[1] Xin X Z, Liu L W, Liu Y J and Leng J S 2020 4D printing auxetic metamaterials with tunable, programmable, and reconfigurable mechanical properties Adv. Funct. Mater. 30 2004226
[2] GuoXG et al 2020 Designing mechanical metamaterials with kirigami-inspired, hierarchical constructions for giant positive and negative thermal expansion Adv. Mater. 33 202004919
[3] Nicolaou Z G and Motter A E 2012 Mechanical metamaterials with negative compressibility transitions Nat. Mater. 11 608–13
[4] Wang J, Dai G L and Huang J P 2020 Thermal metamaterial: fundamental, application, and outlook iScience 23 101637
[5] XuGQ,DongKC,LiY, LiHG,LiuKP, LiLQ,Wu JQ and Qiu C-W 2020 Tunable analog thermal material Nat. Commun. 11 6028
[6] Yang S, Wang J, Dai G L, Yang F B and Huang J P 2021 Controlling macroscopic heat transfer with thermal metamaterials: theory, experiment and application Phys. Rep. 908 1–65
[7] Fang N, Xi D J, Xu J Y, Ambati M, Srituravanich W, Sun C and Zhang X 2006 Ultrasonic metamaterials with negative modulus Nat. Mater. 5 452–6
[8] Fok L, Ambati M and Zhang X 2008 Acoustic metamaterials MRS Bull. 33 931–4
[9] Lu M-H, Feng L and Chen Y-F 2009 Phononic crystals and acoustic metamaterials Mater. Today 12 34–42
[10] Smith D R, Pendry J B and Wiltshire M C K 2004 Metamaterials and negative refractive index Science 305 788–92
[11] Cai W S, Chettiar U K, Kildishev A V and Shalaev V M 2007 Optical cloaking with metamaterials Nat. Photon. 1 224–7
[12] Feng J W, Fu J Z, Yao X H and He Y 2022 Triply periodic minimal surface (TPMS) porous structures: from multi-scale design, precise additive manufacturing to multidisciplinary applications Int. J. Extrem. Manuf. 4 022001
[13] Ruan J Q, Chen Y F, Lu M H and Zhu S N 2014 Metamaterial based on elastic mechanics Sci. Sin. Technol. 44 1261–70
[14] Ho D T and Schwingenschl.gl U 2021 Designing graphene origami structures with a giant isotropic negative coefficient of thermal expansion Extreme Mech. Lett. 47 101357
[15] Yu XL,ZhouJ,LiangHY, JiangZYandWu LL2018 Mechanical metamaterials associated with stiffness, rigidity and compressibility: a brief review Prog. Mater. Sci. 94 114–73
[16] Wu K, Zhao X G, Bifano T G, Anderson S W and Zhang X 2022 Auxetics-inspired tunable metamaterials for magnetic resonance imaging Adv. Mater. 34 2109032
[17] Wu L L, Xi X Q, Li B and Zhou J 2018 Multi-stable mechanical structural materials Adv. Eng. Mater. 20 1700599
[18] Shan S C, Kang S H, Raney J R, Wang P, Fang L C, Candido F, Lewis J A and Bertoldi K 2015 Multistable architected materials for trapping elastic strain energy Adv. Mater. 27 4296–301
[19] ZhuSW, WangB,Tan XJ,HuJQ,WangLC,ZhouZG and Chen S 2021 A novel bi-material negative stiffness metamaterial in sleeve-type via combining rigidity with softness Compos. Struct. 262 113381
[20] Zhang H, Wu J, Fang D N and Zhang Y H 2021 Hierarchical mechanical metamaterials built with scalable tristable elements for ternary logic operation and amplitude modulation Sci. Adv. 7 eabf1966
[21] Shi J H, Mofatteh H, Mirabolghasemi A, Desharnais G and Akbarzadeh A 2021 Programmable multistable perforated shellular Adv. Mater. 33 2102423
[22] Pal A, Restrepo V, Goswami D and Martinez R V 2021 Exploiting mechanical instabilities in soft robotics: control, sensing, and actuation Adv. Mater. 33 2006939
