Design, fabrication, and characterization of hierarchical mechanical metamaterials

Abstract

Natural mechanical materials, such as bamboo and bone, often exhibit superior specific mechanical properties due to their hierarchical porous architectures. Using the principle of hierarchy as inspiration can facilitate the development of hierarchical mechanical metamaterials (HMMs) across multiple length scales via 3D printing. In this work, we propose self-similar HMMs that combine octet-truss (OCT) architecture as the first and second orders, with cubic architecture as the third or more orders. These HMMs were fabricated using stereolithography 3D printing, with the length sizes ranging from approximately 200 µm to the centimeter scale. The compressive stress–strain behaviors of HMMs exhibit a zigzag characteristic, and the toughness and energy absorption can be significantly enhanced by the hierarchical architecture. The compressive moduli are comparable to that of natural materials, and the strengths are superior to that of most polymer/metal foams, alumina hollow/carbon lattices, and other natural materials. Furthermore, the flexural stress–strain curves exhibit a nonlinear behavior, which can be attributed to the hierarchical architecture and local damage propagation. The relatively high mechanical properties can be attributed to the synergistic effect of the stretch-dominated OCT architecture and the bending-dominated cube architecture. Lastly, an ultralight HMM-integrated unmanned aerial vehicle (HMM-UAV) was successfully designed and printed. The HMM-UAV is ~85% lighter than its bulk counterpart, remarkably extending the flight duration time (~53%). This work not only provides an effective design strategy for HMMs but also further expands the application benchmark of HMMs.

Key words： 3D printing; mechanical metamaterials; hierarchical architecture; mechanical behavior; unmanned aerial vehicle (UAV)

Nomenclature

Abbreviations
BCC	Body center cubic
FDM	Fused deposition modeling
FE	Finite element
HMM	Hierarchical mechanical metamaterial
HMM-UAV	HMM-integrated unmanned aerial vehicle
MTS	Material testing system
OCT	Octet-truss
SLA	Stereolithography
SLM	Selective laser melting
STL	Standard Tessellation Language
TPL	Two-photon lithography
UAV	Unmanned aerial vehicle
Variables
b	Width of the sample
C	Correlation coefficient
d	Thickness of the sample
D	Deflection at the center of the sample
E	Effective Young’s moduli of the HMMs
Eb	Effective Young’s moduli of base material
F	Load recorded by the force transducer
l	Length of each strut
L	Support span length
σ	Effective stress of the HMMs
σb	Effective stress of the base material
ε	Flexural strain
\rho	Density of the HMMS
{\rho }_{\text{b}}	Density of the base material
R	Strut diameter
\overline{R}	Equivalent strut diameter

Acknowledgement

The authors would like to gratefully acknowledge the financial support of the National Natural Science Foundation of China (Grant No. 51905350).

Electronic Supplementary Material

The supplementary material can be found in the online version of this article at https://doi.org/10.1007/s11465-023-0776-9 and are accessible to authorized users.

Conflict of Interest

The authors declare that they have no conflict of interest.

References

1 Meza L R , Zelhofer A J , Clarke N , Mateos A J , Kochmann D M , Greer J R . Resilient 3D hierarchical architected metamaterials. Proceedings of the National Academy of Sciences, 2015, 112(37): 11502–11507

2 Ansari F , Sjöstedt A , Larsson P T , Berglund L A , Wågberg L . Hierarchical wood cellulose fiber/epoxy biocomposites–materials design of fiber porosity and nanostructure. Composites Part A: Applied Science and Manufacturing, 2015, 74: 60–68

3 Ray A K , Mondal S , Das S K , Ramachandrarao P . Bamboo—a functionally graded composite-correlation between microstructure and mechanical strength. Journal of Materials Science, 2005, 40(19): 5249–5253

4 Tan T , Rahbar N , Allameh S M , Kwofie S , Dissmore D , Ghavami K , Soboyejo W O . Mechanical properties of functionally graded hierarchical bamboo structures. Acta Biomaterialia, 2011, 7(10): 3796–3803

5 Song J , Gao L , Lu Y . In situ mechanical characterization of structural bamboo materials under flexural bending. Experimental Techniques, 2017, 41(6): 565–575

6 Song J , Surjadi J U , Hu D Y , Lu Y . Fatigue characterization of structural bamboo materials under flexural bending. International Journal of Fatigue, 2017, 100: 126–135

7 Habibi M K , Samaei A T , Gheshlaghi B , Lu J , Lu Y . Asymmetric flexural behavior from bamboo’s functionally graded hierarchical structure: underlying mechanisms. Acta Biomaterialia, 2015, 16: 178–186

8 Yin H F , Zhou J , Wen G L , Wu Z T . Crushing analysis and optimization for bio-inspired hierarchical 3D cellular structure. Composite Structures, 2022, 286: 115333

9 Libonati F , Gu G X , Qin Z , Vergani L , Buehler M J . Bone-inspired materials by design: toughness amplification observed using 3D printing and testing. Advanced Engineering Materials, 2016, 18(8): 1354–1363

10 Velasco-Hogan A , Deheyn D D , Koch M , Nothdurft B , Arzt E , Meyers M A . On the nature of the transparent teeth of the deep-sea dragonfish, Aristostomias scintillans. Matter, 2019, 1(1): 235–249

11 Zou M , Xu S C , Wei C G , Wang H X , Liu Z Z . A bionic method for the crashworthiness design of thin-walled structures inspired by bamboo. Thin-Walled Structures, 2016, 101: 222–230

