Modares Mechanical Engineering

Modares Mechanical Engineering

Experimental and Numerical Analysis of Energy Absorption in 3D-Printed Auxetic and Combined Lattice Structures Under Quasi-Static Loading

Document Type : Original Research

Authors
Hadi Safi Valilu 1
Mohammad Ali Saeimi Sadigh 1
Moosa Sajed 2
Vahid Tavousi 3
1 Department of Mechanical Engineering, Azarbaijan Shahid Madani University
2 Department of Mechanical Engineering Azarbaijan Shahid Madani university
3 Faculty of Mechanical Engineering, K.N. Toosi University of Technology
10.48311/mme.2025.27793
Abstract
This study presents an experimental and numerical analysis of the energy absorption (EA) performance of four types of 3D-printed polylactic acid (PLA) lattice structures under quasi-static compression. The structures included two uniform designs honeycomb (Sample 1) and re-entrant (Sample 2) and two hybrid designs (Samples 3 and 4) combining these unit cells. Experimental testing and finite element simulation revealed that the hybrid designs significantly outperformed their uniform counterparts. Between the cases, sample 4 achieved the highest specific energy absorption (SEA) of 2.41 kJ/kg, surpassing Sample 1 (1.51 kJ/kg) by 62% and Sample 2 (1.65 kJ/kg) by 33%. It also exhibited the highest total EA of 120.15 J and a mean crushing force (MCF) of 5982.96 N. Sample 3 followed closely with an SEA of 2.24 kJ/kg. Finite element analysis showed strong correlation with experimental data, with differences in SEA values across all samples ranging from 9.36% to 16.67%. The results conclusively demonstrate that strategic geometric hybridization of unit cells is a highly effective method for enhancing EA metrics in lightweight structures.
Keywords
Auxetic Structures
Lattice Structures
Energy Absorption
3D Printing
Hybrid Design

Subjects

[1] Paygozar, B. and M.S. Sadigh, A new hybrid energy absorption mechanism subjected to axial loading. Journal of Central South University, 2020. 27(1): p. 76-87. https://doi.org/10.1007/s11771-020-4279-0.
[2] Paygozar, B. and M.S. Sadigh, Practicability of metallic hybrid systems in enhancing the energy absorption capacity: expansion and buckling mechanisms. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2020. 42(6): p. 307. https://doi.org/10.1007/s40430-020-02405-3.
[3] A. Ghaedizadeh, J. Shen, X. Ren, and Y. M. Xie, "Tuning the performance of metallic auxetic metamaterials by using buckling and plasticity," Materials, vol. 9, no. 1, p. 54, 2016.
[4] R. Critchley, I. Corni, J. A. Wharton, F. C. Walsh, R. J. Wood, and K. R. Stokes, "A review of the manufacture, mechanical properties and potential applications of auxetic foams," physica status solidi (b), vol. 250, no. 10, pp. 1963-1982, 2013, doi: https://doi.org/10.1002/pssb.201248550.
[5] J. Shen, S. Zhou, X. Huang, and Y. M. Xie, "Simple cubic three‐dimensional auxetic metamaterials," physica status solidi (b), vol. 251, no. 8, pp. 1515-1522, 2014, doi: https://doi.org/10.1002/pssb.201451304.
[6] X. Ren, R. Das, P. Tran, T. D. Ngo, and Y. M. Xie, "Auxetic metamaterials and structures: a review," Smart materials and structures, vol. 27, no. 2, p. 023001, 2018, doi: https://doi.org/10.1088/1361-665X/aaa61c.
[7] X. Y. Zhang and X. Ren, "A simple methodology to generate metamaterials and structures with negative Poisson's ratio," physica status solidi (b), vol. 257, no. 10, p. 2000439, 2020, doi: https://doi.org/10.1002/pssb.202000439.
[8] N. Novak, M. Vesenjak, and Z. Ren, "Auxetic cellular materials-a review," Strojniški vestnik-Journal of Mechanical Engineering, vol. 62, no. 9, pp. 485-493, 2016, doi: https://doi.org/10.5545/sv-jme.2016.3656.
[9] C. Luo, C. Z. Han, X. Y. Zhang, X. G. Zhang, X. Ren, and Y. M. Xie, "Design, manufacturing and applications of auxetic tubular structures: A review," Thin-Walled Structures, vol. 163, p. 107682, 2021, doi: https://doi.org/10.1016/j.tws.2021.107682.
