# Advanced Numerical Analysis of Transport Packaging
## 4 Discussion  
The proposed methodology for the evaluation of the reduction in the box load-bearing capacity under transport loading conditions and possible consequent damages was extensively validated in [30]. Therefore, such an approach is effectively adopted in the present research, to deepen the understanding of and to further investigate the dependence of \(\Delta BCT^{ij}\) on cardboard material structural and mechanical parameters, for various case combinations of cardboard materials and box geometries. Since the transport loading condition may create permanent plastic deformations, buckling and damage in the packaging box, a consolidated understanding of the observed responses shall be developed through the interpretation of the structural behaviour of the analysed system, specifically for constitutive material properties, structural configurations, boundary conditions and loading effects. In particular, it is worth observing that material parameters may produce multiple effects related both to the anisotropic constitutive parameters of each layer and to the shell-homogenised mechanical parameters. Such features have been revealed to influence the expected box compression response from a material viewpoint. With respect to the numerically tested examples, this is observed when comparing the computational outcomes for varying cardboard materials (i = 1, 2, 3,...13). With regard to the mechanical constitutive parameters, the discussion of the gathered results may highlight that increases in mechanical properties (namely for higher quality constituent cardboard) tend to reduce the sensitivity of the box compression response to reduction effects. Moreover, geometrical box design turns out to be a key parameter in influencing the extent of reduction in the box load-bearing capacity, where box sizes and shape ratios can significantly alter the structural response while varying the stiffness and strength of box cardboard side wall panels (i.e., structural shell elements). The numerical and graphical outcomes gathered in the previous section allow us to identify this behavioural response and its related trends under corresponding varying box designs (j = I, II, III). To reach more developed conclusions, it is worth observing that the constitutive material and structural effects may also be considered combined effects that mutually influence the box load bearing capacity and the possible reduction in it. Among the investigated relationships and trends between constitutive constants (Table 2), material structural parameters (Table 1) and/or box designs (Figure 1) with the reduction in the box load bearing capacity, we will briefly discuss the seemingly linear correlation observed with the cardboard bending stiffness, focusing on the cardboard box sidewall bending stiffness of structural shells. Therefore, from the results obtained and summarised, it is possible to observe that the proposed globally unified measures of such structural responses and interpretations represent a guideline methodology for the assessment of the possible load bearing capacity reduction of cardboard boxes under transport load conditions, as well as an efficient approach for the structural interpretation of such conditions, for engineering research and industrial application. One of the key conclusions of this study is that the reduction in compressive strength never exceeded 20%. This conclusion is a practical indication of what the impact of strength reductions due to transport loads in simple flap boxes with the aforementioned designs could be. To the best of the authors' knowledge, no studies have addressed the reduction in box strength caused by transport loads. The available scientific literature includes studies that, at a more general level, evaluate the impact of various packaging transportation solutions, such as palletising methods, on sustainability [47]. However, more specific research directly addressing the aspects considered in this study remains unavailable.