An analytical model of blast resistance for all-metallic sandwich panels subjected to shallow-buried explosives

Abstract

When subjected to localized blast loading from shallow-buried explosives (e.g., mines buried under sand), how would a sandwich structure dynamically perform has been extensively investigated, both experimentally and numerically, but not analytically. This study aimed therefore to establish an analytical model for preliminary assessment of using sandwich panels with square honeycomb cores for protective applications against shallow-buried explosions, with the influence of boundary conditions (e.g., simply supported versus fully clamped) accounted for. The resulting maximum permanent deflection of the sandwich panel was expressed as an explicit function of explosive mass, sand density, sand moisture content, depth of burial, stand-off distance as well as key sandwich panel geometrical parameters. For validation, the model predictions were compared with existing experimental measurements as well as numerical results obtained with the method of finite elements, with good agreement achieved. The validated analytical model was subsequently employed to quantify the effects of various influencing factors. The maximum deflection was found to increase with increasing explosive mass, sand density, and sand moisture content, but with decreasing stand-off distance. As the height of core was increased, the maximum deflection decreased firstly and then increased, suggesting that selecting a proper core height was critical in the design of sandwich panel constructions for optimal blast resistance. Regardless of boundary conditions, an intersection point existed between the normalize deflection versus normalized impulse curves that correspond separately to the sandwich panel and its monolithic counterpart of equal mass. When the normalized impulse had a magnitude smaller than the intersection value, the sandwich panel exhibited a superior blast resistance to the monolithic one, while the opposite held when the normalized impulse was located to the right of intersection. The normalized impulse corresponding to the intersection was dependent upon face sheet thickness, core height, and core relative density. The proposed analytical model provides valuable guidance for designing high-performance protective structures against intensive impulsive loadings.

Appendix A

1.1 Validation of assumed equivalence between non-uniform and uniform blast loadings

To validate the assumed equivalence between non-uniform and uniform blast loadings, numerical simulations with the method of finite elements were performed. Figure 

Fig. 11

Maximum permanent deflections of sandwich panel subjected to non-uniform and uniform blast loading, with explosive mass m_e varied from 2 to 6 kg, at intervals of 1 kg

11 plotted the predicted maximum permanent deflections $\overline{W} = {W \mathord{\left/ {\vphantom {W {L_{{\text{h}}} }}} \right. \kern-\nulldelimiterspace} {L_{{\text{h}}} }}$ of a sandwich panel subjected to both non-uniform and uniform blast loadings, with the explosive mass m_e varied from 2 to 6 kg with d_e/h_e = 3, at intervals of 1 kg). Table

Table 7 Relative errors of calculated maximum permanent deflections of sandwich panel subjected to non-uniform and uniform blast loadings

7 compared the corresponding relative errors. For the comparison, the sandwich panel had a normalized mass of ${{\overline{M}} \mathord{\left/ {\vphantom {{\overline{M}} {\left( {\rho_{{\text{f}}} L_{{\text{h}}} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\rho_{{\text{f}}} L_{{\text{h}}} } \right)}} = 0.02$, a normalized core height of $\overline{h}_{{\text{c}}} = {{h_{{\text{c}}} } \mathord{\left/ {\vphantom {{h_{{\text{c}}} } {L_{{\text{h}}} }}} \right. \kern-\nulldelimiterspace} {L_{{\text{h}}} }} = 0.10$, and a relative density of $\overline{\rho }_{{\text{c}}} = 0.04$. In addition, the stand-off distance H was 400 mm, the depth of burial δ_b was 100 mm, the sand density ρ_s was 2200 kg/m³, and the sand moisture content w_s was 0. It was seen from Fig. 3 and Table 7 that the maximum permanent deflections of sandwich panel subjected to non-uniform blast loading were slightly different from those under uniform blast loading, with a maximum relative error less than 6%. Figure 

Fig. 12

Screenshots of numerically simulated deformation evolution of sandwich panel subjected to (a) non-uniform blast loading, and b uniform blast loading, with m_e = 3 kg

12 compares the deformation evolution of sandwich panel subjected to non-uniform blast loading with that under uniform blast loading, with the explosive mass fixed at m_e = 3 kg. The core in the middle of sandwich is considerably compressed under non-uniform blast loading as shown in Fig. 12(a), while it is not obviously compressed under uniform blast loading as shown in Fig. 12(b). However, although the deformation mode under non-uniform loading is different from that under uniform loading, the results of Fig. 11 and Table 7 demonstrate that the equivalent method is accurate in predicting the maximum permanent deflection of a sandwich panel. The assumed equivalence between non-uniform and uniform blast loadings in predicting the maximum permanent deflection is therefore validated.