[10] R. Lakes and K. Elms, "Indentability of conventional and negative Poisson's ratio foams," Journal of Composite Materials, vol. 27, no. 12, pp. 1193-1202, 1993, doi: https://doi.org/10.1177/002199839302701203.
[11] V. H. Carneiro, J. Meireles, and H. Puga, "Auxetic materials—A review," Materials Science-Poland, vol. 31, pp. 561-571, 2013, doi: https://doi.org/10.2478/s13536-013-0140-6.
[12] Adibeig, M.R., et al., Quasi-static simulation and fatigue life estimation of fused filament fabrication of polylactic acid specimens using finite element method. Journal of Manufacturing Processes, 2023. 106: p. 202-213., https://doi.org/10.1016/j.jmapro.2023.09.071.
[13] Adibeig, M.R., F. Vakili-Tahami, and M.-A. Saeimi-Sadigh, Numerical and experimental investigation on creep response of 3D printed Polylactic acid (PLA) samples. Part I: The effect of building direction and unidirectional raster orientation. Journal of the Mechanical Behavior of Biomedical Materials, 2023. 145: p. 106025. https://doi.org/10.1016/j.jmbbm.2023.106025
[14] G. Imbalzano, P. Tran, T. D. Ngo, and P. V. Lee, "A numerical study of auxetic composite panels under blast loadings," Composite Structures, vol. 135, pp. 339-352, 2016, doi: https://doi.org/10.1016/j.compstruct.2015.09.038.
[15] A. Alomarah, D. Ruan, S. Masood, and Z. Gao, "Compressive properties of a novel additively manufactured 3D auxetic structure," Smart Materials and Structures, vol. 28, no. 8, p. 085019, 2019, doi: https://doi.org/10.1088/1361-665X/ab0dd6.
[16] J. Simpson and Z. Kazancı, "Crushing investigation of crash boxes filled with honeycomb and re-entrant (auxetic) lattices," Thin-Walled Structures, vol. 150, p. 106676, 2020, doi: https://doi.org/10.1016/j.tws.2020.106676.
[17] G. Imbalzano, S. Linforth, T. D. Ngo, P. V. S. Lee, and P. Tran, "Blast resistance of auxetic and honeycomb sandwich panels: Comparisons and parametric designs," Composite Structures, vol. 183, pp. 242-261, 2018, doi: https://doi.org/10.1016/j.compstruct.2017.03.018.
[18] S. Xie, Z. Feng, H. Zhou, and D. Wang, "Three-point bending behavior of Nomex honeycomb sandwich panels: Experiment and simulation," Mechanics of Advanced Materials and Structures, vol. 28, no. 18, pp. 1917-1931, 2021, doi: https://doi.org/10.1080/15376494.2020.1712751.
[19] H. Taghipoor, A. Eyvazian, F. Musharavati, T. Sebaey, and A. Ghiaskar, "Experimental investigation of the three-point bending properties of sandwich beams with polyurethane foam-filled lattice cores," in Structures, 2020, vol. 28: Elsevier, pp. 424-432, doi: https://doi.org/10.1016/j.istruc.2020.08.082.
[20] J. Xiang and J. Du, "Energy absorption characteristics of bio-inspired honeycomb structure under axial impact loading," Materials Science and Engineering: A, vol. 696, pp. 283-289, 2017, doi: https://doi.org/10.1016/j.msea.2017.04.044.
[21] H. Tan, Z. He, K. Li, E. Li, A. Cheng, and B. Xu, "In-plane crashworthiness of re-entrant hierarchical honeycombs with negative Poisson’s ratio," Composite Structures, vol. 229, p. 111415, 2019, doi: https://doi.org/10.1016/j.compstruct.2019.111415.
[22] F. Sun, C. Lai, and H. Fan, "In-plane compression behavior and energy absorption of hierarchical triangular lattice structures," Materials & Design, vol. 100, pp. 280-290, 2016, doi: https://doi.org/10.1016/j.matdes.2016.03.023.
[23] D. Zhang, Q. Fei, J. Liu, D. Jiang, and Y. Li, "Crushing of vertex-based hierarchical honeycombs with triangular substructures," Thin-Walled Structures, vol. 146, p. 106436, 2020, doi: https://doi.org/10.1016/j.tws.2019.106436.
[24] D. Xiao, X. Chen, Y. Li, W. Wu, and D. Fang, "The structure response of sandwich beams with metallic auxetic honeycomb cores under localized impulsive loading-experiments and finite element analysis," Materials & Design, vol. 176, p. 107840, 2019, doi: https://doi.org/10.1016/j.matdes.2019.107840.
