3D PRINTING OF MULTI-MATERIAL MECHANICAL METAMATERIAL AND ITS ENGINEERING APPLICATIONS

Mechanical metamaterials are man-made materials dominated by geometry and composition. Unlike bulky materials, their unconventional mechanical properties have attracted strong research interest from researchers in the engineering field. The advent of advanced 3D printing technologies has ushered in a new era for mechanical metamaterials that enabled them with have high manufacturing efficiency and complex structures. However, most of the traditional 3D printing technologies use a single material for printing, resulting in a fixed geometry and monotonous mechanical properties of mechanical metamaterials once fabricated. This is one of the long-standing challenges of mechanical metamaterials in engineering applications. Here, I propose to use the self-developed multi-material 3D printing technology to broaden the application scope of mechanical metamaterials, so that they have more functional design space beyond the structure. By combining the multi-material 3D printing method with a wide range of materials (e.g. brittle and ductile, rigid and soft, rate-dependent and rate-independent) and unique mechanical designs, I have fabricated and characterized a wide range of mechanical metamaterials with excellent mechanical and/or functional properties.

I first conduct a comprehensive review and summary of the development and latest progress in the field of mechanical metamaterial. I here provide solutions to address the following three inherent limitations that commonly exist in mechanical metamaterials: foldability and load-bearing capacity, high stiffness and damping, as well as high strength and toughness.

(1) Traditional origami mechanical metamaterials are mainly manually made by single material (thesis or plastic film such as PET), or single material 3D printed, resulting in the inability to achieve both folding and load-bearing of origami metamaterials at the same time. For the first time, I proposed a multi-material FDM 3D printing technology based on the wrapping method. By wrapping rigid materials with soft materials and connecting them to form a hinge, the hinge effectively solved the interface debonding problem between multiple materials. Based on this wrapping-based multi-material 3D printing method, I designed a foldable and load-bearing push-to-pull origami mechanical metamaterial, which can effectively convert out-of-plane loads into in-plane deformation of soft materials and finally dissipate the energy. Impact tests show that the origami-mechanical metamaterial can greatly reduce the initial impact peak at impact energies up to 72J without secondary impacts;

(2) Conventional bulky damping materials have a limited amount of energy dissipated by the polymer chains due to finite compression deformations and easy densification, leading to poor damping performance. To overcome this constraint, we have developed a 3D printable material possessing high damping factor, high rate-dependent, and large elongation. By designing the material with a dual energy dissipation mechanism through hydrogen bonding and dynamic coordination bond, it achieved an ultra-high strain energy dissipation density (26.8 J/cm3) and a modulus increase of up to a hundredfold. By utilizing our in-house multi-material 3D printing technology, we have successfully developed a push-to-pull structure that possesses energy dissipation adaptability by combining the damping material. This push-to-pull structure can be adopted to artificial intervertebral disc and could avoid nerve pain by the zero Poisson ratio design. The push-to-pull design enabled the structure with outstanding energy absorption capability in both compression and torsion settings, as well as remarkable energy dissipation performance even after being used 1000 times. Moreover, I developed a low-frequency and broadband vibration metastructure based on the push-to-pull 3D unit structure. The metastructure allows for an ultra-wide vibration isolation frequency band of ~109 Hz.

(3) Ceramic materials are of great value in various applications due to their excellent properties. However, their inherent brittleness has always been a major limitation in their use. Despite the capability of 3D printing technology to produce intricate ceramic geometries, ceramics' brittle fracture issue still inhibits its potential applications. We propose a method of toughening ceramic structures through DLP 3D printing combined with micro-macro structural design. In-situ observations confirmed that surface micro-defects caused by the step effect during the printing process can effectively induce crack propagation directions, the macroscopic ceramic structure is designed to regulate the rate of crack propagation, resulting in ultra-high compressive strength and fracture strain. Based on the above research, we combined 3D printing and impregnate processes to create bi-continuous ceramic structures containing multiple materials. Specifically, we introduce TPU as a "soft phase" material and incorporate it into the "rigid phase" ceramic structure. The rigid phase exhibits superior load-carrying capacity as the bullet penetrates, whilst the soft phase functions as a mesh bag, wrapping around the bullet and prolonging its penetration time. Results from quasi-static and impact tests demonstrate that the bi-continuous multi-material ceramic structure has ultra-high fracture toughness and impact energy absorption capabilities;

To summarize, the utilization of self-developed high-performing materials, self-built or improved multi-material 3D printing technology, and the integrated mechanical design of materials and structures have facilitated the development of mechanical metamaterials with vast potential for various applications. These mechanical metamaterials possess extraordinary characteristics such as the coexistence of foldability and load-bearing capacity, high strength and toughness, and high stiffness and damping. The implementation of a multi-material approach possesses the capability of generating a noteworthy transformation in the development and production of advanced mechanical metamaterials for both functional and structural purposes.

1 Bertoldi, K., Vitelli, V., Christensen, J. & Van Hecke, M. Flexible mechanical metamaterials. Nature Reviews Materials 2, 1-11 (2017).
2 Dudte, L. H., Vouga, E., Tachi, T. & Mahadevan, L. Programming curvature using origami tessellations. Nature materials 15, 583-588 (2016).
3 Lv, C., Krishnaraju, D., Konjevod, G., Yu, H. & Jiang, H. Origami based mechanical metamaterials. Scientific reports 4, 5979 (2014).
4 Zhai, Z., Wang, Y., Lin, K., Wu, L. & Jiang, H. In situ stiffness manipulation using elegant curved origami. Science advances 6, eabe2000 (2020).
5 Zhai, Z., Wang, Y. & Jiang, H. Origami-inspired, on-demand deployable and collapsible mechanical metamaterials with tunable stiffness. Proceedings of the National Academy of Sciences 115, 2032-2037 (2018).
6 Fang, H., Chu, S. C. A., Xia, Y. & Wang, K. W. Programmable self‐locking origami mechanical metamaterials. Advanced Materials 30, 1706311 (2018).
