## 2 Bio-Inspired Corrugated Core Sandwich Structure  
A lightweight structure was our main goal in designing the skin structure for the TPS panel that would satisfy the thermal stress and thermal deflection limits. The density of each part in the whole sandwich structure needed to be decreased. Thus, in this study, we employed the corrugated core sandwich structure inspired from natural material that had a lower density compared with the dense structure used in our previous TPS panel-solid plate, Inconel 625 [5; 6]. The unit cell consisted of three parts: the outer face sheet, corrugated cores (unidirectional and bidirectional cores), and the inner face sheet. The face sheets are used as the impact surface layer and the bio-inspired corrugated core take  
Figure 2: Sinusoidal structure of the mantis shrimp’s dactyl club, reproduced from the work of [31]. (**a**) _Odontodactylus scyllarus_ mantis shrimp with the dactyl club marked in red, (**b**) the dactyl club was separated from the body, (**c**) a computerized tomography scan of the section, (**d**) microstructure of the impact region, (**e**) higher magnification of the impact region showing the sinusoidal shape, (**f**) a three-dimensional model of the sinusoidal shape. the function of impact protection like the ordered herringbone or wrinkle pattern. For fabrication of the corrugated core sandwich structure, the main shape of the core was modified from the original sinusoidal wave and the bi-sinusoidal wave, which are mathematically expressed in Equation (1). \[z(x,y)=f\cos\Bigl{(}\frac{2\pi}{L}x\cdot n_{x}\Bigr{)}\times\cos\Bigl{(}\frac{2 \pi}{L}y\cdot n_{x}\Bigr{)}, \tag{1}\]  
where \(x\) and \(y\) represent the longitudinal and transverse direction of the plane, \(z\) is the thickness direction (perpendicular to the plane), \(n_{x}\) and \(n_{y}\) are the number of waves along the two directions in the plane, \(L\) is the length of the unit cell (21.2 mm), and \(f\) is the amplitude of cosine wave (3.78). The upper peak and the lower peak of the sinusoidal and bi-sinusoidal shapes were flattened with the cutting planes so that the corrugated cores could be successfully welded to the outer and inner face sheets, as shown in Figure 3a,b. Figure 3b,c show the unit cells of the unidirectionally and bidirectionally corrugated core sandwich structure, respectively. The geometrical sizes of the unit cells are given in Table 1. The full sandwich structure models are presented in Figure 4. Each sandwich structure consists of \(8\times 8\)-unit cells with a length of 170 mm. The sandwich structure must bear the maximum temperature of about 1100 K at the outer face sheet. Therefore, we needed to choose materials with high strength that could endure high-temperature loads. Furthermore, fracture toughness is essential to the sandwich structure to prevent possible impact from orbital debris in space. We chose two metallic materials to design the corrugated core sandwich structures: Inconel 625 superalloy and stainless steel 304. Owing to the complex sinusoidal perturbation of the corrugated cores, the bending characteristics of the two corrugated cores and flattened corrugated cores were difficult to obtain; therefore, the three-dimensional unit cell model of the two corrugated cores was built in a CAD software using the expression in Equation (1), as shown in Figure 3a,b. The area moment of inertia of each corrugated core about the axes on the midplane of the structure was calculated. The results of the area moment of inertia are shown in Table 2. Obviously, the area moment of inertia of the unidirectional core was larger than that of the bidirectional core. Therefore, the unidirectional core structure would bend less than the bidirectional core structure. Figure 3: Conceptual design and dimensions of a unit cell, unit: mm.