[23] ChiYD,LiYB,ZhaoY, HongYY, TangYCandYinJ 2022 Bistable and multistable actuators for soft robots: structures, materials, and functionalities Adv. Mater. 34 2110384
[24] PanF,LiYL,LiZY,YangJL,LiuBandChenYL20193D pixel mechanical metamaterials Adv. Mater. 31 1900548
[25] Wu S, Ze Q, Dai J Z, Udipi N, Paulino G H and Zhao R K 2021 Stretchable origami robotic arm with omnidirectional bending and twisting Proc. Natl Acad. Sci. USA 118 e2110023118
[26] Faber J A, Udani J P, Riley K S, Studart A R and Arrieta A F 2020 Dome-patterned metamaterial sheets Adv. Sci. 7 2001955
[27] Song Y P, Panas R M, Chizari S, Shaw L A, Jackson J A, Hopkins J B and Pascall A J 2019 Additively manufacturable micro-mechanical logic gates Nat. Commun. 10 882
[28] Melancon D, Forte A E, Kamp L M, Gorissen B and Bertoldi K 2022 Inflatable origami: multimodal deformation via multistability Adv. Funct. Mater. 32 2201891
[29] Lin X, Pan F, Yang K, Guan J, Ding B, Liu Y Z, Yang K J, Liu B and Chen Y L 2021 A stair-building strategy for tailoring mechanical behavior of re-customizable metamaterials Adv. Funct. Mater. 31 2101808
[30] Aksoy B and Shea H 2022 Multistable shape programming of variable-stiffness electromagnetic devices Sci. Adv. 8 eabk0543
[31] Deng B L, Zanaty M, Forte A E and Bertoldi K 2022 Topological solitons make metamaterials crawl Phys. Rev. Appl. 17 014004
[32] Ze Q, Wu S, Nishikawa J, Dai J Z, Sun Y, Leanza S, Zemelka C, Novelino L S, Paulino G H and Zhao R R 2022 Soft robotic origami crawler Sci. Adv. 8 eabm7834
[33] Kim Y, van den Berg J and Crosby A J 2021 Autonomous snapping and jumping polymer gels Nat. Mater. 20 1695–701
[34] Chen T, Pauly M and Reis P M 2021 A reprogrammable mechanical metamaterial with stable memory Nature 589 386–90
[35] MeiT, MengZQ,ZhaoKJandChenCQ2021A mechanical metamaterial with reprogrammable logical functions Nat. Commun. 12 7234
[36] Yasuda H, Tachi T, Lee M and Yang J 2017 Origami-based tunable truss structures for non-volatile mechanical memory operation Nat. Commun. 8 962
[37] Raney J R, Nadkarni N, Daraio C, Kochmann D M, Lewis J A and Bertoldi K 2016 Stable propagation of mechanical signals in soft media using stored elastic energy Proc. Natl Acad. Sci. USA 113 9722–7
[38] Chen Y Z and Jin L H 2021 Reusable energy-absorbing architected materials harnessing snapping-back buckling of wide hyperelastic columns Adv. Funct. Mater. 31 2102113
[39] Frenzel T, Findeisen C, Kadic M, Gumbsch P and Wegener M 2016 Tailored buckling microlattices as reusable light-weight shock absorbers Adv. Mater. 28 5865–70
[40] Vasios N, Deng B L, Gorissen B and Bertoldi K 2021 Universally bistable shells with nonzero Gaussian curvature for two-way transition waves Nat. Commun. 12 695
[41] Jin L S, Khajehtourian R, Mueller J, Rafsanjani A, Tournat V, Bertoldi K and Kochmann D M 2020 Guided transition waves in multistable mechanical metamaterials Proc. Natl Acad. Sci. USA 117 2319–25
[42] Cao Y T, Derakhshani M, Fang Y H, Huang G L and Cao C Y 2021 Bistable structures for advanced functional systems Adv. Funct. Mater. 31 2106231
[43] Zhang H, Wu J, Zhang Y H and Fang D N 2021 Multistable mechanical metamaterials: a brief review Trans. Nanjing Univ. Aeronaut. Astronaut. 38 1–17