12 Dong L . Mechanical response of Ti–6Al–4V hierarchical architected metamaterials. Acta Materialia, 2019, 175: 90–106

13 Xu X , Zhang Y , Fang J G , Chen X B , Liu Z , Xu Y N , Gao Y K . Axial mechanical properties and robust optimization of foam-filled hierarchical structures. Composite Structures, 2022, 289: 115501

14 Zheng X Y , Smith W , Jackson J , Moran B , Cui H C , Chen D , Ye J C , Fang N , Rodriguez N , Weisgraber T , Spadaccini C M . Multiscale metallic metamaterials. Nature Materials, 2016, 15(10): 1100–1106

15 Song J , Gao L B , Cao K , Zhang H T , Xu S , Jiang C C , Surjadi J U , Xu Y M , Lu Y . Metal-coated hybrid meso-lattice composites and their mechanical characterizations. Composite Structures, 2018, 203: 750–763

16 Kaur M , Yun T G , Han S M , Thomas E L , Kim W S . 3D printed stretch-dominated micro-trusses. Materials & Design, 2017, 134: 272–280

17 Schumacher C , Bickel B , Rys J , Marschner S , Daraio C , Gross M . Microstructures to control elasticity in 3D printing. ACM Transactions on Graphics, 2015, 34(4): 136

18 Song J , Chen Y J , Cao K , Lu Y , Xin J H , Tao X M . Fully controllable design and fabrication of three-dimensional lattice supercapacitors. ACS Applied Materials & Interfaces, 2018, 10(46): 39839–39850

19 Ling C , Cernicchi A , Gilchrist M D , Cardiff P . Mechanical behaviour of additively-manufactured polymeric octet-truss lattice structures under quasi-static and dynamic compressive loading. Materials & Design, 2019, 162: 106–118

20 Song J , Zhou W Z , Wang Y J , Fan R , Wang Y C , Chen J Y , Lu Y , Li L X . Octet-truss cellular materials for improved mechanical properties and specific energy absorption. Materials & Design, 2019, 173: 107773

21 Gao L B , Song J , Jiao Z B , Liao W B , Luan J H , Surjadi J U , Li J Y , Zhang H T , Sun D , Liu C T , Lu Y . High-entropy alloy (HEA)-coated nanolattice structures and their mechanical properties. Advanced Engineering Materials, 2018, 20(1): 1700625

22 Meza L R , Das S , Greer J R . Strong, lightweight, and recoverable three-dimensional ceramic nanolattices. Science, 2014, 345(6202): 1322–1326

23 Mieszala M , Hasegawa M , Guillonneau G , Bauer J , Raghavan R , Frantz C , Kraft O , Mischler S , Michler J , Philippe L . Micromechanics of amorphous metal/polymer hybrid structures with 3D cellular architectures: size effects, buckling behavior, and energy absorption capability. Small, 2017, 13(8): 1602514

24 Rashed M G , Ashraf M , Mines R A W , Hazell P J . Metallic microlattice materials: a current state of the art on manufacturing, mechanical properties and applications. Materials & Design, 2016, 95: 518–533

25 Cansizoglu O , Harrysson O , Cormier D , West H , Mahale T . Properties of Ti–6Al–4V non-stochastic lattice structures fabricated via electron beam melting. Materials Science and Engineering: A, 2008, 492(1–2): 468–474

26 DongLDeshpandeVWadleyH. Mechanical response of Ti–6Al–4V octet-truss lattice structures. International Journal of Solids and Structures, 2015, 60–61: 107–124

27 Truby R L , Lewis J A . Printing soft matter in three dimensions. Nature, 2016, 540(7633): 371–378

28 Zein I , Hutmacher D W , Tan K C , Teoh S H . Fused deposition modeling of novel scaffold architectures for tissue engineering applications. Biomaterials, 2002, 23(4): 1169–1185

29 Jang D C , Meza L R , Greer F , Greer J R . Fabrication and deformation of three-dimensional hollow ceramic nanostructures. Nature Materials, 2013, 12(10): 893–898

30 Li X Y , Gao H J . Smaller and stronger. Nature Materials, 2016, 15(4): 373–374

31 Tancogne-Dejean T , Spierings A B , Mohr D . Additively-manufactured metallic micro-lattice materials for high specific energy absorption under static and dynamic loading. Acta Materialia, 2016, 116: 14–28

32 Luo C , Zhao W K , Du Z P , Yu L J . A neural network based landing method for an unmanned aerial vehicle with soft landing gears. Applied Sciences, 2019, 9(15): 2976

33 Rus D , Tolley M T . Design, fabrication and control of soft robots. Nature, 2015, 521(7553): 467–475

34 Xiao R , Feng X B , Fan R , Chen S J , Song J , Gao L B , Lu Y . 3D printing of titanium-coated gradient composite lattices for lightweight mandibular prosthesis. Composites Part B: Engineering, 2020, 193: 108057

35 Morales J , Castelo I , Serra R , Lima P U , Basiri M . Vision-based autonomous following of a moving platform and landing for an unmanned aerial vehicle. Sensors, 2023, 23(2): 829

36 Gibson L J . Cellular solids. MRS Bulletin, 2003, 28(4): 270–274

37 Goh G D , Agarwala S , Goh G L , Dikshit V , Sing S L , Yeong W Y . Additive manufacturing in unmanned aerial vehicles (UAVs): challenges and potential. Aerospace Science and Technology, 2017, 63: 140–151