Modeling of re-entrant structures on an airfoil

Authors

DOI:

https://doi.org/10.29105/ingenierias29.101-998

Keywords:

Ti–Zr alloy, superelastic properties, re-entrant geometries, simulation, airfoil

Abstract

The superelastic properties of a Ti-Zr shape memory alloy were investigated using a re-entrant auxetic core structure embedded within an airfoil, through nonlinear finite element analysis. First, a constitutive model was developed to capture the superelastic mechanical response of the alloy. Subsequently, a numerical model of re-entrant auxetic structures was implemented, employing beam elements for improved computational efficiency. Simple and complex chiral configurations provided enhanced structural flexibility and load-bearing capability, exhibiting large displacements under limited stress levels. The numerical results showed good agreement with experimental data, demonstrating the potential of superelastic auxetic cores as an effective solution for smooth morphing airfoil applications.

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Author Biographies

Ricardo Parga Montemayor, Universidad Autónoma de Nuevo León

Ph.D. in Aeronautical Engineering from the Universidad Autónoma de Nuevo León and is currently conducting a postdoctoral research stay at the University of Tsukuba. His research work focuses on the analysis, characterization, and development of shape memory alloys.

Luis Alberto López Pavón, Universidad Autónoma de Nuevo León

Ph.D. in Materials Engineering from the Autonomous University of Nuevo León (UANL) in 2011, with a postdoctoral appointment at the University of Tsukuba. He is a member of the National System of Researchers and Researcher Candidates (SNII), Level I, and was recognized with the PRODEP Desirable Profile in 2015. He has served as Head of the Biomedical Engineering Educational Program at UANL since 2020.

Luis Arturo Reyes Osorio, Universidad Autónoma de Nuevo León

Mechanical and Administrative Engineering, as well as M.Sc. and Ph.D. degrees in Materials Engineering from the Universidad Autónoma de Nuevo León (UANL). He is a professor at FIME-UANL, where his research focuses on structures, manufacturing, and simulation. He is the leader of the Academic Body UANL-CA-378 and a member of the National System of Researchers and Researcher Candidates (SNII), Level II, with extensive scientific output, thesis supervision experience, and active participation in academic research projects.

Diego Reducindo Almanza, Universidad Autónoma de Nuevo León

Automotive Mechanical Engineer from the Universidad Autónoma de Zacatecas (UAZ) and M.Sc. in Aeronautical Engineering from the Universidad Autónoma de Nuevo León (UANL), currently pursuing a Ph.D. His research focuses on flexible mechanisms for aeronautical and biomedical applications. He has participated in aerospace rocketry competitions and teaches courses in Zacatecas, where he also advises student teams. His expertise includes mechanical design, smart materials, and numerical simulation.

Octavio García Salazar, Universidad Autónoma de Nuevo León

Electronic Engineer (2000) from ITL and M.Sc. in Electrical Engineering (2003), also from ITL. He earned a Ph.D. in Systems Control from the University of Technology of Compiègne in 2009. He completed a CNRS postdoctoral fellowship at LAFMIA-CINVESTAV in 2011 and served as a visiting researcher at CINVESTAV Monterrey in 2012. Since January 2013, he has been a Full-Time Professor at FIME-UANL. He is a member of the National System of Researchers and Researcher Candidates (SNII), Level II, and his research focuses on drones, unmanned aerial systems, and flight dynamics.

References

1. Shaw, J. A. (1995). Thermomechanical aspects of NiTi. Journal of the Mechanics and Physics of Solids, 43(8), 1243–1281. DOI: https://doi.org/10.1016/0022-5096(95)00024-D

2. Fu, J., Yamamoto, A., Kim, H. Y., Hosoda, H., & Miyazaki, S. (2015). Novel Ti-based superelastic alloys with large recovery strain and excellent biocompatibility. Acta Biomaterialia, 17, 56–67. DOI: https://doi.org/10.1016/j.actbio.2015.02.001

3. Li, S., & Nam, T. (2019). Superelasticity and tensile strength of Ti–Zr–Nb–Sn alloys with high Zr content for biomedical applications. Intermetallics, 112, 106545. DOI: https://doi.org/10.1016/j.intermet.2019.106545

4. López, L., Lopez, E., Villalpando, S., Moreno, I., Young, H., & Miyazaki, S. (2018). Effect of heat treatment condition on microstructure and superelastic properties of Ti–24Zr–10Nb–2Sn. Journal of Alloys and Compounds, 782, 893–898. DOI: https://doi.org/10.1016/j.jallcom.2018.12.266

5. Lopez, L., Young, H., Hosoda, H., & Miyazaki, S. (2015). Effect of Nb content and heat treatment temperature on superelastic properties of Ti–24Zr–(8–12)Nb–2Sn alloys. Materials Science Division, University of Tsukuba.