7 Schenk, M. & Guest, S. D. Origami folding: A structural engineering approach. Origami 5, 291-304 (2011).
8 Liu, J. et al. Fabrication, dynamic properties and multi-objective optimization of a metal origami tube with Miura sheets. Thin-Walled Structures 144, 106352 (2019).
9 Ma, J. & You, Z. Energy absorption of thin-walled square tubes with a prefolded origami pattern—part I: geometry and numerical simulation. Journal of applied mechanics 81, 011003 (2014).
10 Deleo, A. A., O’Neil, J., Yasuda, H., Salviato, M. & Yang, J. Origami-based deployable structures made of carbon fiber reinforced polymer composites. Composites Science Technology 191, 108060 (2020).
11 Ye, H., Ma, J., Zhou, X., Wang, H. & You, Z. Energy absorption behaviors of pre-folded composite tubes with the full-diamond origami patterns. Composite Structures 221, 110904 (2019).
12 Chen, Z., Li, Y. & Li, Q. Hydrogel-driven origami metamaterials for tunable swelling behavior. Materials Design 207, 109819 (2021).
13 Liu, G., Zhao, Y., Wu, G. & Lu, J. Origami and 4D printing of elastomer-derived ceramic structures. Science Advances 4, eaat0641 (2018).
14 Wang, R. et al. Direct 4D printing of ceramics driven by hydrogel dehydration. Nature Communications 15, 758 (2024).
15 Belke, C. H. & Paik, J. Mori: a modular origami robot. IEEE/ASME Transactions on Mechatronics 22, 2153-2164 (2017).
16 Miyashita, S., Guitron, S., Ludersdorfer, M., Sung, C. R. & Rus, D. in 2015 IEEE international conference on robotics and automation (ICRA). 1490-1496 (IEEE).
17 Ahmed, A. R., Gauntlett, O. C. & Camci-Unal, G. Origami-inspired approaches for biomedical applications. ACS omega 6, 46-54 (2020).
18 Sargent, B. et al. An origami-based medical support system to mitigate flexible shaft buckling. Journal of Mechanisms Robotics 12, 041005 (2020).
19 Boreanaz, M., Belingardi, G. & Maia, C. D. F. Application of the origami shape in the development of automotive crash box. Material Design Processing Communications 2, e181 (2020).
20 Morgan, J., Magleby, S. P. & Howell, L. L. An approach to designing origami-adapted aerospace mechanisms. Journal of Mechanical Design 138, 052301 (2016).21 Zhou, C., Wang, B., Ma, J. & You, Z. Dynamic axial crushing of origami crash boxes. International journal of mechanical sciences 118, 1-12 (2016).22 Ye, H., Zhou, X., Ma, J., Wang, H. & You, Z. Axial crushing behaviors of composite pre-folded tubes made of KFRP/CFRP hybrid laminates. Thin-Walled Structures 149, 106649 (2020).23 Basily, B. B. & Elsayed, E. Dynamic axial crushing of multilayer core structures of folded Chevron patterns. International Journal of Materials Product Technology 21, 169-185 (2004).24 Du, Y., Song, C., Xiong, J. & Wu, L. Fabrication and mechanical behaviors of carbon fiber reinforced composite foldcore based on curved-crease origami. Composites Science Technology 174, 94-105 (2019).25 Herrmann, A. S., Zahlen, P. C. & Zuardy, I. in Sandwich Structures 7: Advancing with Sandwich Structures and Materials: Proceedings of the 7th International Conference on Sandwich Structures, Aalborg University, Aalborg, Denmark, 29–31 August 2005. 13-26 (Springer).26 Gao, J. & You, Z. Origami-inspired Miura-ori honeycombs with a self-locking property. Thin-Walled Structures 171, 108806 (2022).27 Fischer, S., Heimbs, S., Kilchert, S., Klaus, M. & Cluzel, C. in International SAMPE Europe Conference, Paris.28 Heimbs, S. Foldcore sandwich structures and their impact behaviour: an overview. Dynamic failure of composite sandwich structures, 491-544 (2012).29 Schenk, M. & Guest, S. D. Geometry of Miura-folded metamaterials. Proceedings of the National Academy of Sciences 110, 3276-3281 (2013).30 Silverberg, J. L. et al. Using origami design principles to fold reprogrammable mechanical metamaterials. Science 345, 647-650 (2014).31 Tachi, T. Rigid-foldable thick origami. Origami 5, 253-264 (2011).32 Gattas, J. M. & You, Z. Geometric assembly of rigid-foldable morphing sandwich structures. Engineering Structures 94, 149-159 (2015).33 Felton, S. M. et al. Self-folding with shape memory composites. Soft Matter 9, 7688-7694 (2013).34 Zhou, X., Yu, D., Shao, X., Zhang, S. & Wang, S. Research and applications of viscoelastic vibration damping materials: A review. Composite Structures 136, 460-480 (2016).35 Rao, M. D. Recent applications of viscoelastic damping for noise control in automobiles and commercial airplanes. Journal of sound vibration 262, 457-474 (2003).36 Roebben, G., Duan, R.-G., Sciti, D. & Van der Biest, O. Assessment of the high temperature elastic and damping properties of silicon nitrides and carbides with the impulse excitation technique. Journal of the European Ceramic Society 22, 2501-2509 (2002).37 Ritchie, I. & Pan, Z.