3.2.1.2. Stage II: explosive product-curved panel interaction

The expansion of the explosive begins to interact with the front face-sheet of curved sandwich panel at this stage. It is seen from Figure 15 that the explosive product-curved panel interaction lasts over a time period of approximately 32 μs, from approximately t = 28 μs to t = 60 μs, corresponding the duration of the contact force between the explosive product and target structure almost becomes to zero. Figure 15 shows the interaction of the explosive product with the curved panel, accompanied with the upward distortion as a result of the reflection from the curved target panel. Indentation deformation is first occurred in the central region of front face-sheet of the specimen, and then it extends both outward and downward with the transfer of blast impulse. Back face-sheet of the specimen has little deformation at this stage. Once the coupling interaction is completed (i.e., the contact force becomes to zero at t = 60 μs),

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In this stage, there is no coupling effect between the explosive product and the structure, and the curved sandwich panel remained to deform under the inertia, as shown in Figure 16. The central indentation failure of the front face-sheet is formed by gradually compressing the foam core, and the deformation extends outward until to the external clamped boundaries by traveling plastic hinges. The deformation of the curved sandwich panel structure is mainly governed by the plastic bending and stretching, accompanied with the slight oscillation. The whole curved sandwich panel finally presents a global dishing shape, and the maximum

Figure 17 compares the experimental and simulated permanent deflection at the central point of the back face-sheet. It is shown that all data points are close to the line of perfect match, which represents that the simulated data are agreed well with the experimental results. In order to better understand the deformation mechanism of curved sandwich panel, the progressions of deflections at several key nodes (as shown in Figure 18) along the central

the high-explosive model should be manually deleted from the finite element code.

3.2.1.3. Stage III: deformation of curved sandwich panel under its own inertia

deflection of the back face-sheet occurs at the central point of the specimen.

3.2.2. Deflection response of the back face-sheet

Figure 17. Comparison of experimental and numerical back-face deflection.

Figure 16. A typical process of curved sandwich panel deformation.

front face-sheet of the specimen, and then it extends both outward and downward with the transfer of blast impulse. Back face-sheet of the specimen has little deformation at this stage. Once the coupling interaction is completed (i.e., the contact force becomes to zero at t = 60 μs), the high-explosive model should be manually deleted from the finite element code.

#### 3.2.1.3. Stage III: deformation of curved sandwich panel under its own inertia

In this stage, there is no coupling effect between the explosive product and the structure, and the curved sandwich panel remained to deform under the inertia, as shown in Figure 16. The central indentation failure of the front face-sheet is formed by gradually compressing the foam core, and the deformation extends outward until to the external clamped boundaries by traveling plastic hinges. The deformation of the curved sandwich panel structure is mainly governed by the plastic bending and stretching, accompanied with the slight oscillation. The whole curved sandwich panel finally presents a global dishing shape, and the maximum deflection of the back face-sheet occurs at the central point of the specimen.

## 3.2.2. Deflection response of the back face-sheet

3.2.1.2. Stage II: explosive product-curved panel interaction

134 Contact and Fracture Mechanics

Figure 16. A typical process of curved sandwich panel deformation.

The expansion of the explosive begins to interact with the front face-sheet of curved sandwich panel at this stage. It is seen from Figure 15 that the explosive product-curved panel interaction lasts over a time period of approximately 32 μs, from approximately t = 28 μs to t = 60 μs, corresponding the duration of the contact force between the explosive product and target structure almost becomes to zero. Figure 15 shows the interaction of the explosive product with the curved panel, accompanied with the upward distortion as a result of the reflection from the curved target panel. Indentation deformation is first occurred in the central region of

> Figure 17 compares the experimental and simulated permanent deflection at the central point of the back face-sheet. It is shown that all data points are close to the line of perfect match, which represents that the simulated data are agreed well with the experimental results. In order to better understand the deformation mechanism of curved sandwich panel, the progressions of deflections at several key nodes (as shown in Figure 18) along the central

Figure 17. Comparison of experimental and numerical back-face deflection.

circumferential and longitudinal directions are presented in Figure 19. Both circumferential and longitudinal nodes for the front and back face-sheets have the similar deformation trend. At ~300 μs, all the nodes, except the node C5, have the maximum transient deflections, and then the deflection of these nodes decreases obviously due to the rebound of the elastic

deformation until the whole deformation process is finished. The deformation of the back facesheet obviously lags behind that of the front face-sheet, and the central point deflection of back face-sheet is also smaller than that of front face-sheet due to the foam core compression.

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Figure 20 shows the histories of plastic dissipation of the components of a curved sandwich panel (R250-h0.8-C10-r15%-B3) subjected to blast loading. In the early stage of the response, the front face-sheet compresses the aluminum foam core, resulting in core crushing and significant energy dissipation. It can be found from Figure 20 that most of energy is dissipated by the large deformation of front face-sheet and core compression and core constitutes a major

Effects of the impulse level and geometric configuration on the energy absorption of the components of the curved sandwich panels were indicated in a stack bar diagram in Figure 21. The partition of energy absorption of specimens is compared and analyzed in terms of the impulse level (specimen nos. 1–3), face-sheet thickness (specimen nos. 4–6), and core relative density (specimen nos. 7–9). The increase of impulse leads to a rise of total plastic energy dissipation in the specimens. Most of energy dissipation is attributed to large plastic deformation of front face-sheet and core compression. The energy absorption does not present a monotonic relationship with the face-sheet thickness. The specimen with 0.8-mm-thick facesheets has the best energy absorption performance, followed by that of 0.5-mm-thick facesheet, and the worst is that of 1.0-mm-thick face-sheet. This can be explained as follows: the

3.2.3. Energy absorption capability

contribution, which is about 60% of total dissipation.

Figure 20. History of plastic dissipation of sandwich specimen during plastic deformation.

Figure 18. Locations of the circumferential and longitudinal nodes on the face-sheets.

Figure 19. Deflection variation of key points on the face-sheets of the curved sandwich panel. (a) Circumferential (front face-sheet), (b) circumferential (back face-sheet), (c) longitudinal (front face-sheet), and (d) longitudinal (back face-sheet).

deformation until the whole deformation process is finished. The deformation of the back facesheet obviously lags behind that of the front face-sheet, and the central point deflection of back face-sheet is also smaller than that of front face-sheet due to the foam core compression.
