## 4 Analysis of Calculation Results
### Damage Degree Prediction Using Dimensionless Number Din\({}^{*}\)  
Extensive numerical simulations were carried out to obtain the damage degree of the box chamber structure. The relationship between the non-dimensional deflection and the non-dimensional number \(D_{in}^{*}\), as well as the division of the damage modes, are shown in Figure 10. Based on the failure mechanisms of the box chamber structure, the equation describing the deformation of the wall plate is proposed based on the dimensionless number \(D_{in}^{*}\)  
\[f(\omega^{*})=\bigg{(}\frac{W}{\textit{phab}}\bigg{)}^{\beta}\bigg{(}\frac{E} {\textit{hab}\sigma_{y}}\bigg{)}^{\gamma}\Big{(}\frac{a}{\hbar}\Big{)} \tag{9}\]  
where \(\omega^{*}\) is the dimensionless deflection (ratio of wall plate deflection to thickness), \(\frac{E}{\textit{hab}\sigma_{y}}\) is the ratio of the explosive energy to the deformation energy of the wall plate, \(\frac{W}{\textit{phab}}\) is the ratio of the explosive equivalent to the mass of the wall plate, and \(\frac{a}{\hbar}\) is the structural scale effect. The influence factor \(\alpha\) is proposed, which is related to the relative strength of impact, and \(\alpha_{1}=1-\mathrm{e}^{-\frac{E}{\sigma_{y}^{\mathrm{th}}}}\) is the yield strength influence factor when \(\alpha_{1}=1\) is completely dominated  
Figure 8: Type of openings. Figure 9: Stress and plastic strain curves at the marker pilot. (**a**) Variation of effective plastic strain; (**b**) Variation of effective strain. by yield strength; \(\alpha_{2}=1-\mathrm{e}^{-\frac{W}{\rho\mathrm{i}\mathrm{i}\mathrm{n}}}\) is the inertia influence factor when \(\alpha_{2}=1\) is completely dominated by inertia. When \(D_{in}^{*}<0.37\) the explosion equivalent is small, the wall plate subjected to the impact force will be flattened or become bent, and all physical phenomena will occur following the easiest route. When the impact load is small, the wall plate deformation by inertia is relatively large and more easily flattened. With the increase of the equivalent, the impact of yield strength increases, the wall plate is more likely to show bend deformation, and the wall plate presents mode I large deflection plastic deformation. At this time, the wall plate deformation degree formula is  
\[f(\omega^{*})=\left(\frac{W}{\rho\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}} \right)^{\alpha_{1}+\alpha_{2}}\left(\frac{E}{\mathrm{i}\mathrm{n}\mathrm{d} \mathrm{e}\mathrm{v}_{g}}\right)^{2-\alpha_{1}-\alpha_{2}}\left(\frac{a}{h}\right) \tag{10}\]  
when \(0.37<D_{in}^{*}<1.15\), the wall plate presents mode I large deflection plastic deformation. When \(1.15<D_{in}^{*}<2.2\) presents mode II wall plate central breach, the damage degree of the wall plate at this stage is dominated by the yield strength. The degree of deformation of the wall plates, and whether they fracture, depends on the plastic strain and the fracture strain. Whether the wall plate is deformed enough to fracture, as well as the degree of the deformation, depends on the plastic strain and fracture strain. When \(2.2<D_{in}^{*}<6.75\), the implosion load is gathered in the box edge and corner, the wall plate presents mode III corner tensile tear damage, and wall plate deflection with an increase of the dimensionless number first increases and then decreases. When the the edges of a wall plates show tensile tear damage, the deformation of the edge is much larger than the center of the plate, resulting in the center part being \"pulled into\" the center of the deflection of a small decline. This stage is dominated by yield strength and inertia together. The box structure under the implosion load produces corner rupture or prismatic tearing, the formation of a pressure relief port, and partial energy release. When \(D_{in}^{*}>6.75\), the wall plate mode IV shear damage, the degree of damage to the wall plate at this stage, is dominated by inertia. When the wall plate is subjected to internal  
Figure 10: The variation of deflection and damage modes of box structures with \(D_{in}^{*}\).