-L. High-damping metals and alloys. Metallurgical Transactions A 22, 607-616 (1991).38 Kawahara, K. Application of high-damping alloy M2052. Key engineering materials 319, 217-224 (2006).39 Saed, M. O. et al. Impact damping and vibration attenuation in nematic liquid crystal elastomers. Nature communications 12, 6676 (2021).40 Shu, Z., You, R. & Zhou, Y. Viscoelastic materials for structural dampers: A review. Construction Building Materials 342, 127955 (2022).41 Alhasan, A. A., Vafaei, M. & C Alih, S. Viscoelastic dampers for protection of structures against seismic actions. Innovative Infrastructure Solutions 7, 309 (2022).42 Zhang, Q., Guo, D. & Hu, G. Tailored mechanical metamaterials with programmable quasi‐zero‐stiffness features for full‐band vibration isolation. Advanced Functional Materials 31, 2101428 (2021).43 Wang, R., Shang, J., Li, X., Luo, Z. & Wu, W. Vibration and damping characteristics of 3D printed Kagome lattice with viscoelastic material filling. Scientific reports 8, 1-13 (2018).44 Savino, R., Criscuolo, L., Di Martino, G. D. & Mungiguerra, S. Aero-thermo-chemical characterization of ultra-high-temperature ceramics for aerospace applications. Journal of the European Ceramic Society 38, 2937-2953 (2018).45 Kaya, H. The application of ceramic-matrix composites to the automotive ceramic gas turbine. Composites science technology 59, 861-872 (1999).46 Chevalier, J. & Gremillard, L. Ceramics for medical applications: A picture for the next 20 years. Journal of the European Ceramic Society 29, 1245-1255 (2009).47 Buchanan, R. C. Ceramic materials for electronics. (CRC press, 2018).48 Charlton, D. G., Roberts, H. W. & Tiba, A. Measurement of select physical and mechanical properties of 3 machinable ceramic materials. Quintessence international 39 (2008).49 Sakai, M. & Bradt, R. Fracture toughness testing of brittle materials. International Materials Reviews 38, 53-78 (1993).50 Knott, J. F. Fundamentals of fracture mechanics. (Gruppo Italiano Frattura, 1973).51 Ohji, T., Jeong, Y. K., Choa, Y. H. & Niihara, K. Strengthening and toughening mechanisms of ceramic nanocomposites. Journal of the American Ceramic Society 81, 1453-1460 (1998).52 Gu, Y., Xia, K., Wu, D., Mou, J. & Zheng, S. Technical characteristics and wear-resistant mechanism of nano coatings: a review. Coatings 10, 233 (2020).53 Kabel, J. et al. Ceramic composites: A review of toughening mechanisms and demonstration of micropillar compression for interface property extraction. Journal of materials research 33, 424-439 (2018).54 Bai, R. et al. Ceramic toughening strategies for biomedical applications. Frontiers in Bioengineering Biotechnology 10, 840372 (2022).55 Shaikeea, A. J. D., Cui, H., O’Masta, M., Zheng, X. R. & Deshpande, V. S. The toughness of mechanical metamaterials. Nature materials 21, 297-304 (2022).56 Jang, D., Meza, L. R., Greer, F. & Greer, J. R. Fabrication and deformation of three-dimensional hollow ceramic nanostructures. Nature materials 12, 893-898 (2013).57 Bauer, J. et al. Additive manufacturing of ductile, ultrastrong polymer-derived nanoceramics. Matter 1, 1547-1556 (2019).58 Sajadi, S. M. et al. Damage-tolerant 3D-printed ceramics via conformal coating. Science Advances 7, eabc5028 (2021).59 Sun, L., Dong, P., Zeng, Y. & Chen, J. Fabrication of hollow lattice alumina ceramic with good mechanical properties by Digital Light Processing 3D printing technology. Ceramics International 47, 26519-26527 (2021).60 Li, Z. et al. Additive manufacturing of lightweight and high-strength polymer-derived SiOC ceramics. Virtual Physical Prototyping 15, 163-177 (2020).61 Meza, L. R., Das, S. & Greer, J. R. Strong, lightweight, and recoverable three-dimensional ceramic nanolattices. Science 345, 1322-1326 (2014).62 Schwentenwein, M. & Homa, J. Additive manufacturing of dense alumina ceramics. International Journal of Applied Ceramic Technology 12, 1-7 (2015).63 Lantada, A. D., de Blas Romero, A., Schwentenwein, M., Jellinek, C. & Homa, J. Lithography-based ceramic manufacture (LCM) of auxetic structures: present capabilities and challenges. Smart Materials Structures 25, 054015 (2016).64 Shen, M. et al. Mechanical properties of 3D printed ceramic cellular materials with triply periodic minimal surface architectures. Journal of the European Ceramic Society 41, 1481-1489 (2021).65 Wegst, U. G., Bai, H., Saiz, E., Tomsia, A. P. & Ritchie, R. O. Bioinspired structural materials. Nature materials 14, 23-36 (2015).66 San Ha, N. & Lu, G. A review of recent research on bio-inspired structures and materials for energy absorption applications. Composites Part B: Engineering 181, 107496 (2020).67 Yin, Z., Hannard, F. & Barthelat, F. Impact-resistant nacre-like transparent materials. Science 364, 1260-1263 (2019).68 Chen, Y. et al. Bioinspired construction of micronano lignocellulose into an impact resistance “wooden armor” with bouligand structure. ACS nano 16, 7525-7534 (2022).69 Sabet, F. A., Su, F. Y., McKittrick, J. & Jasiuk, I. Mechanical properties of model two‐phase composites with continuous compared to discontinuous phases. Advanced Engineering Materials 20, 1800505 (2018).70 Huang, W. et al. A natural impact-resistant bicontinuous composite nanoparticle coating. Nature Materials 19, 1236-1243 (2020).71 Sun, J. et al. 3D printing of ceramic composite with biomimetic toughening design. Additive Manufacturing 58, 103027 (2022).72 Levy, G. N., Schindel, R. & Kruth, J.