[44] ChiYD,HongYY, ZhaoY, LiYBandYinJ2022 Snapping for high-speed and high-efficient butterfly stroke–like soft swimmer Sci. Adv. 8 eadd3788
[45] Lakes R S 2001 Extreme damping in composite materials with a negative stiffness phase Phys. Rev. Lett. 86 2897–900
[46] Moore B, Jaglinski T, Stone D S and Lakes R S 2006 Negative incremental bulk modulus in foams Phil. Mag. Lett. 86 651–9
[47] Li J, Arora N and Rudykh S 2021 Elastic instabilities, microstructure transformations, and pattern formations in soft materials Curr. Opin. Solid State Mater. Sci. 25 100898
[48] Fu K J, Zhao Z H and Jin L H 2019 Programmable granular metamaterials for reusable energy absorption Adv. Funct. Mater. 29 1901258
[49] Opdahl P G, Jensen B D and Howell L L 1998 An investigation into compliant bistable mechanisms ASME 1998 Design Engineering Technical Conf. DETC98/MECH-5914, V5901BT5901A5046 (ASME)
[50] ZhuSW, Tan XJ,WangB,ChenS,HuJQ,MaLand Wu L Z 2019 Bio-inspired multistable metamaterials with reusable large deformation and ultra-high mechanical performance Extreme Mech. Lett. 32 100548
[51] Rafsanjani A, Akbarzadeh A and Pasini D 2015 Snapping mechanical metamaterials under tension Adv. Mater. 27 5931–5
[52] LiuYZ,Pan F, DingB,ZhuYL,YangKJandChenYL 2022 Multistable shape-reconfigurable metawire in 3D space Extreme Mech. Lett. 50 101535
[53] Santer M and Pellegrino S 2011 Concept and design of a multistable plate structure J. Mech. Des. 133 081001
[54] Restrepo D, Mankame N D and Zavattieri P D 2015 Phase transforming cellular materials Extreme Mech. Lett. 4 52–60
[55] Qiu J, Lang J H and Slocum A H 2004 A curved-beam bistable mechanism J. Microelectromech. Syst. 13 137–46
[56] Zhang Y L, Velay-Lizancos M, Restrepo D, Mankame N D and Zavattieri P D 2021 Architected material analogs for shape memory alloys Matter 4 1990–2012
[57] Liu X, Lamarque F, Doré E and Pouille P 2015 Multistable wireless micro-actuator based on antagonistic pre-shaped double beams Smart Mater. Struct. 24 075028
[58] Jeon S-Y, Shen B J, Traugutt N A, Zhu Z Y, Fang L C, Yakacki C M, Nguyen T D and Kang S H 2022 Synergistic energy absorption mechanisms of architected liquid crystal elastomers Adv. Mater. 34 2200272
[59] Tang Y C, Chi Y D, Sun J F, Huang T-H, Maghsoudi O H, Spence A, Zhao J G, Su H and Yin J 2020 Leveraging elastic instabilities for amplified performance: spine-inspired high-speed and high-force soft robots Sci. Adv. 6 eaaz6912
[60] Pandey A, Moulton D E, Vella D and Holmes D P 2014 Dynamics of snapping beams and jumping poppers Europhys. Lett. 105 24001
[61] Hamouche W, Maurini C, Vincenti A and Vidoli S 2016 Basic criteria to design and produce multistable shells Meccanica 51 2305–20
[62] Gorissen B, Melancon D, Vasios N, Torbati M and Bertoldi K 2020 Inflatable soft jumper inspired by shell snapping Sci. Robot. 5 eabb1967
[63] Shao H Q, Wei S Z, Jiang X, Holmes D P and Ghosh T K 2018 Bioinspired electrically activated soft bistable actuators Adv. Funct. Mater. 28 1802999
[64] Armon S, Efrati E, Kupferman R and Sharon E 2011 Geometry and mechanics in the opening of chiral seed pods Science 333 1726–30
[65] Daynes S, Potter K D and Weaver P M 2008 Bistable prestressed buckled laminates Compos. Sci. Technol. 68 3431–7
[66] Forterre Y, Skotheim J M, Dumais J and Mahadevan L 2005 How the Venus flytrap snaps Nature 433 421–5
