## 4 Core Topology Optimisation  
From the analyses and conclusions in the previous sections, it is clear that the core has the most significant role in the energy absorption process: it absorbs approximately 90% of the energy, contributing with less than 30% of the mass of the structure. Consequently, the most efficient way to increase energy absorption and blast performance of the sandwich plate is to optimise the core. However, for armour and protection applications, increasing the efficiency of the sandwich panel should be done by increasing both the energy absorption of the skins and core, whilst keeping the areal density unchanged. This section discusses a number of approaches that are designed to maximise the energy absorption of the plate, based on numerical simulations, namely by changing the configuration of the core. This follows the conceptual ideas presented by a number of other authors [15; 16; 17; 49]. However, in these works--which include a wavy core between skins--the energy absorption is increased under quasi-static loading. A set of sinusoidal core shapes with flat aluminium plane skins were chosen to promote an increase of the energy absorption under blasts event. Figure 10 shows an example. This geometry is also chosen due to its relative ease of manufacture and assembly, because only the core needs to be modified. Figure 9: Kinetic energy \(E_{\text{k}}\) and internal energy \(E_{\text{i}}\) for the individual components of the sandwich plate (skins and core), for core thicknesses of (**a**) 10 mm (NL20-10) and (**b**) 15 mm (NL20-15). Dashed line indicates separation between core compression and core bending and stretching. The optimum configuration was found by optimising the geometrical amplitude and frequency of the sinusoidal wave defining the shape of the core. The centre line of the core is defined by \(z=A\cos(\omega x/W)\), where \(z\) is the out of plane coordinate, \(A\) is the wave amplitude, \(W\) is the width of the plate (in this case \(W=100\) mm), \(\omega=2\pi f\) is the angular frequency, and \(f\) the frequency. As \(f\) increases, the distance between the peaks (\(w=W/f\)) is reduced, as shown in Figure 10. The particular combinations of amplitude and frequency tested are listed in Table 7. The areal density of the panel was kept constant to isolate the energy absorption as the parameter being optimised. Additionally, the core geometrical amplitude was kept between the thickness of the NL20-10 and NL20-15 plates, in order to ensure consistency with the validation analyses described in previous sections. To maximise computational efficiency, the above simulations were simplified and only the Load Blast Enhanced method was used. Moreover, the numerical model, as shown in Figure 10, only takes into account the free span of the sandwich. Boundary conditions representative of the experimental testing rig were implemented, where the edge of the rear skin was fixed by restricting displacements but not rotations. Additionally, the nodes on the edges of the front skin are guided--their movement is only constrained along \(x\) and \(y\). The materials models and LBE approaches are the same as described in the previous sections and a reference case is included for comparison. The results presented in Figure 11a,b show the kinematics of the plates during the blast impact. These figures show the velocities of the central nodes on the front and rear face sheets for the simulations listed in Table 7. Figure 11a shows the results for different amplitudes of the sinusoidal core shape with constant frequency \(f=4\), compared to the reference case. It is observed that the front