-P. Rapid manufacturing and rapid tooling with layer manufacturing (LM) technologies, state of the art and future perspectives. CIRP annals 52, 589-609 (2003).73 Azlin, M. et al. 3D printing and shaping polymers, composites, and nanocomposites: A review. Polymers 14, 180 (2022).74 Chang, J. et al. Advanced material strategies for next-generation additive manufacturing. Materials 11, 166 (2018).75 Ge, Q. et al. Projection micro stereolithography based 3D printing and its applications. International Journal of Extreme Manufacturing 2, 022004 (2020).76 Saha, S. K. et al. Scalable submicrometer additive manufacturing. Science 366, 105-109 (2019).77 Sydney Gladman, A., Matsumoto, E. A., Nuzzo, R. G., Mahadevan, L. & Lewis, J. A. Biomimetic 4D printing. Nature materials 15, 413-418 (2016).78 Cano-Vicent, A. et al. Fused deposition modelling: Current status, methodology, applications and future prospects. Additive manufacturing 47, 102378 (2021).79 Song, J. et al. Metal-coated hybrid meso-lattice composites and their mechanical characterizations. Composite Structures 203, 750-763 (2018).80 Ambrosi, A. & Pumera, M. 3D-printing technologies for electrochemical applications. Chemical society reviews 45, 2740-2755 (2016).81 Coulter, F. B., Coulter, B. S., Papastavrou, E. & Ianakiev, A. J. D. P. Production techniques for 3D printed inflatable elastomer structures: part II—four-axis direct ink writing on irregular double-curved and inflatable surfaces. 3D Printing Additive Manufacturing 5, 17-28 (2018).82 Grosskopf, A. K. et al. Viscoplastic matrix materials for embedded 3D printing. ACS applied materials interfaces 10, 23353-23361 (2018).83 Chen, Z. et al. Advanced Fabrication of Mechanical Metamaterials Based on Micro/Nanoscale Technology. Advanced Engineering Materials 25, 2300750 (2023).84 Garechana, G., Rio-Belver, R., Bildosola, I. & Cilleruelo-Carrasco, E. A method for the detection and characterization of technology fronts: Analysis of the dynamics of technological change in 3D printing technology. Plos one 14, e0210441 (2019).85 Gao, Z. et al. Additively manufactured high-energy-absorption metamaterials with artificially engineered distribution of bio-inspired hierarchical microstructures. Composites Part B: Engineering 247, 110345 (2022).86 Huang, J., Qin, Q. & Wang, J. A review of stereolithography: Processes and systems. Processes 8, 1138 (2020).87 Zheng, X. et al. Multiscale metallic metamaterials. Nature materials 15, 1100-1106 (2016).88 Wang, P. et al. Enhanced multi-material 4D printing hybrid composites based on shape memory polymer/thermoplastic elastomer. Smart Materials Structures 32, 055025 (2023).89 Weeks, R. D., Truby, R. L., Uzel, S. G. & Lewis, J. A. Embedded 3D Printing of Multimaterial Polymer Lattices via Graph‐Based Print Path Planning. Advanced Materials 35, 2206958 (2023).90 Malas, A. et al. Reactive jetting of high viscosity nanocomposites for dielectric elastomer actuation. Advanced Materials Technologies 7, 2101111 (2022).91 Deng, X., Zhang, G., Yu, Z., Shao, G. & Li, L. Manufacturing of mesoscale non-assembly mechanism with water-soluble support in projection stereolithography process. Journal of Manufacturing Processes 85, 658-665 (2023).92 Faber, J. A., Arrieta, A. F. & Studart, A. R. Bioinspired spring origami. Science 359, 1386-1391 (2018).93 Skylar-Scott, M. A., Mueller, J., Visser, C. W. & Lewis, J. A. Voxelated soft matter via multimaterial multinozzle 3D printing. Nature 575, 330-335 (2019).94 Hubbard, J. D. et al. Fully 3D-printed soft robots with integrated fluidic circuitry. Science Advances 7, eabe5257 (2021).95 Hensleigh, R. et al. Charge-programmed three-dimensional printing for multi-material electronic devices. Nature Electronics 3, 216-224 (2020).96 Chen, D. & Zheng, X. Multi-material additive manufacturing of metamaterials with giant, tailorable negative Poisson’s ratios. Scientific reports 8, 1-8 (2018).97 Wang, Q. et al. Lightweight mechanical metamaterials with tunable negative thermal expansion. Physical review letters 117, 175901 (2016).98 Kowsari, K., Akbari, S., Wang, D., Fang, N. X. & Ge, Q. High-efficiency high-resolution multimaterial fabrication for digital light processing-based three-dimensional printing. 3D Printing Additive Manufacturing 5, 185-193 (2018).99 Bertoldi, K., Vitelli, V., Christensen, J. & van Hecke, M. Flexible mechanical metamaterials. Nat. Rev. Mater 2, doi:10.1038/natrevmats.2017.66 (2017).100 Kadic, M., Milton, G. W., van Hecke, M. & Wegener, M. 3D metamaterials. Nat. Rev. Phys 1, 198-210, doi:10.1038/s42254-018-0018-y (2019).101 Surjadi, J. U. et al. Mechanical metamaterials and their engineering applications. Adv Eng Mater 21, 1800864 (2019).102 Wegener, M. Metamaterials beyond optics. Science 342, 939-940 (2013).103 Bauer, J., Kraus, J. A., Crook, C., Rimoli, J. J. & Valdevit, L. Tensegrity Metamaterials: Toward Failure-Resistant Engineering Systems through Delocalized Deformation. Adv. Mater 33, e2005647, doi:10.1002/adma.202005647 (2021).104 Coulais, C., Sounas, D. & Alu, A. Static non-reciprocity in mechanical metamaterials. Nature 542, 461-464, doi:10.1038/nature21044 (2017).105 Frenzel, T., Kadic, M. & Wegener, M. Three-dimensional