of 60 SCSs. Furthermore, by approximating the SCS cross-section as a triangle, we derived a linear approximation relationship between L and the fold angle θ. The R2 values of the derived approximations were all close to one, which were consistent with the linear relationship between L and θ. Based on this approximation, we derived a model for d and w of the SCS, which allowed for the design of an SCS with the desired shape. Thereafter, we developed a methodology to design the SCS of the desired shape by self-folding a paper.
Furthermore, we conducted 36 three-point bending tests on 12 types of SCSs with different design parameters to evaluate their mechanical properties. By evaluating the mechanical properties, we established the design theory of an SCS with high stiffness. Corrugated structures have higher second area moments at higher amplitudes \cite{timoshenko1959theory} . However, the three-point bending test results revealed that the SCS with the highest amplitude deformed significantly under loading, and the second area moment decreased. This is because the SCS exhibited a non-uniform stiffness of printed and unprinted parts in its self-folded structure. To fabricate an SCS with higher strength, it is not sufficient to simply design a higher amplitude. In particular, it is necessary to consider the stiffness distribution throughout the SCS. Moreover, we evaluated the mechanical property of the SCS stacked with 2, 3, and 10 sheets to verify the strength-enhancing effect of the stacking sheets. As observed, the second area moment of 10 sheets was 1461% higher than that of one sheet.
The proposed SCS could be designed and fabricated rapidly to achieve the desired shape and stiffness. As the material is paper, the SCS is inexpensive and recyclable. Additionally, the flexibility of the paper material allows for it to be stacked without occupying a significant amount of space, even after forming the SCS. Moreover, it improves the stiffness without requiring additional components. Hence, the proposed SCS is a promising smart core material that self-folds while maintaining the stiffness required by the core material of the sandwich structure. Moreover, it does not create space before or after self-folding, and demonstrates a high transport performance. Based on the stiffness investigation, it was confirmed that the SCS exhibits anisotropic stiffness. Hence, the SCS can be used in applications that require load-bearing, such as the core material of sandwich structures; in addition to anisotropy, e.g., as morphing wings and the skeleton of pneumatic actuators \cite{li2017fluid}. More complex and robust structures can be created by filling the printer with various chemicals and ordering the folding sequence \cite{shigemune2021programming}. By printing electrodes on the same paper surface, the application of intelligent core materials with integrated actuators and sensors can be realized in the future \cite{shigemune2017printed}.
Supporting Information
The supporting information file related to our article is hosted on Authorea.
Conflict of Interest
The authors declare no conflict of interest.
Acknowledgements
This work was supported by JSPS KAKENHI, grant numbers 18H05895 and 19K20377. This research is supported by Adaptable and Seamless Technology transfer Program through Target-driven R&D (A-STEP) from Japan Science and Technology Agency (JST) Grant Number JPMJTM20CK. This research is supported by SIT International Research Center for Green Electronics. We would like to thank Editage (
www.editage.com) for English language editing.