[25] E. Pei, J. Shen, and J. Watling, "Direct 3D printing of polymers onto textiles: experimental studies and applications," Rapid Prototyping Journal, vol. 21, no. 5, pp. 556-571, 2015, doi: https://doi.org/10.1108/RPJ-09-2014-0126.
[26] M. Kowalska, M. Woźniak, M. Kijek, P. Mitrosz, J. Szakiel, and P. Turek, "Management of validation of HPLC method for determination of acetylsalicylic acid impurities in a new pharmaceutical product," Scientific Reports, vol. 12, no. 1, p. 1, 2022, doi: https://doi.org/10.1038/s41598-021-99269-x.
[27] H. Rahman, E. Yarali, A. Zolfagharian, A. Serjouei, and M. Bodaghi, "Energy absorption and mechanical performance of functionally graded soft–hard lattice structures," Materials, vol. 14, no. 6, p. 1366, 2021, doi: https://doi.org/10.3390/ma14061366.
[28] D. Photiou, S. Avraam, F. Sillani, F. Verga, O. Jay, and L. Papadakis, "Experimental and numerical analysis of 3d printed polymer tetra-petal auxetic structures under compression," Applied Sciences, vol. 11, no. 21, p. 10362, 2021, doi: https://doi.org/10.3390/app112110362.
[29] M. S. Rad, H. Hatami, R. Alipouri, A. F. Nejad, and F. Omidinasab, "Determination of energy absorption in different cellular auxetic structures," Mechanics & Industry, vol. 20, no. 3, p. 302, 2019, doi: https://doi.org/10.1051/meca/2019019.
[30] A. Yousefi, S. Jolaiy, M. Lalegani Dezaki, A. Zolfagharian, A. Serjouei, and M. Bodaghi, "3D‐Printed soft and hard meta‐structures with supreme energy absorption and dissipation capacities in cyclic loading conditions," Advanced Engineering Materials, vol. 25, no. 4, p. 2201189, 2023, doi: https://doi.org/10.1002/adem.202201189.
[31] D. Li, J. Yin, L. Dong, and R. S. Lakes, "Strong re-entrant cellular structures with negative Poisson’s ratio," Journal of materials science, vol. 53, no. 5, pp. 3493-3499, 2018, doi: https://doi.org/10.1007/s10853-017-1809-8.
[32] M.-H. Fu, Y. Chen, and L.-L. Hu, "Bilinear elastic characteristic of enhanced auxetic honeycombs," Composite Structures, vol. 175, pp. 101-110, 2017, doi: https://doi.org/10.1016/j.compstruct.2017.04.007.
[33] M.-H. Fu, Y. Chen, and L.-L. Hu, "A novel auxetic honeycomb with enhanced in-plane stiffness and buckling strength," Composite Structures, vol. 160, pp. 574-585, 2017, doi: https://doi.org/10.1016/j.compstruct.2016.10.090.
[34] X. Li, Z. Lu, Z. Yang, and C. Yang, "Directions dependence of the elastic properties of a 3D augmented re-entrant cellular structure," Materials & Design, vol. 134, pp. 151-162, 2017, doi: https://doi.org/10.1016/j.matdes.2017.08.024.
[35] M. Zahed, R. Ardeshiri Jouneghani, and M. Safarabadi, "Reinforcement of 3D‐printed re‐entrant structures using additional supports under three‐point bending, experimental and numerical analyses," Advanced Engineering Materials, vol. 26, no. 1, p. 2301252, 2024, doi: https://doi.org/10.1002/adem.202301252.
[36] H. Wang, Z. Lu, Z. Yang, and X. Li, "A novel re-entrant auxetic honeycomb with enhanced in-plane impact resistance," Composite Structures, vol. 208, pp. 758-770, 2019, doi: https://doi.org/10.1016/j.compstruct.2018.10.024.
[37] M. S. Ebrahimi, R. Hashemi, and E. Etemadi, "In-plane energy absorption characteristics and mechanical properties of 3D printed novel hybrid cellular structures," journal of materials research and technology, vol. 20, pp. 3616-3632, 2022, doi: https://doi.org/10.1016/j.jmrt.2022.08.064.