mechanical metamaterials with a twist. Science 358, 1072-1074 (2017).106 Wang, Q. et al. Lightweight mechanical metamaterials with tunable negative thermal expansion. Phys. Rev. Lett 117, 175901 (2016).107 Zheng, X. et al. Ultralight, ultrastiff mechanical metamaterials. Science 344, 1373-1377 (2014).108 Shan, S. et al. Multistable Architected Materials for Trapping Elastic Strain Energy. Adv. Mater 27, 4296-4301, doi:10.1002/adma.201501708 (2015).109 Li, S., Fang, H., Sadeghi, S., Bhovad, P. & Wang, K. W. Architected origami materials: How folding creates sophisticated mechanical properties. Adv. Mater 31, 1805282 (2019).110 Ning, X. et al. Assembly of advanced materials into 3D functional structures by methods inspired by origami and kirigami: a review. Adv. Mater. Interfaces 5, 1800284 (2018).111 Fang, H., Chu, S. C. A., Xia, Y. & Wang, K. W. Programmable self‐locking origami mechanical metamaterials. Adv. Mater 30, 1706311 (2018).112 Schenk, M. & Guest, S. D. Geometry of Miura-folded metamaterials. Proc. Natl. Acad. Sci. U.S.A. 110, 3276-3281, doi:10.1073/pnas.1217998110 (2013).113 Yasuda, H. & Yang, J. Reentrant origami-based metamaterials with negative Poisson’s ratio and bistability. Phys. Rev. Lett 114, 185502 (2015).114 Filipov, E. T., Tachi, T. & Paulino, G. H. Origami tubes assembled into stiff, yet reconfigurable structures and metamaterials. Proc. Natl Acad. Sci. USA 112, 12321-12326, doi:10.1073/pnas.1509465112 (2015).115 Ma, J., Song, J. & Chen, Y. An origami-inspired structure with graded stiffness. Int. J. Mech. Sci 136, 134-142, doi:10.1016/j.ijmecsci.2017.12.026 (2018).116 Yasuda, H., Tachi, T., Lee, M. & Yang, J. Origami-based tunable truss structures for non-volatile mechanical memory operation. Nat. Commun. 8, 1-7 (2017).117 Zhai, Z., Wang, Y., Lin, K., Wu, L. & Jiang, H. In situ stiffness manipulation using elegant curved origami. Sci. Adv 6, eabe2000 (2020).118 Waitukaitis, S., Menaut, R., Chen, B. G.-g. & Van Hecke, M. Origami multistability: From single vertices to metasheets. Phys. Rev. Lett 114, 055503 (2015).119 Liu, K., Tachi, T. & Paulino, G. H. Invariant and smooth limit of discrete geometry folded from bistable origami leading to multistable metasurfaces. Nat. Commun. 10, 1-10 (2019).120 Melancon, D., Gorissen, B., García-Mora, C. J., Hoberman, C. & Bertoldi, K. Multistable inflatable origami structures at the metre scale. Nature 592, 545-550 (2021).121 Evans, T. A., Lang, R. J., Magleby, S. P. & Howell, L. L. Rigidly foldable origami gadgets and tessellations. Royal Soc. Open Sci. 2, 150067 (2015).122 Reis, P. M., Jiménez, F. L. & Marthelot, J. Transforming architectures inspired by origami. Proc. Natl. Acad. Sci. U.S.A. 112, 12234-12235 (2015).123 Lang, R. J., Tolman, K. A., Crampton, E. B., Magleby, S. P. & Howell, L. L. A Review of Thickness-Accommodation Techniques in Origami-Inspired Engineering. Appl Mech Rev 70, doi:10.1115/1.4039314 (2018).124 Edmondson, B. J., Lang, R. J., Magleby, S. P. & Howell, L. L. in International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. V05BT08A054 (American Society of Mechanical Engineers).125 Hoberman, C. Folding structures made of thick hinged sheets. (2010).126 Ku, J. S. & Demaine, E. D. Folding flat crease patterns with thick materials. J Mech Robot 8, 031003 (2016).127 Zirbel, S. A. et al. Accommodating thickness in origami-based deployable arrays. J. Mech. Des. 135 (2013).128 Lang, R. J., Nelson, T., Magleby, S. & Howell, L. Thick rigidly foldable origami mechanisms based on synchronized offset rolling contact elements. J Mech Robot 9, 021013 (2017).129 Nelson, T. G., Lang, R. J., Magleby, S. P. & Howell, L. L. in 2018 International Conference on Reconfigurable Mechanisms and Robots (ReMAR). 1-8 (IEEE).130 Shahrubudin, N., Lee, T. C. & Ramlan, R. An overview on 3D printing technology: Technological, materials, and applications. Procedia Manuf. 35, 1286-1296 (2019).131 Bodaghi, M., Noroozi, R., Zolfagharian, A., Fotouhi, M. & Norouzi, S. 4D printing self-morphing structures. Materials 12, 1353 (2019).132 Mehrpouya, M., Azizi, A., Janbaz, S. & Gisario, A. Investigation on the functionality of thermoresponsive origami structures. Adv Eng Mater 22, 2000296 (2020).133 Wickeler, A. L. & Naguib, H. E. Novel origami-inspired metamaterials: Design, mechanical testing and finite element modelling. Mater. Des 186, 108242 (2020).134 Zolfagharian, A., Kaynak, A., Khoo, S. Y. & Kouzani, A. Pattern-driven 4D printing. Sens. Actuator A Phys. 274, 231-243 (2018).135 Wagner, M. A., Huang, J.