The sandwich structure consists of two-face sheets sandwiching the core material. A honeycomb core is widely used as one of the core materials \cite{he2019effect}. However, the manufacture of honeycomb cores is complicated and costly. Therefore, extensive research on honeycomb cores based on the origami technique has been conducted \cite{saito2014manufacture}. In this regard, the origami technique enables manufacturing honeycomb cores without tedious processing. Folded cores, inspired by origami, are also being developed as alternative core materials. Examples include the Miura-ori, commonly used to shape folded cores \cite{miura2009science}, and creases similar to Ron Resch's patterns \cite{resch1968self}. Folded cores can be manufactured from various sheet materials by a simple process and tailored into various shapes that meet specific functional requirements \cite{zhou2017thermal}. Thus, the origami technique has been applied to core materials for sandwich structures.
On the contrary, corrugated cores are stiff, perpendicular to the corrugation, and flexible in the parallel direction, and anisotropy exists in the structure \cite{yokozeki2006mechanical}. This property is leveraged in load-bearing applications, such as corrugated cardboards, roofs, and walls and morphing wings \cite{dayyani2015mechanics}. By contrast, the folded core is stiff in both perpendicular and parallel directions. The stiff direction of a corrugated core with linear creases is more than 75 times stiffer than that of the folded core \cite{woodruff2021curved} \cite{gilewski2014comparative} . The closed-cell structures also create problems of air and humidity retention, which can increase the total weight and erode core properties \cite{katzman2008moisture}. Conversely, corrugated cores have open channels in one direction, which minimizes these problems.
Corrugated, honeycomb, and folded cores can be easily fabricated using the origami technique. Origami structures can be fabricated by folding manually or using robotic devices \cite{balkcom2008robotic}, but this method is not efficient for mass production at small or large scales or for remote applications. Mass production is possible using manufacturing equipment, but large machines require space allocation and initial investment, and the compression process consumes large amounts of energy. It also compromises the tailor-made feature of creating structures with desired mechanical properties in a short time.
To overcome these shortcomings, self-folding techniques have been studied for the automatic fabrication of origami structures \cite{peraza2014origami}. Self-folding generally uses smart materials that respond to external stimuli, such as shape memory alloy (SMA)\cite{peraza2013design}, shape memory polymer (SMP)\cite{ge2016multimaterial}, and hydrogel\cite{an2016predicting}. The crease pattern is pre-defined for these smart materials, and the application of heat or light triggers automatic folding. Since external stimuli automatically form the origami structure, rapid manufacture and autonomous assembly at remote sites are possible without human intervention. Moreover, since 3D structures can be constructed by simply changing the 2D crease patterns, a variety of origami structures can be created. Liu et al. proposed self-folding SMP sheets using light. They defined crease patterns to fold SMP sheets by 90° and fabricated a rectangular shape. By changing the crease patterns, the fold angle was adjusted to 60°, and a tetrahedron structure was formed\cite{liu2012self}.
Other than the origami technique, core materials for sandwich structures are manufactured by compression molding\cite{rejab2013mechanical}, hot press molding\cite{du2018fabrication}, embossing with rollers, and other methods\cite{heimbs2013foldcore}. However, these manufacturing methods require molds and rollers for each design requirement, which increases the cost, time, and energy required to form the structure. Therefore, the development of core sandwich structures using smart active materials, which are named smart cores, has also been investigated\cite{feng2020creative}. Tolley et al. fabricated a self-folding origami consisting of a three-layer shape memory composite with SMP as the intermediate layer to form a Miura-ori structure\cite{tolley2014self}. Evans et al. fabricated a micro-scale self-folding origami consisting of three layers of photo-cross-linkable copolymers with a thermosensitive hydrogel as the intermediate layer. They realized a Miura-ori structure by controlling the fold angle\cite{na2015programming}. However, studies on the mechanical properties of the smart core sandwich structures are scarce. Hubbard et al. fabricated corrugated structures with rectangular, square, trapezoidal, and triangular waveforms using stimuli-responsive thermoplastic sheets\cite{hubbard2021stiff}. They conducted compression and tensile tests by varying the wavenumbers of the fabricated corrugated structures and investigated the effects of the wavenumbers on the compressive and tensile properties of the structures. However, mechanical properties were not investigated with respect to varying amplitude and wavelength , which are important structural parameters of the corrugated structure when using the tailor-made feature of the self-folding methods.
In this study, we developed a corrugated structure made of a smart material. A design theory of the structure was proposed, and its mechanical properties were evaluated. We named the developed structure “self-folded corrugated structure (SCS).” Using the reaction between a smart material and inkjet printed ink, the structure was formed autonomously without applying any external energy. First, we proposed a structural model to predict the final shape of the SCS from the printed pattern. By calculating the fold angle from the proposed model, a linear relationship between the printed linewidth and the fold angle was obtained as in the conventional method\cite{shigemune2016origami}, which validated the proposed model. The design parameters of the SCS were the printed line width and number of printed lines. SCSs with various amplitudes and wavelengths were formed by varying the parameters. Secondly, the mechanical properties of the SCS were evaluated by conducting a three-point bending test. The results showed that the SCS had anisotropic stiffness, which is one of the typical properties of corrugated structures. In addition, the higher the amplitude of the SCS, the higher the second area moment, as in the theoretical equation of the second area moment of corrugated structures. As a characteristic of the SCS, we also confirmed that, for a large wavelength range, the structure collapses due to the flexibility of the paper itself. Furthermore, we found that the SCS is sufficiently flexible for easy stacking after self-folding. The structural strength of the SCS can be improved exponentially by stacking structures. Thus, the fabrication system of the SCS provided stiffness to a sheet of paper, which is innately flexible to be applied as a core material. Since the only fabrication method is the application of solution by inkjet printing, the corrugated structure with the desired stiffness can be created rapidly according to the desired applications. Moreover, the SCS can be stacked without occupying much space, thus minimizing energy consumption during transportation and reducing the transportation costs. Therefore, the SCS is expected to be developed as a novel smart core due to its high stiffness, digital manufacturing ability, and high transportability.
Concept of the self-folded corrugated structure