[67] Chen Z, Guo Q H, Majidi C, Chen W Z, Srolovitz D J and Haataja M P 2012 Nonlinear geometric effects in mechanical bistable morphing structures Phys. Rev. Lett. 109 114302
[68] Guest S D and Pellegrino S 2006 Analytical models for bistable cylindrical shells Proc. R. Soc. A 462 839–54
[69] Silverberg J L, Evans A A, Mcleod L, Hayward R C, Hull T, Santangelo C D and Cohen I 2014 Using origami design principles to fold reprogrammable mechanical metamaterials Science 345 647–50
[70] Wang Z J, Jing L Q, Yao K, Yang Y H, Zheng B, Soukoulis C M, Chen H S and Liu Y M 2017 Origami-based reconfigurable metamaterials for tunable chirality Adv. Mater. 29 1700412
[71] FangHB,ChuSCA,XiaYTandWangKW2018 Programmable self-locking origami mechanical metamaterials Adv. Mater. 30 1706311
[72] Waitukaitis S, Menaut R, Chen B G G and Van Hecke M 2015 Origami multistability: from single vertices to metasheets Phys. Rev. Lett. 114 055503
[73] Zhai Z R, Wu L L and Jiang H Q 2021 Mechanical metamaterials based on origami and kirigami Appl. Phys. Rev. 8 041319
[74] Xu R, He Y L, Li X, Lu M H and Chen Y F 2023 Snap-fit mechanical metamaterials Appl. Mater. Today 30 101714
[75] Zhang Y F, Wang Y J and Chen C Q 2019 Ordered deformation localization in cellular mechanical metamaterials J. Mech. Phys. Solids 123 28–40
[76] Ding J N and Van Hecke M 2022 Sequential snapping and pathways in a mechanical metamaterial J. Chem. Phys. 156 204902
[77] Florijn B, Coulais C and Van Hecke M 2014 Programmable mechanical metamaterials Phys. Rev. Lett. 113 175503
[78] Chen Y Z and Jin L H 2018 Geometric role in designing pneumatically actuated pattern-transforming metamaterials Extreme Mech. Lett. 23 55–66
[79] Zhang Y F, Li B, Zheng Q S, Genin G M and Chen C Q 2019 Programmable and robust static topological solitons in mechanical metamaterials Nat. Commun. 10 5605
[80] Rafsanjani A and Pasini D 2016 Bistable auxetic mechanical metamaterials inspired by ancient geometric motifs Extreme Mech. Lett. 9 291–6
[81] Shang X, Liu L, Rafsanjani A and Pasini D 2018 Durable bistable auxetics made of rigid solids J. Mater. Res. 33 300–8
[82] Silverberg J L, Na J-H, Evans A A, Liu B, Hull T C, Santangelo C, Lang R J, Hayward R C and Cohen I 2015 Origami structures with a critical transition to bistability arising from hidden degrees of freedom Nat. Mater. 14 389–93
[83] Liu K, Pratapa P P, Misseroni D, Tachi T and Paulino G H 2022 Triclinic metamaterials by tristable origami with reprogrammable frustration Adv. Mater. 34 2107998
[84] Li L L, Li B and Chen G M 2022 A non-transit fully compliant tristable mechanism capable of direct switching between every two stable positions Mech. Syst. Signal Process. 169 108597
[85] Fang X, Wen J H, Cheng L, Yu D L, Zhang H J and Gumbsch P 2022 Programmable gear-based mechanical metamaterials Nat. Mater. 21 869–76
[86] MengZQ,LiuMC,Yan HJ,GeninGMandChenCQ 2022 Deployable mechanical metamaterials with multistep programmable transformation Sci. Adv. 8 eabn5460
[87] Boston D M, Phillips F R, Henry T C and Arrieta A F 2022 Spanwise wing morphing using multistable cellular metastructures Extreme Mech. Lett. 53 101706
[88] Li W C, Wang F W, Sigmund O and Zhang X S 2022 Digital synthesis of free-form multimaterial structures for realization of arbitrary programmed mechanical responses Proc. Natl Acad. Sci. USA 119 e2120563119