-L., Okle, P., Paik, J. & Spolenak, R. Hinges for origami-inspired structures by multimaterial additive manufacturing. Mater. Des 191, 108643 (2020).136 Gattas, J. M., Wu, W. & You, Z. Miura-base rigid origami: parameterizations of first-level derivative and piecewise geometries. J. Mech. Des. 135 (2013).137 Fang, H., Li, S. & Wang, K. W. Self-locking degree-4 vertex origami structures. Proc. Math. Phys. Eng. Sci. 472, 20160682, doi:10.1098/rspa.2016.0682 (2016).138 Yuan, L., Dai, H., Song, J., Ma, J. & Chen, Y. The behavior of a functionally graded origami structure subjected to quasi-static compression. Mater. Des 189, doi:10.1016/j.matdes.2020.108494 (2020).139 Rees, D. W. A. in Mechanics of Optimal Structural Design 525-535 (2009).140 Lu, G. & Yu, T. Energy absorption of structures and materials. (Elsevier, 2003).141 Ahn, K. K. Active pneumatic vibration isolation system using negative stiffness structures for a vehicle seat. Journal of Sound Vibration 333, 1245-1268 (2014).142 Le, T. D. & Ahn, K. K. A vibration isolation system in low frequency excitation region using negative stiffness structure for vehicle seat. Journal of Sound Vibration 330, 6311-6335 (2011).143 Mansour, H., Arzanpour, S. & Golnaraghi, F. Design of a solenoid valve based active engine mount. Journal of Vibration Control 18, 1221-1232 (2012).144 Mahdisoozani, H. et al. Performance enhancement of internal combustion engines through vibration control: state of the art and challenges. Applied Sciences 9, 406 (2019).145 Yu, D., Kwak, J. B., Park, S. & Lee, J. Dynamic responses of PCB under product-level free drop impact. Microelectronics Reliability 50, 1028-1038 (2010).146 Back, J.-H. et al. Shock absorption of semi-interpenetrating network acrylic pressure-sensitive adhesive for mobile display impact resistance. International Journal of Adhesion Adhesives 99, 102558 (2020).147 Rahimzadeh, T., Arruda, E. M. & Thouless, M. Design of armor for protection against blast and impact. Journal of the Mechanics Physics of Solids 85, 98-111 (2015).148 Tang, F. et al. Protective performance and dynamic behavior of composite body armor with shear stiffening gel as buffer material under ballistic impact. Composites Science Technology 218, 109190 (2022).149 Zhu, G., Sun, G., Yu, H., Li, S. & Li, Q. Energy absorption of metal, composite and metal/composite hybrid structures under oblique crushing loading. International Journal of Mechanical Sciences 135, 458-483 (2018).150 Zhang, L. et al. Energy absorption characteristics of metallic triply periodic minimal surface sheet structures under compressive loading. Additive Manufacturing 23, 505-515 (2018).151 Sun, M., Bai, Y., Li, M., Fan, S. & Cheng, L. Structural design and energy absorption mechanism of laminated SiC/BN ceramics. Journal of the European Ceramic Society 38, 3742-3751 (2018).152 Schroer, A., Wheeler, J. M. & Schwaiger, R. Deformation behavior and energy absorption capability of polymer and ceramic-polymer composite microlattices under cyclic loading. Journal of Materials Research 33, 274-289 (2018).153 Boria, S., Scattina, A. & Belingardi, G. Axial energy absorption of CFRP truncated cones. Composite Structures 130, 18-28 (2015).154 Grozdanov, S. & Polonyi, J. Viscosity and dissipative hydrodynamics from effective field theory. Physical Review D 91, 105031 (2015).155 Xu, Z.-D., Ge, T. & Liu, J. Experimental and theoretical study of high-energy dissipation-viscoelastic dampers based on acrylate-rubber matrix. Journal of Engineering Mechanics 146, 04020057 (2020).156 Zhao, C. et al. Dynamic behavior of impact hardening elastomer: A flexible projectile material with unique rate-dependent performance. Composites Part A: Applied Science and Manufacturing 143, doi:10.1016/j.compositesa.2021.106285 (2021).157 Zhao, C., Gong, X., Wang, S., Jiang, W. & Xuan, S. Shear Stiffening Gels for Intelligent Anti-impact Applications. Cell Reports Physical Science 1, doi:10.1016/j.xcrp.2020.100266 (2020).158 Isioma, N., Muhammad, Y., Sylvester, O. D., Innocent, D. & Linus, O. Cold flow properties and kinematic viscosity of biodiesel. Universal Journal of Chemistry 1, 135-141 (2013).159 Wu, Q. et al. Highly stretchable and self-healing “solid–liquid” elastomer with strain-rate sensing capability. ACS applied materials interfaces 11, 19534-19540 (2019).160 Wang, Z. et al. Three-dimensional printing of functionally graded liquid crystal elastomer. Science advances 6, eabc0034 (2020).161 Peng, X. et al. 4D Printing of Freestanding Liquid Crystal Elastomers via Hybrid Additive Manufacturing. Adv Mater 34, e2204890, doi:10.1002/adma.202204890 (2022).162 Mistry, D. et al. Soft elasticity optimises dissipation in 3D-printed liquid crystal elastomers. Nat Commun 12, 6677, doi:10.1038/s41467-021-27013-0 (2021).163 Traugutt, N. A. et al. Liquid-Crystal-Elastomer-Based Dissipative Structures by Digital Light Processing 3D Printing. Adv Mater 32, e2000797, doi:10.1002/adma.202000797 (2020).164 Li, S. et al. Digital light processing of liquid crystal elastomers for self-sensing artificial muscles. Science Advances 7, eabg3677 (2021).165 Shan, S. et al. Multistable Architected Materials for Trapping Elastic Strain Energy. Adv Mater 27, 4296-4301, doi:10.1002/adma.201501708 (2015).166 Janbaz, S., Narooei, K., Van Manen, T. & Zadpoor, A. Strain rate–dependent mechanical metamaterials. Science advances 6, eaba0616 (2020).167 Dykstra, D. M. J., Busink, J., Ennis, B. & Coulais, C. Viscoelastic Snapping Metamaterials. Journal of Applied Mechanics 86, doi:10.1115/1.4044036 (2019).168 Deshpande, V., Ashby, M. & Fleck, N. Foam topology: bending versus stretching dominated architectures. Acta materialia 49, 1035-1040 (2001).169 Ye, H. et al. Multimaterial 3D printed self-locking thick-panel origami metamaterials. Nature Communications 14, 1607 (2023).170 Cheng, J. et al. Centrifugal multimaterial 3D printing of multifunctional heterogeneous objects. Nature Communications 13, 7931 (2022).171 Hu, L. et al. Design of high-energy-dissipation, deformable binder for high-areal-capacity silicon anode in lithium-ion batteries. Chemical Engineering Journal 420, 129991 (2021).172 Huang, J. et al. Ultrahigh energy-dissipation elastomers by precisely tailoring the relaxation of confined polymer fluids. Nat Commun 12, 3610, doi:10.1038/s41467-021-23984-2 (2021).173 Zeng, X. et al. Ultrahigh energy-dissipation thermal interface materials through anneal-induced disentanglement. ACS Materials Letters 4, 874-881 (2022).174 Ding, Y. & Sokolov, A. P. Breakdown of time− temperature superposition principle and universality of chain dynamics in polymers. Macromolecules 39, 3322-3326 (2006).175 Park, B. et al. Cuticular pad–inspired selective frequency damper for nearly dynamic noise–free bioelectronics. Science 376, 624-629 (2022).176 Whatley, B. R. & Wen, X. Intervertebral disc (IVD): Structure, degeneration, repair and regeneration. Materials Science Engineering: C 32, 61-77 (2012).177 Freemont, A. The cellular pathobiology of the degenerate intervertebral disc and discogenic back pain. Rheumatology 48, 5-10 (2009).178 Hoy, D. et al. The global burden of low back pain: estimates from the Global Burden of Disease 2010 study. Annals of the rheumatic diseases 73, 968-974 (2014).179 Sloan, S. R., Jr. et al. Combined nucleus pulposus augmentation and annulus fibrosus repair prevents acute intervertebral disc degeneration after discectomy. Sci Transl Med 12, doi:10.1126/scitranslmed.aay2380 (2020).180 Helgeson, M. D., Bevevino, A. J. & Hilibrand, A. S. Update on the evidence for adjacent segment degeneration and disease. The spine journal 13, 342-351 (2013).181 Li, C., Jiang, T., He, Q. & Peng, Z. Stiffness-mass-coding metamaterial with broadband tunability for low-frequency vibration isolation. Journal of Sound and Vibration 489, doi:10.1016/j.jsv.2020.115685 (2020).182 Padture, N. P. Advanced structural ceramics in aerospace propulsion. Nat. Mater. 15, 804-809, doi:10.1038/nmat4687 (2016).183 Li, F. et al. Ultrahigh piezoelectricity in ferroelectric ceramics by design. Nat. Mater. 17, 349-354, doi:10.1038/s41563-018-0034-4 (2018).184 Li, J. et al. Grain-orientation-engineered multilayer ceramic capacitors for energy storage applications. Nat. Mater. 19, 999-1005, doi:10.1038/s41563-020-0704-x (2020).185 Zhang, M. et al. 3D printing of Haversian bone-mimicking scaffolds for multicellular delivery in bone regeneration. Sci. Adv. 6, eaaz6725 (2020).186 Liu, Z. et al. Lead-free (Ag,K)NbO3 materials for high-performance explosive energy conversion. Sci. Adv. 6, eaba0367 (2020).187 Duan, C. et al. Highly durable, coking and sulfur tolerant, fuel-flexible protonic ceramic fuel cells. Nature 557, 217-222, doi:10.1038/s41586-018-0082-6 (2018).188 Nakamura, Y., Sakai, Y., Azuma, M. & Ohkoshi, S.-i. Long-term heat-storage ceramics absorbing thermal energy from hot water. Sci. Adv. 6, eaaz5264 (2020).189 Wilkerson, R. P. et al. High-temperature damage-tolerance of coextruded, bioinspired (“nacre-like”), alumina/nickel compliant-phase ceramics. Scripta Mater. 158, 110-115, doi:10.1016/j.scriptamat.2018.08.046 (2019).190 Wuchina, E., Opila, E., Opeka, M., Fahrenholtz, B. & Talmy, I. UHTCs: Ultra-high temperature ceramic materials for extreme environment applications. Electrochem. Soc. Interface 16, 30-36 (2007).191 Pelissari, P. I. B. G. B. et al. Nacre-like ceramic refractories for high temperature applications. J. Eur. Ceram. Soc. 38, 2186-2193, doi:10.1016/j.jeurceramsoc.2017.10.042 (2018).192 Baitalik, S. & Kayal, N. Thermal shock and chemical corrosion resistance of oxide bonded porous SiC ceramics prepared by infiltration technique. J. Alloy. Compd. 781, 289-301, doi:10.1016/j.jallcom.2018.12.046 (2019).193 Yazdani Sarvestani, H. et al. Bioinspired stochastic design: Tough and stiff ceramic systems. Adv. Funct. Mater. 32, doi:10.1002/adfm.202108492 (2021).194 Studart, A. R. Additive manufacturing of biologically-inspired materials. Chem. Soc. Rev. 45, 359-376, doi:10.1039/c5cs00836k (2016).195 Wegst, U. G. K., Bai, H., Saiz, E., Tomsia, A. P. & Ritchie, R. O. Bioinspired structural materials. Nat. Mater. 14, 23-36 (2015).196 Yan, X. et al. Recent advancements in biomimetic 3D printing materials with enhanced mechanical properties. Front. Mater. 8, 518886, doi:10.3389/fmats.2021.518886 (2021).197 Ritchie, R. O. The conflicts between strength and toughness. Nat. Mater. 10, 817-822, doi:10.1038/nmat3115 (2011).198 Yin, Z., Hannard, F. & Barthelat, F. Impact-resistant nacre-like transparent materials. Science 364, 1260-1263 (2019).199 Cheng, Y. et al. ZrB2-based "brick-and-mortar" composites achieving the synergy of superior damage tolerance and ablation resistance. ACS Appl. Mater. Interfaces 12, 33246-33255, doi:10.1021/acsami.0c08206 (2020).200 Rahimizadeh, A. et al. Engineering toughening mechanisms in architectured ceramic-based bioinspired materials. Mater. Des. 198, 109375 (2021).201 Chen, S.