[38] A. Alomarah, S. H. Masood, I. Sbarski, B. Faisal, Z. Gao, and D. Ruan, "Compressive properties of 3D printed auxetic structures: experimental and numerical studies," Virtual and Physical Prototyping, vol. 15, no. 1, pp. 1-21, 2020, doi: https://doi.org/10.1080/17452759.2019.1644184.
[39] R. Johnston and Z. Kazancı, "Analysis of additively manufactured (3D printed) dual-material auxetic structures under compression," Additive Manufacturing, vol. 38, p. 101783, 2021, doi: https://doi.org/10.1016/j.addma.2020.101783.
[40]S. Yuan, C. K. Chua, and K. Zhou, "3D‐printed mechanical metamaterials with high energy absorption," Advanced Materials Technologies, vol. 4, no. 3, p. 1800419, 2019, doi: https://doi.org/10.1002/admt.201800419.
[41] J. Wu, Y. Zhang, F. Zhang, Y. Hou, and X. Yan, "A bionic tree-liked fractal structure as energy absorber under axial loading," Engineering Structures, vol. 245, p. 112914, 2021, doi: https://doi.org/10.1016/j.engstruct.2021.112914.
[42] M. Najafi, H. Ahmadi, and G. Liaghat, "Experimental investigation on energy absorption of auxetic structures," Materials today: proceedings, vol. 34, pp. 350-355, 2021, doi: https://doi.org/10.1016/j.matpr.2020.06.075.
[43] T. Tancogne-Dejean, A. B. Spierings, and D. Mohr, "Additively-manufactured metallic micro-lattice materials for high specific energy absorption under static and dynamic loading," Acta Materialia, vol. 116, pp. 14-28, 2016, doi: https://doi.org/10.1016/j.actamat.2016.05.054.
[44] N. Sui, X. Yan, T.-Y. Huang, J. Xu, F.-G. Yuan, and Y. Jing, "A lightweight yet sound-proof honeycomb acoustic metamaterial," Applied Physics Letters, vol. 106, no. 17, 2015, doi: https://doi.org/10.1063/1.4919235.
[45] S. J. Yeo, M. J. Oh, and P. J. Yoo, "Structurally controlled cellular architectures for high‐performance ultra‐lightweight materials," Advanced Materials, vol. 31, no. 34, p. 1803670, 2019, doi: https://doi.org/10.1002/adma.201803670.
[46] N. K. Choudhry, B. Panda, and U. S. Dixit, "Energy absorption characteristics of fused deposition modeling 3D printed auxetic re-entrant structures: a review," Journal of Materials Engineering and Performance, vol. 32, no. 20, pp. 8981-8999, 2023, doi: https://doi.org/10.1007/s11665-023-08243-3.
[47] H. Y. Sarvestani, A. Akbarzadeh, H. Niknam, and K. Hermenean, "3D printed architected polymeric sandwich panels: Energy absorption and structural performance," Composite Structures, vol. 200, pp. 886-909, 2018, doi: https://doi.org/10.1016/j.compstruct.2018.04.002.
[48] N. Namvar, A. Zolfagharian, F. Vakili-Tahami, and M. Bodaghi, "Reversible energy absorption of elasto-plastic auxetic, hexagonal, and AuxHex structures fabricated by FDM 4D printing," Smart Materials and Structures, vol. 31, no. 5, p. 055021, 2022, doi: https://doi.org/10.1088/1361-665X/ac6291.
[49] R. Sarkhosh, "Enhanced Specific Energy Absorption in Honeycomb Structures with Novel Spiral Reinforcement and Foam Filling," Polymer Engineering & Science, 2025, doi: https://doi.org/10.1002/pen.27294.
[50] R. Sarkhosh, "Enhanced crashworthiness and energy absorption properties of honeycomb structures with a novel sunflower-inspired design," Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 47, no. 7, p. 322, 2025, doi: https://doi.org/10.1007/s40430-025-05634-6.
[51] R. Sarkhosh, A. Farrokhabadi, and H. Zarei, "Crashworthiness characteristics of composite cylindrical energy absorbers filled with honeycomb and foam under quasi-static loading," J. Braz. Soc. Mech. Sci. Eng., vol. 44, no. 8, p. 346, 2022, doi: https://doi.org/10.1007/s40430-022-03651-3.
[52] Ebrahimi, M.S., R. Hashemi, and E. Etemadi, In-plane energy absorption characteristics and mechanical properties of 3D printed novel hybrid cellular structures. journal of materials research and technology, 2022. 20: p. 3616-3632
Modares Mechanical Engineering
Volume 25, Issue 9
September 2025
Pages 555-565