[89] Haghpanah B, Salari-Sharif L, Pourrajab P, Hopkins J and Valdevit L 2016 Multistable shape-reconfigurable architected materials Adv. Mater. 28 7915–20
[90] Choi G P T, Dudte L H and Mahadevan L 2019 Programming shape using kirigami tessellations Nat. Mater. 18 999–1004
[91] Meng Z Q, Liu M C, Zhang Y F and Chen C Q 2020 Multi-step deformation mechanical metamaterials J. Mech. Phys. Solids 144 104095
[92] Yang H and Ma L 2018 Multi-stable mechanical metamaterials with shape-reconfiguration and zero Poisson’s ratio Mater. Des. 152 181–90
[93] Saadi M A S R, Maguire A, Pottackal N T, Thakur M S H, Ikram M M, Hart A J, Ajayan P M and Rahman M M 2022 Direct ink writing: a 3D printing technology for diverse materials Adv. Mater. 34 2108855
[94] Yan J,HuangSZ,LimYV, XuTT, KongDZ,LiXJ, Yang H Y and Wang Y 2022 Direct-ink writing 3D printed energy storage devices: from material selectivity, design and optimization strategies to diverse applications Mater. Today 54 110–52
[95] Dudek P 2013 FDM 3D printing technology in manufacturing composite elements Arch. Metall. Mater. 58 1415–8
[96] Cheng C Y, Xie H, Xu Z Y, Li L, Jiang M N, Tang L, Yang K K and Wang Y Z 2020 4D printing of shape memory aliphatic copolyester via UV-assisted FDM strategy for medical protective devices Chem. Eng. J. 396 125242
[97] Garland A P et al 2020 Coulombic friction in metamaterials to dissipate mechanical energy Extreme Mech. Lett. 40 100847
[98] Waheed U, Myant C W and Dobson S N 2020 Boolean AND/OR mechanical logic using multi-plane mechanical metamaterials Extreme Mech. Lett. 40 100865
[99] Mao J-J, Wang S, Tan W and Liu M C 2022 Modular multistable metamaterials with reprogrammable mechanical properties Eng. Struct. 272 114976
[100] AndreuA,SuPC,KimJH,NgCS,KimS,KimI,LeeJ, Noh J, Subramanian A S and Yoon Y J 2021 4D printing materials for vat photopolymerization Addit. Manuf. 44 102024
[101] XuY, MaoHC,LiuCY, DuZY, Yan WJ,YangZY, Partanen J and Chen Y 2023 Hopping light vat photopolymerization for multiscale fabrication Small 19 2205784
[102] Surjadi J U et al 2022 Lightweight, ultra-tough, 3D-architected hybrid carbon microlattices Matter 5 4029–46
[103] Saccone M A, Gallivan R A, Narita K, Yee D W and Greer J R 2022 Additive manufacturing of micro-architected metals via hydrogel infusion Nature 612 685–90
[104] Wang P R, Berry D B, Song Z Q, Kiratitanaporn W, Schimelman J, Moran A, He F, Xi B, Cai S Q and Chen S C 2020 3D printing of a biocompatible double network elastomer with digital control of mechanical properties Adv. Funct. Mater. 30 1910391
[105] Zhang X, Wang Y, Tian Z H, Samri M, Moh K, Mcmeeking R M, Hensel R and Arzt E 2022 A bioinspired snap-through metastructure for manipulating micro-objects Sci. Adv. 8 eadd4768
[106] Ge Q, Li Z Q, Wang Z L, Kowsari K, Zhang W, He X N, Zhou J L and Fang N X 2020 Projection micro stereolithography based 3D printing and its applications Int. J. Extrem. Manuf. 2 022004
[107] TED 2013 The emergence of “4D printing” (available at: www.ted.com/talks/skylar_tibbits_the_emergence_of_4d_ printing)
[108] Fu P et al 2022 4D printing of polymers: techniques, materials, and prospects Prog. Polym. Sci. 126 101506
[109] Yuan C, Wang F F and Ge Q 2021 Multimaterial direct 4D printing of high stiffness structures with large bending curvature Extreme Mech. Lett. 42 101122
