## 4 Thermomechanical Performance
**(a)** Surface temperatures of stainless steel unidirectionally corrugated core sandwich structure and (b) temperature differences between outer and inner face sheets. The results showed that the UCS structure had less deflection than the BCS structure. However, the UCS structure has a weaker strength in the line with the direction perpendicular to the core direction, and the deflection distribution could differ from each direction location of the structure; therefore, it could result in several local wrinkles on the surface structure of the unidirectional corrugated core sandwich structure. Specifically, the localized wrinkles were found at the locations near the corner of the unidirectional corrugated core sandwich structure, as marked with circles in Figure 15a,c. While the bidirectional core structure provides a similar strength in the two directions, the deflection distribution could be similar for the two directions, as shown in Figure 15b,d. Note that the present corrugated core sandwich structure was intended to be employed for the skin structure of a metallic TPS panel, which needed to be as smooth as possible to prevent the boundary layer transition [53]. The localized wrinkles could result in the local boundary layer transition, which could increase local aerodynamic heating. Therefore, the use of a bidirectional core structure was preferred over the unidirectional core structure for such the skin structure of a metallic TPS panel. On the basis of the discussion earlier about the advantage of the bidirectional core structure for the skin structure of spaceflight vehicle, we only fabricated the bidirectionally corrugated core sandwich structure for our thermomechanical test. However, for applications such as nuclear engineering, civil engineering, or automotive engineering, the unidirectional core sandwich structure could be an excellent candidate along with the bidirectional core sandwich structure. The investigation on the performance of these two structures for other applications should be associated with the types of load and possible constraints. The corresponding deflections of the UCS and BCS, made of Inconel and stainless steel materials, with the two applied heating rates are shown in Figures 16 and 17, respectively. Note that, if the temperature difference is positive, zero, or negative, the sandwich structures will bow out, stay flat, or bow in, respectively. The deflections follow the general tendency of the temperature differences shown in Figure 14b. With the applied high heating rate, the maximum deflections were 1.32 mm for the Inconel UCS and 1.62 mm for the BCS. For the stainless steel, they were 1.74 mm for the UCS and 2.04 mm for the BCS. With the applied low heating rate, the maximum deflections were 1.11 mm for  
Figure 15: Simulation results of stainless steel corrugated core sandwich structures. Displacement contour (**a**) at 485 s for the unidirectional core and (**b**) at 445 s for the bidirectional core, with a low heating rate. Displacement contour (**c**) at 398 s for the unidirectional core and (**d**) at 400 s for the bidirectional core, with a high heating rate, unit: mm. the Inconel UCS and 1.32 mm for the BCS. They were 1.49 mm for the stainless steel UCS and 1.71 mm for the BCS. In general, the maximum deflection of the BCS was larger than that of the UCS, and the sandwich structures made of Inconel resulted in a smaller deflection than those made of stainless steel. The deflections decreased from the maximum values to 0 mm at 2000 s, after which they went to negative and achieved minimum values at 2400 s (after touchdown). We were concerned about the bow-out deflection in the heating stage because the vehicle was in the flight path of a mission, and this bowing out into the boundary layer of the external surface of the vehicle could cause flow disturbances and lead to a transition of the boundary layer from laminar to turbulent, thereby greatly increasing the incident heating [7; 53].