3. Finite element simulations

Based on the experiments, corresponding finite element (FE) simulations have been undertaken by employing the nonlinear, explicit finite element code LS-DYNA 970.

## 3.1. FE model

Since the curved sandwich panel is symmetric about x-z and y-z planes, only a quarter of the curved panel was modeled, as shown in Figure 13. The entire model comprises 53,166 nodes and 61,257 elements. The LY-12 face-sheets were modeled by Belytschko-Tsay shell element,

Figure 13. FE model of the 1/4 curved sandwich panel and charge.

while the foam core was modeled by the default brick element. Similarly, one quarter of the charge was modeled shown in Figure 13, and eight-node brick elements with arbitrary Lagrange-Eulerian (ALE) formulation were adopted.

The mechanical behavior of face-sheets were represented by material model 3 of LS-DYNA (\*MAT\_PLASTIC\_KINEMATIC), while the aluminum foam core was modeled by material model 63 of LS-DYNA (\*MAT\_CRUSHALBE\_FOAM). A high-explosive material model (\*MAT\_HIGH\_ EXPLOSIVE\_BURN) incorporating the JWL equation of state (EOS\_JWL) was used to describe the material property of the TNT charge:

$$p = A \left( 1 - \frac{\omega}{R\_1 V} \right) e^{-R\_1 V} + B \left( 1 - \frac{\omega}{R\_2 V} \right) e^{-R\_2 V} + \frac{\omega E}{V} \tag{15}$$

where p is the blast pressure, E is the internal energy per initial volume, V is the initial relative volume, and ω, A, B, R1, and R<sup>2</sup> are the material constants, respectively. The material parameters of the curved sandwich panel and TNT charge are kept the same as experimental ones.

The bolts used in the tests to clamp the curved panels to the fixture were represented by nodal constraints in the numerical model. Symmetric boundary conditions about x-z and y-z planes were imposed. The blast load imparted on the front face-sheet of curved sandwich panel was defined with algorithm of \*CONTACT\_ERODING\_SURFACE\_TO\_SURFACE. Automatic, surface-to-surface contact options were generally used for curved sandwich panels.

## 3.2. Simulation results and discussion

sandwich panels with higher relative densities (15 and 18%) can decrease the average deflection, by 46.6 and 55.9%, respectively. However, for R = 500 mm sandwich panels, it is difficult to quantify the effect of core relative density on the structural response of specimens, due to the

The influence of curvature is deduced primarily from Figure 10. Two major influences can be identified: (i) the blast resistance of single-curvature sandwich panels with the larger radius of curvature is better, and (ii) a comparison between the response of the curved sandwich panels and the solid shell counterparts with the same mass is made, as stated in Section 2.2.2. Obviously, the deformation of curved sandwich panels with the smaller radius of curvature is governed by local penetration failure, while the deformation of the larger radius of curvature specimens is the global deformation with bending and stretching dominants. The larger deformation zone of the latter appears to contribute the greater plastic energy absorption and thus

Based on the experiments, corresponding finite element (FE) simulations have been under-

Since the curved sandwich panel is symmetric about x-z and y-z planes, only a quarter of the curved panel was modeled, as shown in Figure 13. The entire model comprises 53,166 nodes and 61,257 elements. The LY-12 face-sheets were modeled by Belytschko-Tsay shell element,

taken by employing the nonlinear, explicit finite element code LS-DYNA 970.

large variability in both impulse and deflection.

130 Contact and Fracture Mechanics

enhances the resistance to blast loading.

3. Finite element simulations

Figure 13. FE model of the 1/4 curved sandwich panel and charge.

3.1. FE model

2.2.5. Influence of specimen curvature on the shock resistance

### 3.2.1. Explosion and structural response process

The whole response can be divided into three stages: Stage I (expansion of the explosive), Stage II (explosive product interacts with the curved sandwich panel), and Stage III (plastic deformation of the curved sandwich panel under the inertia).