6. Viet, N. T., Zaki, W., Umer, R., & Xu, Y. (2020). Mathematical model for superelastic shape memory alloy springs with large spring index. International Journal of Solids and Structures, 185–186, 159–169. DOI: https://doi.org/10.1016/j.ijsolstr.2019.08.022

7. Esposito, L., Fraldi, M., Ruocco, E., & Sacco, E. (2021). A shape memory alloy helix model accounting for extension and torsion. European Journal of Mechanics - A/Solids, 89, 104281. DOI: https://doi.org/10.1016/j.euromechsol.2021.104281

8. Harkati, E., Daoudi, N., Bezazi, A., Haddad, A., & Scarpa, F. (2017). In-plane elasticity of a multi re-entrant auxetic honeycomb. Composite Structures, 180, 130–139. DOI: https://doi.org/10.1016/j.compstruct.2017.08.014

9. Auricchio, F., & Taylor, R. L. (1997). Shape memory alloys: Modeling and numerical simulation of the finite strain superelastic behavior. Computer Methods in Applied Mechanics and Engineering, 143, 175–194. DOI: https://doi.org/10.1016/S0045-7825(96)01147-4

10. Saleeb, A. F., Natsheh, S. H., & Owusu-Danquah, J. S. (2017). Efficiency of finite element analyses of 55NiTi SMA actuators: Solid versus beam and shell modeling. Finite Elements in Analysis and Design, 136, 58–69. DOI: https://doi.org/10.1016/j.finel.2017.07.011

11. Brinson, L. C. (1993). One-dimensional constitutive behavior of shape memory alloys: Thermomechanical derivation with non-constant material functions and redefined martensite internal variable. Journal of Intelligent Material Systems and Structures, 4, 229–242. DOI: https://doi.org/10.1177/1045389X9300400213

12. Pelton, A., Schroeder, V., Mitchell, M., Gong, X., Barney, M., & Robertson, S. (2008). Fatigue and durability of nitinol stents. Journal of the Mechanical Behavior of Biomedical Materials, 1(2), 153–164. DOI: https://doi.org/10.1016/j.jmbbm.2007.08.001

13. Bianchi, M., Scarpa, F., & Smith, C. W. (2010). Shape memory behavior in auxetic foams: Mechanical properties. Acta Materialia, 58, 858–865. DOI: https://doi.org/10.1016/j.actamat.2009.09.063

14. Hassan, M. R., Scarpa, F., Ruzzene, M., & Mohammed, N. A. (2008). Smart shape memory alloy chiral honeycomb. Materials Science and Engineering A, 481–482, 654–657. DOI: https://doi.org/10.1016/j.msea.2006.10.219

15. Jacobs, S., Coconnier, C., DiMaio, D., Scarpa, F., Toso, M., & Martinez, J. (2012). Deployable auxetic shape memory alloy cellular antenna demonstrator: Design, manufacturing and modal testing. Smart Materials and Structures, 21, 075013. DOI: https://doi.org/10.1088/0964-1726/21/7/075013

16. Rossiter, J., Takashima, K., Scarpa, F., Walters, P., & Mukai, T. (2014). Shape memory polymer hexachiral auxetic structures with tunable stiffness. Smart Materials and Structures, 23, 045007. DOI: https://doi.org/10.1088/0964-1726/23/4/045007

17. Hassan, M. R., Scarpa, F., & Mohamed, N. A. (2009). In-plane tensile behavior of shape memory alloy honeycombs with positive and negative Poisson’s ratio. Journal of Intelligent Material Systems and Structures, 20, 897–905. DOI: https://doi.org/10.1177/1045389X08099605

18. Budarapu, P. R., Y. B., S. S., & Natarajan, R. (2016). Design concepts of an aircraft wing: Composite and morphing airfoil with auxetic structures. Frontiers of Structural and Civil Engineering, 10(4). DOI: https://doi.org/10.1007/s11709-016-0352-z

19. Chen, Z., Wu, X., Wang, Z., & Shao, J. (2020). Concepts for morphing airfoil using novel auxetic lattices. En Z. Jing (Ed.), Proceedings of the International Conference on Aerospace System Science and Engineering 2019 (ICASSE 2019) (Lecture Notes in Electrical Engineering, Vol. 622). Springer. DOI: https://doi.org/10.1007/978-981-15-1773-0_20

20. Huang, J., Zhang, Q., Scarpa, F., Liu, Y., & Leng, J. (2017). In-plane elasticity of a novel auxetic honeycomb design. Composites Part B: Engineering, 110, 72–82. DOI: https://doi.org/10.1016/j.compositesb.2016.11.011

21. Yang, L., Harrysson, O., West, H., & Cormier, D. (2015). Mechanical properties of 3D re-entrant honeycomb auxetic structures realized via additive manufacturing. International Journal of Solids and Structures, 69–70, 475–490. DOI: https://doi.org/10.1016/j.ijsolstr.2015.05.005

