# Advanced Numerical Analysis of Transport Packaging
## 5 Conclusions  
This study examines the impact of different types of corrugated cardboard on the reduction in the compressive load-bearing capacity of packaging after exposure to standard transportation loads. Thirteen types of cardboard and three box designs were analysed using the finite element method to simulate both static and dynamic transport conditions, following the standards of applying vertical vibrations to simulate the conditions of packaging being transported. Mechanical tests on the cardboard materials, including edge crush and bending tests, provided data for modelling the material properties, with simulations accounting for plastic deformation and vibration effects. The results highlight how varied material properties influence the structural integrity of packaging differently, offering insights for optimising packaging resilience during transport.  
One of the most interesting observations was that as the bending stiffness of the boards in the machine direction increased, the strength loss of the packaging due to transport loads also increased with an apparently linear trend. Other material constants, such as the ECT value, shear stiffness, torsional stiffness, and moduli of elasticity, did not show any significant or explicit correlation.  
In view of possible future developments, the mechanical interpretation of the box compression response may provide an effective tool for the assessment of packaging transport and damage conditions, as well as for cardboard box design improvements, related to post-buckling design and detailing reinforcement through the use of accessories. Therefore, additional analyses are planned to examine more complex box designs, incorporating both strengthening elements, such as tapes, and weakening features, such as perforations and holes, to determine whether similar trends may be observed despite these modifications.  
Conceptualisation, [PERSON] ([PERSON]), [PERSON] ([PERSON]); methodology, D.M. and T.G. ([PERSON]); software, D.M. and. A.C.; validation, D.M. and A.K.-P.; formal analysis, A.C. and D.M.; investigation, A.C., D.M.; writing--original draft preparation, A.C., A.K.-P. and T.G. ([PERSON]); writing--review and editing, A.C., A.K.-P., [PERSON] ([PERSON]) and [PERSON] ([PERSON]); visualisation, A.C.; supervision, [PERSON] ([PERSON]) and [PERSON] ([PERSON]); project administration, [PERSON] ([PERSON]); funding acquisition, [PERSON] ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
The research was funded within the grant of The National Centre for Research and Development under the number POIR.01.01.01-00-0002/21.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
This work was published within the grant of The National Centre for Research and Development under the number POIR.01.01.01-00-0002/21.  
The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  
In addition to the graphical results presented in Section 3, this appendix reports on the completed set of data on the percentage reduction in the box compressive load bearing capacity (\(\Delta BCT^{ij}\)) versus material data (refer to Table 1, in Figures A1 and A2) and versus material constitutive parameters (refer to Table 2, in Figures A3-A5).  
Figure A1: Percentage reduction (%) in the box compression test index (\(\Delta BCT^{ij}\)) versus \(SST\) (Nm), for various materials (thirteen dots) and dimensions (j = I, II, III).