## 4 Thermomechanical Performance
While the bow-in deflection in the cooling stage had negative values after 2000 s, the vehicle was approaching the ground and the largest deflection was observed when the vehicle was on the ground; thus, the bowing in of the sandwich structures may not cause significant overheating issues related to boundary layer transition, as also reported by the authors of [8; 12]. There was some inward permanent deflection of the sandwich structures after one mission. The permanent deflection for the sandwich structures made of stainless steel was bigger than that made of Inconel because of the lower material strength. However, the inward permanent deflection of the two sandwich structures was very small compared with the total thickness of the sandwich structures. This may be because the residual stress appeared locally near the corners and edges of the sandwich structures, as further discussed in the next paragraph. Figure 18 shows the von Mises stress contours of the UCS and BCS at 5000 s. The maximum von Mises stresses in both thermal loads were approximately 510 MPa and 390 MPa for the sandwich structures made of Inconel and stainless steel, respectively, and did not exceed the ultimate strength of Inconel 625 (827 MPa), as shown in Figure 18a-d, and stainless steel 304 (505 MPa), as shown in Figure 18e-h.  
Figure 16: Total deflection of sandwich structures made of Inconel: (**a**) unidirectional core, (**b**) bidirectional core. Figure 17: Total deflection of sandwich structures made of stainless steel: (**a**) unidirectional core, (**b**) bidirectional core. Figure 18: Stress distribution of the unidirectionally corrugated core sandwich structure (UCS) and bidirectionally corrugated core sandwich structure (BCS) at 5000 s. The von Mises stress scaled from 0–510 MPa for the Inconel UCS (**a**) low heating rate and (**b**) high heating rate; and for the Inconel BCS (**c**) low heating rate and (**d**) high heating rate. The von Mises stress scaled from 0–390 MPa for the stainless steel UCS (**e**) low heating rate and (**f**) high heating rate; and for the stainless steel BCS (**g**) low heating rate and (**h**) high heating rate. For the sandwich structures made of Inconel material, the area of von Mises stress levels exceeding 420 MPa were very localized, as shown in the close-up view in Figure 18a-d, whereas the highest von Mises stress levels elsewhere were less than 250 MPa, which was well within the material allowable strength (Inconel 625 yield strength: 420 MPa [39; 40]). The high-stress areas occurred in several elements of the corrugated cores closest to the edges and the four corners of the sandwich structures. The high stress distribution may be because of the boundary conditions of the sandwich structures, which were the simply supported conditions applied on the four edges of the inner face sheet. For the sandwich structures made of stainless steel 304 under the low heating rate, there were several areas located near the four corners and the edges of the sandwich structures where the von Mises stress exceeded 210 MPa, while most areas of the sandwich structures resulted in low stress within the material allowable (stainless steel yield strength: 210 MPa [41]), as shown in the close-up views in Figure 18e,g. For the sandwich structures made of stainless steel 304 under a high heating rate, more areas located at the four corners and the edges of the sandwich structures had von Mises stress exceeding 210 MPa, as shown in the close-up view in Figure 18f,h. Although the sandwich structures made of stainless steel under the high heating rate did not fail because the stress was below the ultimate strength of the material, the plastic deformation resulted in larger permanent deformation in more regions of the sandwich structures, as shown in Figure 16. Therefore, the use of stainless steel for the sandwich structures under such a high heating rate needs to be considered in terms of stress failure and permanent deformation.