Optimum Sandwich Structures

An option towards finding the egg–box structure with the highest energy absorption capacity is the combination of two or more geometries in the form of sandwich structures. A sandwich panel can have many forms; from as simple as the addition of thin sheets on the top and base of an egg–box, to an arrangement of several egg–box structures of similar or different geometries, positioned on top of one another along the vertical axis. An egg–box sandwich panel sample is shown in Figure 5.62.

the best and most practical. The rational requirements are for the force–displacement curve to have a low load peak and a lengthy plateau. Therefore, any sandwich combination should be studied to fit the needs of its specific application.

Figure 5.62 – Typical Aluminium Egg–box Sandwich Panel

As a result of a comparative review of Figures 5.2 to 5.60 provided in the previous section, a list of most and least appropriate geometries in terms of both peak load and plateau length is derived and presented in Table 5.4. This can be used to create optimised sandwich panels, by the combination of the aluminium egg–boxes simulated for the purpose of this study.

Aspect Level Force kN Length mm Geometry

Peak Load Min 0.1 3 75deg – t0.8 – p20 Avg–low 1.5 35 45deg – t0.8 – p60 @ d5 Mean 2 25 45deg – t1.0 – p45 Avg–high 2.2 58 30deg – t0.8 – p45 Max 6 110 15deg – t1.2 – p60 Plateau Length Min 0.14 2.5 75deg – t1.2 – p20 Mean 2 25 45deg – t1.0 – p45 Max 2.5 120 15deg – t0.8 – p60 @ d5

The sandwich arrangement can consist of more than two geometries. However, bearing in mind the foremost use of egg–box structures as vehicle parts, combinations of more than two geometries can increase the height (depth) of the sandwich panel to impractically large values. It is important in the optimisation of the egg–box structure for its dimensions and shape to suit its function.

The egg–box sandwich panel can be made by combining the maximum plateau length and the minimum peak load. The setback is the opposite effect of these two factors. For a maximum plateau length, the peak load too rises to an undesired high value and vice versa. Hence, some compromise should be made to find geometries that attain both qualities. The geometries with the mean and average values provided in Table 5.4 satisfy the requirement to a reasonable extent.

In order for the sandwich panel produced to have maximum efficiency, the structures of ω , t=0.8mm, p=60mm, d=5mm and ω , t=0.8mm, p=60mm,

d=5mm are selected to provide minimum peak load and maximum plateau length,

respectively. The selected cell models have been highlighted in Table 5.4. It can be seen that both structures have the same thickness value; this counts as a facilitating factor in the fabrication of the geometries, serving towards the optimisation target.

When positioned at the top of the sandwich structure, the geometrical features of the model with the low peak load will act towards effectively reducing the damage by absorbing the sudden shock of the impactor. The sandwich structure then follows through an extended deformation procedure as the loads are transferred to the geometry, placed in the lower part of the sandwich.

A finite element model of the above combination is produced in ANSYS/LS– DYNA®. The model goes through the same impact exercise as the rest of the egg– box geometries in order to compare the outcome of this improved model with the result curves previously presented. Figure 5.63 (a) shows a cross section of the finite element model for the proposed sandwich panel. In Figure 5.63 (b) the model has been expanded to enable enhanced visualisation of the simulation. The aluminium sheet, the impactor and the supporting surface have also been scaled accordingly. The actual FE model consists of the single cells of part (a) of Figure 5.63.

(a) Single Cell Cross Section

(b) 3D Expanded Sandwich Panel (Total Height of 265mm)

To avoid unexpected deformations, a thin flat sheet of aluminium is placed between the two geometries as shown in Figure 5.63(a). The boundary conditions remain similar to those applied in the simulation of individual egg–box structures to allow for a true comparison of the outcomes.

Use of resins or welding in the production of the sandwich panel affects its performance and the accuracy of the comparative study of the results. It is therefore assumed that the two geometries and the middle sheet are restricted from movement in all lateral directions and contact conditions are applied to all outer surfaces as in the previous simulations. Hence, a condition in which the panels are boxed in by solid vertical surfaces is simulated.

The aluminium sheet placed between the two geometries has a thickness of 0.8mm, which will immediately deform when subject to forces, due to its flat, thin geometry. Thus, while keeping the geometries in their correct position, it does not significantly add to the strength of the sandwich structure, also allowing for a fair comparison of results.

Summing the height of the two geometries and the aluminium sheet, the entire structure has a total height of approximately 265mm, which in comparison, with the maximum height of the individual egg–boxes of this study being over 200mm, is a reasonably low height.

Figure 5.64 shows the force–displacement curves for the proposed sandwich structure (solid curve), the trend–line of this curve (dashed line) and the curves of each individual cell participating in the construction of the sandwich panel. It is evident that this structure displays a comparatively low peak load of less than 2kN, as expected and an exceptionally extended deformation length of 229mm which agrees with the entire height of the sandwich panel.

In addition, compared to the curves of each individual cell, it can be observed from Figure 5.64 that the ideal initial peak load of the 45deg–t0.8–d5–p60 model (obtained from Figure 5.34) is reflected in the sandwich panel while the length of the plateau in the proposed panel consists of the sum of the energy absorption length of 45deg–t0.8–d5–p60 and 15deg–t0.8–d5–p60 (from Figure 5.10) cells. The plateau

has in fact a desirable smooth consistency. This indicates that the proposed model is a comparatively optimised option.

Figure 5.64 – Comparison of FE Analysis for Optimised Sandwich Panel and Individual Optimum Egg–box Components

It is expected from an optimised structure to have a reasonably low weight relevant to its energy absorption capacity. The entire sandwich structure, including the middle sheet, has a mass of 0.1kg per cell which results in a 2.5kg mass for a 5×5 cell unit panel.

From a review of the structural weight and the total energy absorbed by each of the individual egg–box cells used in the proposed sandwich panel against the same measures of the optimised sandwich structure, it is shown that: while the sandwich panel has an average weight gain of 3.5% in comparison to the two individual cells, its total amount of energy absorbed is increased by roughly 33%. Such level of increase in energy absorption capacity, in proportion to the amount of weight gain is commendable. 0 1 2 3 4 5 6 7 8 9 10 0 50 100 150 200 250 Fo rc e K N Displacement mm

Optimised Sandwich Panel 45deg-t8-d5-p60

15deg-t8-d5-p60 Trendline

Additionally, the sandwich structure shows a 490% increase in the amount of energy absorbed, in comparison to the optimum egg–box structure with ω ,

t=0.8mm, p=45mm, d=5mm, while there exists a 10% increase in structural weight

between the two. Despite the large percentage of weight gain, the enhancement in the energy absorption, in addition to the comparatively similar initial peak load, makes the proposed sandwich structure an ideal candidate.

An experimental dynamic impact test of the sandwich structure can further confirm its suitability for use as an optimum aluminium energy absorber. However, the expensive and time consuming series of practical tests which lead to this structure have been prevented with the use of the less costly, repeatable finite element simulation method.