Finite-Element Modeling and Optimization of 3D-Printed Auxetic Reentrant Structures with Stiffness Gradient under Low-Velocity Impact
Publication: Journal of Engineering Mechanics
Volume 147, Issue 7
Abstract
Additive manufacturing technologies such as fused filament fabrication (FFF) allow the production of metastructures with global properties that can be tailored to their specific application. This study simulated and optimized an auxetic re-entrant structure with a stiffness gradient for enhanced energy absorption with low acceleration peaks under different low-velocity impact conditions. The finite-element method (FEM) was used, and appropriate constitutive models were fitted to static and dynamic tensile and compressive data of acrylonitrile butadiene styrene (ABS) tested under various strain rates. A Johnson–Cook plasticity model demonstrated the best compromise between accuracy and computational efficiency. A simulation strategy using explicit FEM was developed to simulate additively manufactured auxetic metastructures under impact conditions. There was good agreement between the model prediction and the experimentally observed structural response. A parametric optimization was implemented to enhance the energy absorption capability with low acceleration peaks of a graded auxetic re-entrant structure for different impact velocities.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This study was conducted in the course of an exchange program between Washington State University (WSU) and Zurich University of Applied Sciences (ZHAW) with support of a scholarship by the Hirschmann Foundation, which is gratefully acknowledged. Special thanks are further due to Professor Dr. Robert Eberlein and Matthias Huber for their support in testing and material modeling, and to Ralf Pfrommer for helpful discussions concerning explicit modeling.
References
Aliheidari, N., J. Christ, R. Tripuraneni, S. Nadimpalli, and A. Ameli. 2018. “Interlayer adhesion and fracture resistance of polymers printed through melt extrusion additive manufacturing process.” In Vol. 156 of Materials and design, 351–361. Amsterdam, Netherlands: Elsevier.
Aliheidari, N., R. Tripuraneni, A. Ameli, and S. Nadimpalli. 2017. “Fracture resistance measurement of fused deposition modeling 3D printed polymers.” Polym. Test. 156 (Oct): 351–361. https://doi.org/10.1016/j.matdes.2018.07.001.
Álvarez Elipe, J. C., and A. Díaz Lantada. 2012. “Comparative study of auxetic geometries by means of computer-aided design and engineering.” Smart Mater. Struct. 21 (10): 105004. https://doi.org/10.1088/0964-1726/21/10/105004.
Avellaneda, M., and P. J. Swart. 1998. “Calculating the performance of 1–3 piezoelectric composites for hydrophone applications: An effective medium approach.” J. Acoust. Soc. Am. 103 (3): 1449–1467. https://doi.org/10.1121/1.421306.
Baur, E., S. Brinkmann, T. A. Osswald, and E. Schmachtenberg. 2007. “Kunststoffe im Vergleich.” In Saechtling Kunststoff Taschenbuch, 746–747. Munich City, Germany: Carl Hanser Verlag.
Bergström, J. 2015. Mechanics of solid polymers. Amsterdam, Netherlands: Elsevier.
Berinskii, I. E. 2016. “Elastic networks to model auxetic properties of cellular materials.” Int. J. Mech. Sci. 115–116 (Sep): 481–488. https://doi.org/10.1016/j.ijmecsci.2016.07.038.
Brûlé, S., S. Enoch, and S. Guenneau. 2020. “Emergence of seismic metamaterials: Current state and future perspectives.” Phys. Lett. Sect. A: Gener. At. Solid State Phys. 384 (1): 126034. https://doi.org/10.1016/j.physleta.2019.126034.
Cantrell, J., et al. 2017. “Experimental characterization of the mechanical properties of 3D printed ABS and polycarbonate parts.” Rapid Protot. J. 23 (4): 811–824. https://doi.org/10.1108/rpj-03-2016-0042.
Christ, J. F., N. Aliheidari, A. Ameli, and P. Pötschke. 2017. “3D printed highly elastic strain sensors of multiwalled carbon nanotube/thermoplastic polyurethane nanocomposites.” Mater. Des. 131 (Oct): 394–401. https://doi.org/10.1016/j.matdes.2017.06.011.
Christ, J. F., N. Aliheidari, P. Pötschke, and A. Ameli. 2018. “Bidirectional and stretchable piezoresistive sensors enabled by multimaterial 3D printing of carbon nanotube/thermoplastic polyurethane nanocomposites.” Polymers 11 (1): 11. https://doi.org/10.3390/polym11010011.