-M. et al. Biomimetic twisted plywood structural materials. Natl. Sci. Rev. 5, 703-714, doi:10.1093/nsr/nwy080 (2018).202 An, Y., Yang, Y., Jia, Y., Han, W. & Cheng, Y. Mechanical properties of biomimetic ceramic with Bouligand architecture. J. Am. Ceram. Soc. 105, 2385-2391, doi:10.1111/jace.18262 (2021).203 Singh, G. & Soundarapandian, S. Bone-like structure by modified freeze casting. Sci. Rep. 10, 7914, doi:10.1038/s41598-020-64757-z (2020).204 Bouville, F. et al. Strong, tough and stiff bioinspired ceramics from brittle constituents. Nat. Mater. 13, 508-514, doi:10.1038/nmat3915 (2014).205 Shaikeea, A. J. D., Cui, H., O'Masta, M., Zheng, X. R. & Deshpande, V. S. The toughness of mechanical metamaterials. Nat. Mater. 21, 297-304, doi:10.1038/s41563-021-01182-1 (2022).206 Surjadi, J. U. & Lu, Y. Design criteria for tough metamaterials. Nat. Mater. 21, 272-274, doi:10.1038/s41563-022-01216-2 (2022).207 Surjadi, J. U. et al. Mechanical metamaterials and their engineering applications. Adv. Eng. Mater. 21, 1800864, doi:10.1002/adem.201800864 (2019).208 Jang, D., Meza, L. R., Greer, F. & Greer, J. R. Fabrication and deformation of three-dimensional hollow ceramic nanostructures. Nat. Mater. 12, 893-898, doi:10.1038/nmat3738 (2013).209 Zheng, X. et al. Ultralight, ultrastiff mechanical metamaterials. Science 344, 1373-1377 (2014).210 Bauer, J. et al. Additive manufacturing of ductile, ultrastrong polymer-derived nanoceramics. Matter 1, 1547-1556, doi:10.1016/j.matt.2019.09.009 (2019).211 Sajadi, S. M. et al. Damage-tolerant 3D-printed ceramics via conformal coating. Sci. Adv. 7, eabc5028 (2021).212 Sun, L., Dong, P., Zeng, Y. & Chen, J. Fabrication of hollow lattice alumina ceramic with good mechanical properties by Digital Light Processing 3D printing technology. Ceram. Int. 47, 26519-26527, doi:10.1016/j.ceramint.2021.06.065 (2021).213 Li, Z. et al. Additive manufacturing of lightweight and high-strength polymer-derived SiOC ceramics. Virtual Phys. Prototy. 15, 163-177, doi:10.1080/17452759.2019.1710919 (2020).214 Shen, M. et al. Mechanical properties of 3D printed ceramic cellular materials with triply periodic minimal surface architectures. J. Eur. Ceram. Soc. 41, 1481-1489, doi:10.1016/j.jeurceramsoc.2020.09.062 (2021).215 Zhao, W., Wang, C., Xing, B., Shen, M. & Zhao, Z. Mechanical properties of zirconia octet truss structures fabricated by DLP 3D printing. Mater. Res. Express 7, 085201, doi:10.1088/2053-1591/aba643 (2020).216 Schwarz, H. A. Gesammelte Mathematische Abhandlungen. Springer, Berlin Vol. 1 (1890).217 Han, L. & Che, S. An overview of materials with triply periodic minimal surfaces and related geometry: from biological structures to self-assembled systems. Adv. Mater. 30, 1705708, doi:10.1002/adma.201705708 (2018).218 Al-Ketan, O. & Abu Al-Rub, R. K. Multifunctional mechanical metamaterials based on triply periodic minimal surface lattices. Adv. Eng. Mater. 21, 1900524, doi:10.1002/adem.201900524 (2019).219 Wang, S. et al. Efficient representation and optimization of TPMS-based porous structures for 3D heat dissipation. Comput. Aided Design 142, 103123, doi:10.1016/j.cad.2021.103123 (2022).220 Ambekar, R. S. et al. Topologically engineered 3D printed architectures with superior mechanical strength. Mater. Today 48, 72-94, doi:10.1016/j.mattod.2021.03.014 (2021).221 Al‐Ketan, O., Pelanconi, M., Ortona, A. & Abu Al‐Rub, R. K. Additive manufacturing of architected catalytic ceramic substrates based on triply periodic minimal surfaces. J. Am. Ceram. Soc. 102, 6176-6193, doi:10.1111/jace.16474 (2019).222 Yao, Y. et al. High performance hydroxyapatite ceramics and a triply periodic minimum surface structure fabricated by digital light processing 3D printing. J. Adv. Ceram. 10, 39-48, doi:10.1007/s40145-020-0415-4 (2021).223 Zhang, L. et al. Pseudo-ductile fracture of 3D printed alumina triply periodic minimal surface structures. J. Eur. Ceram. Soc. 40, 408-416, doi:10.1016/j.jeurceramsoc.2019.09.048 (2020).224 Bauer, J., Hengsbach, S., Tesari, I., Schwaiger, R. & Kraft, O. High-strength cellular ceramic composites with 3D microarchitecture. Proc. Natl. Acad. Sci. U.S.A 111, 2453-2458, doi:10.1073/pnas.1315147111 (2014).225 Mei, H. et al. Ultrahigh strength printed ceramic lattices. J. Alloy. Compd. 797, 786-796, doi:10.1016/j.jallcom.2019.05.117 (2019).226 Colombo, P. Mechanical properties of silicon oxycarbide ceramic foams. J. Am. Ceram. Soc. 84, 2245-2251 (2001).227 Elsayed, H., Chmielarz, A., Potoczek, M., Fey, T. & Colombo, P. Direct ink writing of three dimensional Ti2AlC porous structures. Addit. Manuf. 28, 365-372, doi:10.1016/j.addma.2019.05.018 (2019).228 Gonzalez-Julian, J. et al. High-temperature oxidation and compressive strength of Cr2AlC MAX phase foams with controlled porosity. J. Am. Ceram. Soc. 101, 542-552, doi:10.1111/jace.15224 (2018).229 Belmonte, M. et al. Multifunctional 3D‐printed cellular MAX‐phase architectures. Adv. Mater. Technol. 4, 1900375, doi:10.1002/admt.201900375 (2019).