Abstract
To establish an equivalent model of the core layer of the grid beetle elytron plate (GBEP) and perfect the bionic system of the beetle elytron plate (BEP), the in-plane and out-of-plane equivalent shear moduli of the basic unit of the GBEP core layer are calculated by the energy method, and the accuracy of the expressions is verified by comparison with the results obtained with the finite element method and experiments. The results show that the in-plane and out-of-plane shear moduli can be expressed as functions of \(\eta \), the ratio of trabecula radius to unit width, and the trends of the in-plane and out-of-plane shear moduli of the GBEP core unit with \(\eta \) are discussed. The concept of stiffness per unit volume (SPUV, k) is proposed, and the difference in shear performance (in-plane and out-of-plane) between the GBEP and grid plate (GP) core layer is theoretically revealed for the first time. The SPUV of the GBEP is slightly less than that of the GP for out-of-plane shearing but far better than that of the GP for in-plane shearing. According to the values of the in-plane and out-of-plane SPUVs of the GBEP and GP, a theoretical explanation is given for why the shear performance of the GBEP core is better than that of the GP, and the shear moduli of GBEP core equivalent model are obtained. From the point of view of shear properties, the theoretical basis that the in-plane stiffness of GBEP core cannot be ignored is given for the first time. This paper lays a theoretical foundation for exploring the shear properties of GBEP and its application in practical engineering.
Similar content being viewed by others
Data availability
All data generated or analyzed during this study are included in this published article.
References
Miller, W., Smith, C.W., Scarpa, F., Evans, K.E.: Flatwise buckling optimization of hexachiral and tetrachiral honeycombs. Compos. Sci. Technol. 70, 1049–1056 (2010). https://doi.org/10.1016/j.compscitech.2009.10.022
Wang, D., Bai, Z.: Mechanical property of paper honeycomb structure under dynamic compression. Mater. Des. 77, 59–64 (2015). https://doi.org/10.1016/j.matdes.2015.03.037
He, X.D., Kong, X.H., Shi, L.P., Li, M.W.: High-frequency vibration response of metal honeycomb sandwich structure. Adv. Mat. Res. 79–82, 1727–1730 (2009). https://doi.org/10.4028/www.scientific.net/AMR.79-82.1727
Kodiyalam, S., Nagendra, S., DeStefano, J.: Composite sandwich structure optimization with application to satellite components. AIAA J. 34, 614–621 (1996). https://doi.org/10.2514/3.13112
Zhao, C., Zheng, W., Ma, J., Zhao, Y.: The lateral compressive buckling performance of aluminum honeycomb panels for long-span hollow core roofs. Materials. 9, 444 (2016). https://doi.org/10.3390/ma9060444
Liu, Z., Yu, Y., Yang, Z., Wei, Y., Cai, J., Li, M., Huang, C.: Dynamic experimental studies of A6N01S-T5 aluminum alloy material and structure for high-speed trains. Acta Mech. Sinica. 35(4), 763–772 (2019). https://doi.org/10.1007/s10409-018-0830-8
Belingardi, G., Cavatorta, M.P., Duella, R.: Material characterization of a composite–foam sandwich for the front structure of a high speed train. Compos. Struct. 61, 13–25 (2003). https://doi.org/10.1016/S0263-8223(03)00028-X
Hu, B.: Bio-based composite sandwich panel for residential construction. (2006)
Briscoe, C.R., Mantell, S.C., Davidson, J.H., Okazaki, T.: Design procedure for web core sandwich panels for residential roofs. J. Sandw. Struct. Mater. 13, 23–58 (2011). https://doi.org/10.1177/1099636210365441
Chen, H.-J., Tsai, S.W.: Analysis and optimum design of composite grid structures. J. Compos. Mater. 30, 503–534 (1996). https://doi.org/10.1177/002199839603000405
Chen, J.X., Zhang, X.M., Okabe, Y., Xie, J., Xu, M.Y.: Beetle elytron plate and the synergistic mechanism of a trabecular-honeycomb core structure. Sci. China Technol. Sci. 62, 87–93 (2019). https://doi.org/10.1007/s11431-018-9290-1
Chen, J., Xie, J., Zhu, H., Guan, S., Wu, G., Noori, M.N., Guo, S.: Integrated honeycomb structure of a beetle forewing and its imitation. Mater. Sci. Eng. C 32, 613–618 (2012). https://doi.org/10.1016/j.msec.2011.12.020
Chen, J., Ni, Q., Iwamoto, M.: A reinforced sandwich plate with polygonal grid in the middle. (2006)
Hao, N., Chen, J., Song, Y., Zhang, X., Zhao, T., Fu, Y.: A new type of bionic grid plate—the compressive deformation and mechanical properties of the grid beetle elytron plate. J. Sandw. Struct. Mater. (2021). https://doi.org/10.1177/1099636221993872
Chen, J., Hao, N., Pan, L., Hu, L., Du, S., Fu, Y.: Characteristics of compressive mechanical properties and strengthening mechanism of 3D-printed grid beetle elytron plates. J. Mater. Sci. 55, 8541–8552 (2020). https://doi.org/10.1007/s10853-020-04630-6
