## 5 Conclusions  
In this article, we have proposed a novel 3D meta-functional auxetic unit (MFAU) cell with a negative Poisson's ratio (NPR) for 3D printed composite bridge bearing applications. Experimental results have been used to validate numerical models. The models have been used for parametric studies and tailored design of the MFAU in order to develop new insights. The key benefit of using a designed structure with NPR is a high-performance to weight ratio. Their performance under compression was analytically and numerically studied, considering the local buckling failures and also determining the critical buckling loads and the buckling failure curve of the MFAU cell. Validation of the proposed  
Figure 14: Young’s modulus–density Ashby diagram. The diagram compares the proposed material against alternative materials. Figure 13: A comparison of the vertical stiffness of the meta-functional auxetic composite bridge bearing model, with different Young’s moduli and a common bridge bearing at the vertical displacement of 4 mm, between numerical and experimental relationships, respectively. model for additive manufacturing was conducted to obtain vertical stiffness by comparing experimental results. Major conclusions include:  
* Local buckling failure can potentially appear before yielding in the vertical and diagonal columns of the MFAU cell under compression. * The comparative results of the critical buckling load analysis of the vertical and diagonal column between the analytical solutions and the numerical predictions are in good agreement, with less than 0.70% and 0.62%, respectively, when the TPU material is in a linear elastic regime. * The failure curve of the MFAU cell model has been identified in order to predict its local buckling phenomena based on the slenderness ratios. * For bridge bearing applications, the overall compressive behaviour of the MFA composite bridge bearing model shows auxetic behaviour (contraction), with promising crashworthiness under compression. * For additive manufacturing, the findings in this paper indicate that the MFA composite bridge bearing model using a proposed material can, when compared to experimental results, perform well under compression as a common bridge bearing. Thus, fabrication by 3D printing and the development of this design for application could be possible for practical use in the near future. In short, robust analyses demonstrate that the proposed novel 3D auxetic sandwich core model is promising for composite bridge bearing applications. Further studies on the compression-shear behaviour of this novel core model for different environmental conditions will be presented in the future. Conceptualization, S.K. ; methodology, S.K. ; software, S.K. ; validation, PS. ; formal analysis, PS. ; investigation, S.K., P.S. ; resources, S.K. ; writing--original draft preparation, P.S. ; writing--review and editing, S.K. ; visualization, P.S. ; supervision, S.K. ; project administration, S.K. ; funding acquisition, S.K. All authors have read and agreed to the published version of the manuscript. This research was funded by European Commission, grant numbers: H2020-MSCA-RISE No. 691135. The APC was funded by the University of Birmingham Library's Open Access Fund. Not applicable. The data that support the findings of this study are available from the corresponding author upon reasonable request. The first author wishes to thank the Royal Thai Government for his Scholarship at the University of Birmingham. The last author wishes to gratefully acknowledge the Japan Society for Promotion of Science (JSPS) for his JSPS Invitation Research Fellowship (long-term), Grant No. L15701, at the Track Dynamics Laboratory, Railway Technical Research Institute and at Concrete Laboratory, the University of Tokyo, Tokyo, Japan. The JSPS financially supports this work as part of the research project, entitled \"Smart and reliable railway infrastructure\". Special thanks to the European Commission for H2020-MSCA-RISE Project No.