Colón Quintana, J. L., T. Heckner, A. Chrupala, J. Pollock, S. Goris, and T. Osswald. 2019. “Experimental study of particle migration in polymer processing.” Polym. Compos. 40 (6): 2165–2177. https://doi.org/10.1002/pc.25018.
Cui, L., S. Kiernan, and M. D. Gilchrist. 2009. “Designing the energy absorption capacity of functionally graded foam materials.” Mater. Sci. Eng., A 507 (1–2): 215–225. https://doi.org/10.1016/j.msea.2008.12.011.
D’Alessandro, L., V. Zega, R. Ardito, and A. Corigliano. 2018. “3D auxetic single material periodic structure with ultra-wide tunable Bandgap.” Sci. Rep. 8 (1): 2262. https://doi.org/10.1038/s41598-018-19963-1.
de Lima, C. R., and G. H. Paulino. 2019. “Auxetic structure design using compliant mechanisms: A topology optimization approach with polygonal finite elements.” Adv. Eng. Software 129 (May): 69–80. https://doi.org/10.1016/j.advengsoft.2018.12.002.
Dong, Z., Y. Li, T. Zhao, W. Wu, D. Xiao, and J. Liang. 2019. “Experimental and numerical studies on the compressive mechanical properties of the metallic auxetic reentrant honeycomb.” Mater. Des. 182: 108036. https://doi.org/10.1016/j.matdes.2019.108036.
Evans, K. E., and A. Alderson. 2000. “Auxetic materials: Functional materials and structures from lateral thinking!” Adv. Mater. 12 (9): 617–628. https://doi.org/10.1002/(SICI)1521-4095(200005)12:9%3C617::AID-ADMA617%3E3.0.CO;2-3.
Fíla, T., P. Zlámal, O. Jiroušek, J. Falta, P. Koudelka, D. Kytýř, T. Doktor, and J. Valach. 2017. “Impact testing of polymer-filled auxetics using Split Hopkinson Pressure Bar.” Adv. Eng. Mater. 19 (10): 1–13. https://doi.org/10.1002/adem.201700076.
Foster, L., P. Peketi, T. Allen, T. Senior, O. Duncan, and A. Alderson. 2018. “Application of auxetic foam in sports helmets.” Appl. Sci. 8 (3): 354. https://doi.org/10.3390/app8030354.
Fu, M. H., O. T. Xu, L. L. Hu, and T. X. Yu. 2016. “Nonlinear shear modulus of re-entrant hexagonal honeycombs under large deformation.” Int. J. Solids Struct. 80: 284–296. https://doi.org/10.1016/j.ijsolstr.2015.11.015.
Gao, J., M. Xiao, L. Gao J. Yan, and W. Yan. 2020. “Isogeometric topology optimization for computational design of re-entrant and chiral auxetic composites.” Comput. Methods Appl. Mech. Eng. 362: 112876. https://doi.org/10.1016/j.cma.2020.112876.
Imbalzano, G., S. Linforth, T. D. Ngo, P. V. S. Lee, and P. Tran. 2018. “Blast resistance of auxetic and honeycomb sandwich panels: Comparisons and parametric designs.” Composite Struct. 183 (1): 242–261. https://doi.org/10.1016/j.compstruct.2017.03.018.
ISO (International Organization for Standardization). 2012. Plastics—Determination of tensile properties: Part 2—Test conditions for moulding and extrusion plastics. ISO 5272. London: ISO.
Li, T., F. Liu, and L. Wang. 2020. “Enhancing indentation and impact resistance in auxetic composite materials.” Composites, Part B 198: 108229. https://doi.org/10.1016/j.compositesb.2020.108229.
Masters, I. G., and K. E. Evans. 1996. “Models for the elastic deformation of honeycombs.” Compos. Struct. 35 (4): 403–422. https://doi.org/10.1016/S0263-8223(96)00054-2.
Mir, M., M. N. Ali, J. Sami, and U. Ansari. 2014. “Review of mechanics and applications of auxetic structures.” Adv. Mater. Sci. Eng. 2014: 1–17. https://doi.org/10.1155/2014/753496.
Nadgorny, M., and A. Ameli. 2018. “Functional polymers and nanocomposites for 3D printing of smart structures and devices.” ACS Appl. Mater. Interfaces 10 (21): 17489–17507. https://doi.org/10.1021/acsami.8b01786.