Hoff, N.J.: Bending and buckling of rectangular sandwich plates. (1950)
Phan, C.N., Bailey, N.W., Kardomateas, G.A., Battley, M.A.: Wrinkling of sandwich wide panels/beams based on the extended high-order sandwich panel theory: formulation, comparison with elasticity and experiments. Arch. Appl. Mech. 82, 1585–1599 (2012). https://doi.org/10.1007/s00419-012-0673-x
Carlsson, L.A., Kardomateas, G.A.: Structural and Failure Mechanics of Sandwich Composites. Springer Science & Business Media, Dordrecht (2011)
Frostig, Y., Baruch, M., Vilnay, O., Sheinman, I.: High-order theory for sandwich-beam behavior with transversely flexible core. J. Eng. Mech. 118, 1026–1043 (1992). https://doi.org/10.1061/(ASCE)0733-9399(1992)118:5(1026)
Barut, A., Madenci, E., Anderson, T., Tessler, A.: Equivalent single-layer theory for a complete stress field in sandwich panels under arbitrarily distributed loading. Compos. Struct. 58, 483–495 (2002). https://doi.org/10.1016/S0263-8223(02)00137-X
Tornabene, F., Fantuzzi, N., Viola, E., Batra, R.C.: Stress and strain recovery for functionally graded free-form and doubly-curved sandwich shells using higher-order equivalent single layer theory. Compos. Struct. 119, 67–89 (2015). https://doi.org/10.1016/j.compstruct.2014.08.005
Gibson, L.J., Ashby, M.F.: Cellular Solids. Cambridge University Press (1997)
Gotoh, M., Yamashita, M., Kawakita, A.: Crush behavior of honeycomb structure impacted by drop-hammer and its numerical analysis. J. Soc. Mater. Sci. Jpn. 45, 261–266 (1996). https://doi.org/10.2472/jsms.45.12Appendix_261
Warren, W.E., Kraynik, A.M.: Foam mechanics: the linear elastic response of two-dimensional spatially periodic cellular materials. Mech. Mater. 6, 27–37 (1987). https://doi.org/10.1016/0167-6636(87)90020-2
Du, S., Li, Y., Chen, J.: The calculation of in-plane equivalent elastic parameters of a grid beetle elytra plate core. Mech. Mater. 161, 103999 (2021). https://doi.org/10.1016/j.mechmat.2021.103999
Kaplunov, J., Prikazchikova, L., Alkinidri, M.: Antiplane shear of an asymmetric sandwich plate. Contin. Mech. Thermodyn. 33, 1247–1262 (2021). https://doi.org/10.1007/s00161-021-00969-6
Liu, Y., Liu, W., Gao, W.: Out-of-plane shear property analysis of Nomex honeycomb sandwich structure. J. Reinf. Plast. Compos. 40, 165–175 (2021). https://doi.org/10.1177/0731684420943285
Shi, G., Tong, P.: Equivalent transverse shear stiffness of honeycomb cores. Int. J. Solids Struct. 32, 1383–1393 (1995). https://doi.org/10.1016/0020-7683(94)00202-8
Paul Praveen, A., Jatin, N.V., Raveen, S.M., Vasudevan, R., Ananda Babu, A., Edwin Sudhagar, P.: Comparison of shear rigidity of epoxy and vinyl ester reinforced hybrid honeycomb core. Mater. Today Proc. 22, 2378–2385 (2020). https://doi.org/10.1016/j.matpr.2020.03.362
Penzien, J., Didriksson, T.: Effective shear modulus of honeycomb cellular structure. AIAA J. 2, 531–535 (1964). https://doi.org/10.2514/3.2346
Reissner, E.: Small bending and stretching of sandwich-type shells. (1950)
ASTMC273/C273M-20: Standard test method for shear properties of sandwich core materials, https://www.astm.org/c0273_c0273m-20.html, (2020)
Pan, T., Jiang, Y., He, H., Wang, Y., Yin, K.: Effect of structural build-up on interlayer bond strength of 3D printed cement mortars. Materials. 14, 236 (2021). https://doi.org/10.3390/ma14020236
Chacón, J.M., Caminero, M.A., García-Plaza, E., Núñez, P.J.: Additive manufacturing of PLA structures using fused deposition modelling: effect of process parameters on mechanical properties and their optimal selection. Mater. Des. 124, 143–157 (2017). https://doi.org/10.1016/j.matdes.2017.03.065
Nguyen, H.T., Crittenden, K., Weiss, L., Bardaweel, H.: Experimental modal analysis and characterization of additively manufactured polymers. Polymers 14, 2071 (2022). https://doi.org/10.3390/polym14102071
Chen, J., Hao, N., Zhao, T., Song, Y.: Flexural properties and failure mechanism of 3D-printed grid beetle elytron plates. Int. J. Mech. Sci. 210, 106737 (2021). https://doi.org/10.1016/j.ijmecsci.2021.106737
Chen, J., Hao, N., Song, Y., Yang, J., He, C.: Experimental studies of the shear mechanical properties of 3D-printed grid beetle elytron plates. J. Mater. Sci. 57(35), 16974–16987 (2022)
Acknowledgements
This study was funded by the National Natural Science Foundation of China (Grant No. 51875102).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no known competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Du, S., Hao, N., Chen, J. et al. Calculation of the equivalent shear moduli of the grid beetle elytron plate core layer. Arch Appl Mech 93, 1023–1034 (2023). https://doi.org/10.1007/s00419-022-02311-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-022-02311-1