PSI - Issue 71

A. Kumar et al. / Procedia Structural Integrity 71 (2025) 453–460

459

Fig. 7. (a) Plot for G 13 at various θ and h/l ratios; (b) % error in G 13 at various h/l ratios and θ in the FE and theoretical results

Fig. 8. (a) Plot for G 23 at various θ and h/l ratios; (b) % errors in G 23 at various h/l ratios and θ in the FE and theoretical results

A similar trend can be seen in the G 23 (Fig.8(a)) , where with the increase in cell angles, the G 23 values decrease up to a particular point and then increase. These are happening at h/l =2, 2.5, 3. Whereas at h/l =1.5, the G 23 values are increasing with cell angles. The % error in G 23 increases with a decrease in cell angles at h/l =2.5,3 (Fig.8(b)). The average absolute % error in G 23 is negligible, approximately only 0.4 %. 5. Conclusions A theoretical methodology using Castigliano's second theorem was developed to determine the out-of-plane elastic properties of re-entrant honeycomb structures. This method calculates shear moduli ( G 13 , G 23 ) and Young's modulus ( E 3 ) based on material properties and the geometry of the representative cell element (RCE). Finite element analysis with periodic boundary conditions validated the approach, showing close agreement with theoretical predictions (average errors: 1.88% for E 3 , 2.27% for G 13 , and 0.4% for G 23 ). A parametric study also examined the effects of height-to-length ratio ( h/l ) and cell angles ( θ ), providing insights for optimizing re-entrant honeycomb design. While the present study focused on deriving effective properties, evaluating the fidelity of the homogenized model in replicating full-structure behaviour remains an important avenue for future investigation. References Alderson, K. L., 2000. Auxetic materials: the positive side of being negative. Engineering Science & Education Journal, 9(4), 148-154(6). Dong, Z., Li, Y., Zhao, T., Wu, W., Xiao, D., Liang, J., 2019. Experimental and numerical studies on the compressive mechanical properties of the metallic auxetic reentrant honeycomb. Materials and Design, 182. https://doi.org/10.1016/j.matdes.2019.108036 Gibson, L. J., and Ashby, M. F., 1997. Cellular Solids: Structure and Properties. Cambridge Solid State Science Series. Kanit, T., N’Guyen, F., Forest, S., Jeulin, D., Reed, M., Singleton, S., 2006. Apparent and effective physical properties of heterogeneous materials: Representativity of samples of two materials from food industry. Computer Methods in Applied Mechanics and Engineering, 195(33 – 36), 3960 – 3982. Kumar, A., Muthu, N., Ganesh Narayanan, R., 2024. Prediction of peel strength of sandwich sheets made of aluminium alloys fabricated by friction stir spot welding based hybrid process using cohesive zone modeling and finite element simulations. Engineering Failure Analysis, 162, 1 –