22. Maran, S., Masters, I. G., & Gibbons, G. J. (2020). Additive manufacture of 3D auxetic structures by laser powder bed fusion—Design influence on manufacturing accuracy and mechanical properties. Applied Sciences, 10(21), 7738. DOI: https://doi.org/10.3390/app10217738

23. Fu, M.-H., Chen, Y., & Hu, L.-L. (2017). A novel auxetic honeycomb with enhanced in-plane stiffness and buckling strength. Composite Structures, 160, 574–585. DOI: https://doi.org/10.1016/j.compstruct.2016.10.090

24. Sun, J., Du, L., Scarpa, F., Liu, Y., & Leng, J. (2021). Morphing wingtip structure based on active inflatable honeycomb and shape memory polymer composite skin: A conceptual work. Aerospace Science and Technology, 111, 106541. DOI: https://doi.org/10.1016/j.ast.2021.106541

25. Xu, L., Baxevanis, T., & Lagoudas, D. C. (2019). A three-dimensional constitutive model for the martensitic transformation in polycrystalline shape memory alloys under large deformation. Smart Materials and Structures, 28, 074004. DOI: https://doi.org/10.1088/1361-665X/ab1acb

26. Bornengo, D., Scarpa, F., & Remillat, C. (2005). Evaluation of hexagonal chiral structure for morphing airfoil concept. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 219(3), 185–192. DOI: https://doi.org/10.1243/095441005X30216

27. Heo, H., Ju, J., & Kim, D.-M. (2013). Compliant cellular structures: Application to a passive morphing airfoil. Composite Structures, 106, 560–569. DOI: https://doi.org/10.1016/j.compstruct.2013.07.013

28. Spadoni, A., & Ruzzene, M. (2007). Static aeroelastic response of chiral-core airfoils. Journal of Intelligent Material Systems and Structures, 18(10), 1067–1075. DOI: https://doi.org/10.1177/1045389X06072361

29. Martin, J., Heyder-Bruckner, J.-J., Remillat, C., Scarpa, F., Potter, K., & Ruzzene, M. (2008). The hexachiral prismatic wingbox concept. Physica Status Solidi (b), 245(3), 570–577. DOI: https://doi.org/10.1002/pssb.200777709

30. Shaw, J. A. (2012). Shape memory alloy honeycombs: Experiments and simulation. Proceedings of the 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference.

31. Spadoni, A., & Ruzzene, M. (2007). Numerical and experimental analysis of the static compliance of chiral truss-core airfoils. Journal of Mechanics of Materials and Structures, 2(5), 965–981. DOI: https://doi.org/10.2140/jomms.2007.2.965

32. Qiu, K., Wang, R., Zhu, J., & Zhang, W. (2020). Optimization design of chiral hexagonal honeycombs with prescribed elastic properties under large deformation. Chinese Journal of Aeronautics, 33(3), 902–909. DOI: https://doi.org/10.1016/j.cja.2019.09.025

33. Bettini, P., Airoldi, A., Sala, G., Landro, L. D., Ruzzene, M., & Spadoni, A. (2010). Composite chiral structures for morphing airfoils: Numerical analyses and development of a manufacturing process. Composites Part B: Engineering, 41(2), 133–147. DOI: https://doi.org/10.1016/j.compositesb.2009.10.005

34. Zhu, Y., Wang, Z.-P., & Poh, L. H. (2018). Auxetic hexachiral structures with wavy ligaments for large elasto-plastic deformation. Smart Materials and Structures, 27(5), 055001. DOI: https://doi.org/10.1088/1361-665X/aab33d

35. Heo, H., Ju, J., Kim, D.-M., & Jeon, C.-S. (2011). Passive morphing airfoil with honeycombs. Proceedings of the ASME 2011 International Mechanical Engineering Congress & Exposition (IMECE2011-64350), 263–271. DOI: https://doi.org/10.1115/IMECE2011-64350

Portada: Cuadrirrotor, Centro de Investigación e Innovación en Ingeniería Aeronáutica (CIIIA) de la UANL.

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Published

2026-07-25

How to Cite

Parga Montemayor, R., López Pavón, L. A., Reyes Osorio, L. A., Reducindo Almanza, D., & García Salazar, O. (2026). Modeling of re-entrant structures on an airfoil. Revista Ingenierías, 29(101), 25–37. https://doi.org/10.29105/ingenierias29.101-998

Issue

Vol. 29 No. 101 (2026): Julio-Diciembre

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Artículos

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Copyright (c) 2026 Dr. Ricardo Parga Montemayor, Dr. Luis Alberto López Pavón, Dr. Luis Arturo Reyes Osorio, M.C. Diego Reducindo Almanza, Dr. Luis Alberto López Pavón

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