## 4 Thermomechanical Performance  
Here, we present the results of a typical corrugated core sandwich structure. The resulting surface temperatures of the stainless steel unidirectionally corrugated core sandwich structures and the temperature differences across the stainless steel sandwich structures for the two heating rates are shown in Figure 14. There was a rapid surface temperature rise from 0 s to 500 s, after which the surface temperature rose slowly to peaks of 1113 K and 1015 K at 1800 s for the high heating rate and low heating rate, respectively. This was followed by rapid surface cooling between 1800 and 2200 s. The maximum temperature difference across the sandwich structures was 138 K at 260 s and 119 K at 350 s for the high heating rate and low heating rate, respectively. The temperature differences were close to zero as the temperature of the sandwich structures approached the steady-state and then became negative values, implying that the outer face sheet of the sandwich structures was cooler than the inner face sheet. The minimum temperature differences reached \(-\)137 K and \(-\)120 K at 2400 s for the high heating rate and low heating rate, respectively. It was clear that the temperature difference was largest when the sandwich structures were experiencing rapid heating and cooling. The results of the other sandwich structures are summarized in Table 4. As discussed earlier, the surface temperature of the sandwich structures only depends on the incident heating rate and the emissivity. Table 5 confirms that the surface temperatures of the sandwich structures with the same applied heating rate and emissivity had similar values. The maximum temperature difference between the outer and inner face sheets was very slight among the types of corrugated core. The results also demonstrated that the two sandwich structures had similar effective thermal conductivities. Figure 13: Local permanent deformation. (**a**) Corrugated core sandwich structure after exposed to thermal load in the experiment; (**b**) von-Mises stress at a corner of the simulated model at 5000 s, unit: MPa. Figure 15 shows the displacement contour results of unidirectionally and bidirectionally corrugated core sandwich structures. The displacement contour of the unidirectional core had an ellipse shape owing to its asymmetrical geometry, while the bidirectional core had concentric circles owing to the symmetrical geometry. The displacement of the center point and the corner point in the diagonal line of the outer face sheets, as shown in Figure 15a,b, were used to calculate the deflection. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Materials**} & \multirow{2}{*}{**Core Types**} & \multirow{2}{*}{**Loads**} & \begin{tabular}{c} **Max Outer** \\ **Temperature (K) at** \\ **1800 s** \\ \end{tabular} & \begin{tabular}{c} **Max Temperature** \\ **Difference (K)** \\ \end{tabular} \\ \hline \multirow{3}{*}{Inconel} & \begin{tabular}{c} Unidirectional \\ Bidirectional \\ \end{tabular} & High heating rate & \begin{tabular}{c} 1108 \\ 1111 \\ \end{tabular} & \begin{tabular}{c} 157 \\ 159 \\ \end{tabular} \\ \cline{2-4}  & \begin{tabular}{c} Unidirectional \\ Bidirectional \\ \end{tabular} & Low heating rate & \begin{tabular}{c} 1012 \\ 1014 \\ \end{tabular} & \begin{tabular}{c} 134 \\ 138 \\ \end{tabular} \\ \hline \multirow{3}{*}{Stainless steel} & \begin{tabular}{c} Unidirectional \\ Bidirectional \\ \end{tabular} & High heating rate & \begin{tabular}{c} 1113 \\ 1113 \\ \end{tabular} & \begin{tabular}{c} 138 \\ 142 \\ \end{tabular} \\ \cline{2-4}  & \begin{tabular}{c} Unidirectional \\ Bidirectional \\ \end{tabular} & Low heating rate & \
\begin{tabular}{c} 1015 \\ 1011 \\ \end{tabular} &
\begin{tabular}{c} 118 \\ 124 \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Variation of maximum temperature difference with different corrugated cores. Figure 14: **Temperature results of simulation** at the two locations corresponding to the two heating rates.