## 2 Material Properties and Calculation Model
### Blow-Off Impulse Model of a Composite Reinforced Panel  
According to the temperature distribution of the composite reinforced panel, blow-off impulse elements are obtained after the electric-thermal coupling analysis is done. SOLID69 is then replaced by the explicit dynamic element SOLID164 for blow-off impulse analysis in ANSYS software. This element type has 8 nodes and 3 degrees of freedom per node. The meshing method and number of  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Load step** & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\
**Time/\(\upmu\)s** & 1 & 2 & 2.6 & 3 & 7 & 10 & 10.5 & 11 & 15 & 30 & 50 & 80 \\
**Load/kA** & 46.3 & 58.9 & 60 & 59.5 & 42.6 & 31.5 & 30.3 & 28.5 & 19.1 & 4.2 & 0.57 & 0.028 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The time and current value in each load step of 2.6/10.5 \(\upmu\)s-60 kA.  
Figure 3: Double exponential impulse current waveform. (**a**) Relationship of \(t_{1}/t_{2}\); (**b**) waveform of 2.6/10.5 \(\upmu\)s-0 kA.  
Figure 2: Finite element model and boundary conditions of the composite reinforced panel. (**a**) Boundary conditions in benchmark skin; (**b**) boundary conditions in the T stripper.  
meshes are the same as that in Section 2.2. At the same time, the initial composite materials model in the blow-off impulse area is replaced by a high-explosive material model which is described by Jones-Wilkins-Lee equation of state (JWL EOS). The pressure of JWL EOS is defined as follows:  
\[p=A\bigg{(}1-\frac{\omega}{R_{1}V}\bigg{)}e^{-R_{1}V}+B\bigg{(}1-\frac{\omega}{ R_{2}V}\bigg{)}e^{-R_{2}V}+\frac{\omega E_{0}}{V} \tag{2}\]  
where, \(p\) is the pressure of the high-explosive element. \(V\) is the initial relative volume. \(E_{0}\) is the initial explosion energy per unit volume. \(A\), \(B\), \(R_{1}\), \(R_{2}\), and \(\omega\) are material constants.  
The material type adopted for the area which expects blow-off elements is the 59# constitutive model. This represents that the material type of Mat_composite_failure_solid_model ranks No.59 in keyword user's manual of ANSYS/LS-DYNA. The surrounding sides of the composite reinforced panel are fixed and the unified system of unit kg-m-s is adopted. The constitutive model 59# can be defined as follows:  
\[f=\frac{4\Big{[}\sigma_{1}-\frac{X_{t}-X_{c}}{2}\Big{]}^{2}}{\left(X_{t}+X_{c} \right)^{2}}+\frac{4\Big{[}\sigma_{2}-\frac{Y_{t}-Y_{c}}{2}\Big{]}^{2}}{\left( Y_{t}+Y_{c}\right)^{2}}+\frac{4\Big{[}\sigma_{3}-\frac{Z_{t}-Z_{c}}{2} \Big{]}^{2}}{\left(Z_{t}+Z_{c}\right)^{2}}+\frac{\sigma_{12}^{2}}{S_{12}^{2}} +\frac{\sigma_{13}^{2}}{S_{23}^{2}}+\frac{\sigma_{23}^{2}}{S_{23}^{2}}-1 \tag{3}\]  
where, \(X_{t}\) and \(X_{c}\) are longitudinal tensile and compressive strengths. \(Y_{t}\) and \(Y_{c}\) are transverse tensile and compressive strengths. \(Z_{t}\) and \(Z_{c}\) are normal tensile and compressive strengths. \(S_{12}\) is shear strength in-plane. \(S_{13}\) and \(S_{23}\) are transverse shear strengths. \(f\) is an ellipsoidal function. The whole calculation process is shown in Figure 4. The main parameters of the high-explosive model, JWL EOS and 59# constitutive model are given in Table 7.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Parameters** & \(\rho\)**/kg/m\({}^{3}\)** & \(D\)**/m/s** & \(P_{\text{CJ}}\)**/GPa** & \(A\)**/GPa** & \(B\)**/GPa** & \(R_{1}\) & \(R_{2}\) & \(\omega\) & \(E_{0}\)**/KJ** \\ \hline
**Value** & 1520 & 6718 & 18.5 & 540.9 & 9.4 & 4.5 & 1.1 & 0.35 & \(8\times 10^{6}\) \\ \hline
**Parameters** & \(X_{c}\)**/MPa** & \(X_{t}\)**/MPa** & \(Y_{c}\)**/MPa** & \(Y_{t}\)**/MPa** & \(Z_{c}\)**/MPa** & \(Z_{t}\)**/MPa** & \(S_{12}\)**/MPa** & \(S_{13}\)**/MPa** & \(S_{23}\)**/MPa** \\ \hline
**Value** & 1281 & 1708 & 192 & 34 & 280 & 52 & 128 & 128 & 96 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Main parameters of the high-explosive model, JWL EOS, and 59# constitutive model.  
Figure 4: Calculation process of blow-off impulse analysis.