PolymerFEM. 2020. “PolymerFEM.” Accessed October 31, 2020. https://polymerfem.com/introduction-to-mcalibration/.
Prawoto, Y. 2012. “Seeing auxetic materials from the mechanics point of view: A structural review on the negative Poisson’s ratio.” Comput. Mater. Sci. 58 (Aug): 140–153. https://doi.org/10.1016/j.commatsci.2012.02.012.
Qi, C., A. Remennikov, L. Z. Pei, S. Yang, Z. H. Yu, and T. D. Ngo. 2017. “Impact and close-in blast response of auxetic honeycomb-cored sandwich panels: Experimental tests and numerical simulations.” Composite Struct. 180 (1): 161–178. https://doi.org/10.1016/j.compstruct.2017.08.020.
Ren, X., J. Shen, P. Tran, T. D. Ngo, and Y. M. Xie. 2018. “Auxetic nail: Design and experimental study.” Compos. Struct. 184 (Sep): 288–298. https://doi.org/10.1016/j.compstruct.2017.10.013.
Sarvestani, H. Y., A. H. Akbarzadeh, H. Niknam, and K. Hermenean. 2018. “3D printed architected polymeric sandwich panels: Energy absorption and structural performance.” Composite Structures 200 (Mar): 886–909. https://doi.org/10.1016/j.compstruct.2018.04.002.
Suvariya, J., and S. Lavadiya. 2018. “An investigation on recent trends in metamaterial types and its applications.” i-manager’s J. Mater. Sci. 5 (4): 55. https://doi.org/10.26634/jms.5.4.13974.
Tan, P. J., S. R. Reid, J. J. Harrigan, Z. Zou, and S. Li. 2005. “Dynamic compressive strength properties of aluminium foams. Part I—Experimental data and observations.” J. Mech. Phys. Solids 53 (10): 2174–2205. https://doi.org/10.1016/j.jmps.2005.05.007.
Walley, S. M., and J. E. Field. 1994. “Strain rate sensitivity of polymers in compression from low to high rates.” DYMAT J 1 (3): 211–227.
Wang, K., Y. H. Chang, Y. W. Chen, C. Zhang, and B. Wang. 2015. “Designable dual-material auxetic metamaterials using three-dimensional printing.” Mater. Des. 67: 159–164. https://doi.org/10.1016/j.matdes.2014.11.033.
Wang, Y., W. Zhao, G. Zhou, and C. Wang. 2018. “Analysis and parametric optimization of a novel sandwich panel with double-V auxetic structure core under air blast loading.” Int. J. Mech. Sci. 142–143 (May): 245–254. https://doi.org/10.1016/j.ijmecsci.2018.05.001.
Yang, S., C. Qi, D. Wang, R. Gao, H. Hu, and J. Shu. 2013. “A comparative study of ballistic resistance of sandwich panels with aluminum foam and auxetic honeycomb cores.” Adv. Mech. Eng. 5 (Jan): 1–15. https://doi.org/10.1155/2013/589216.
Zhang, J., G. Lu, and Z. You. 2020. “Large deformation and energy absorption of additively manufactured auxetic materials and structures: A review.” Composites, Part B: Eng. 201 (Apr): 108340. https://doi.org/10.1016/j.compositesb.2020.108340.
Zhang, X. C., H. M. Ding, L. Q. An, and X. L. Wang. 2014. “Numerical investigation on dynamic crushing behavior of auxetic honeycombs with various cell-wall angles.” Adv. Mech. Eng. 7 (2): 679678. https://doi.org/10.1155/2014/679678.
Zheng, Y., Y. Wang, X. Lu, Z. Liao, and J. Qu. 2020. “Evolutionary topology optimization for mechanical metamaterials with auxetic property.” Int. J. Mech. Sci. 179 (Feb): 105638. https://doi.org/10.1016/j.ijmecsci.2020.105638.
Zhou, Z., J. Zhou, and H. Fan. 2017. “Plastic analyses of thin-walled steel honeycombs with re-entrant deformation style.” Mater. Sci. Eng., A 688 (Jan): 123–133. https://doi.org/10.1016/j.msea.2017.01.056.
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Published In
Journal of Engineering Mechanics
Volume 147 • Issue 7 • July 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Sep 9, 2020
Accepted: Dec 22, 2020
Published online: Apr 30, 2021
Published in print: Jul 1, 2021
Discussion open until: Sep 30, 2021
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