[110] Weng S Y, Kuang X, Zhang Q, Hamel C M, Roach D J, Hu N and Jerry Qi H 2021 4D printing of glass fiber-regulated shape shifting structures with high stiffness ACS Appl. Mater. Interfaces 13 12797–804
[111] Tao R,XiL,Wu WW, LiY, LiaoBB,LiuLW, LengJS and Fang D N 2020 4D printed multi-stable metamaterials with mechanically tunable performance Compos. Struct. 252 112663
[112] Spiegel C A, Hackner M, Bothe V P, Spatz J P and Blasco E 2022 4D printing of shape memory polymers: from macro to micro Adv. Funct. Mater. 32 2110580
[113] Jeong H Y, Lee E, Ha S, Kim N and Jun Y C 2019 Multistable thermal actuators via multimaterial 4D printing Adv. Mater. Technol. 4 1800495
[114] Niknam H, Akbarzadeh A, Therriault D and Bodkhe S 2022 Tunable thermally bistable multi-material structure Appl. Mater. Today 28 101529
[115] Toombs J T, Luitz M, Cook C C, Jenne S, Li C C, Rapp B E, Kotz-Helmer F and Taylor H K 2022 Volumetric additive manufacturing of silica glass with microscale computed axial lithography Science 376 308–12
[116] Walker D A, Hedrick J L and Mirkin C A 2019 Rapid, large-volume, thermally controlled 3D printing using a mobile liquid interface Science 366 360–4
[117] Ren Z S, Gao L, Clark S J, Fezzaa K, Shevchenko P, Choi A, Everhart W, Rollett A D, Chen L Y and Sun T 2023 Machine learning–aided real-time detection of keyhole pore generation in laser powder bed fusion Science 379 89–94
[118] Liu G et al 2021 Additive manufacturing of structural materials Mater. Sci. Eng. R 145 100596
[119] Nazir A, Gokcekaya O, Md Masum Billah K, Ertugrul O, Jiang J C, Sun J Y and Hussain S 2023 Multi-material additive manufacturing: a systematic review of design, properties, applications, challenges, and 3D printing of materials and cellular metamaterials Mater. Des. 226 111661
[120] Gu D D, Shi X Y, Poprawe R, Bourell D L, Setchi R and Zhu J H 2021 Material-structure-performance integrated laser-metal additive manufacturing Science 372 eabg1487
[121] Holmes D P and Crosby A J 2007 Snapping surfaces Adv. Mater. 19 3589–93
[122] Fu H et al 2018 Morphable 3D mesostructures and microelectronic devices by multistable buckling mechanics Nat. Mater. 17 268–76
[123] Kuang X, Roach D J, Wu J T, Hamel C M, Ding Z, Wang T J, Dunn M L and Qi H J 2019 Advances in 4D printing: materials and applications Adv. Funct. Mater. 29 1805290
[124] Liu G, Zhao Y, Wu G and Lu J 2018 Origami and 4D printing of elastomer-derived ceramic structures Sci. Adv. 4 eaat0641
[125] Zhang W et al 2022 Stiff shape memory polymers for high-resolution reconfigurable nanophotonics Nano Lett. 22 8917–24
[126] Caprioli M, Roppolo I, Chiappone A, Larush L, Pirri C F and Magdassi S 2021 3D-printed self-healing hydrogels via digital light processing Nat. Commun. 12 2462
[127] Gelebart A H, Jan Mulder D, Varga M, Konya A, Vantomme G, Meijer E W, Selinger R L B and Broer D J 2017 Making waves in a photoactive polymer film Nature 546 632–6
[128] Seyedkanani A and Akbarzadeh A 2022 Magnetically assisted rotationally multistable metamaterials for tunable energy trapping-dissipation Adv. Funct. Mater. 32 2207581
[129] Tan XJ,ChenS,WangB,ZhuSW, Wu LZandSunYG 2019 Design, fabrication, and characterization of multistable mechanical metamaterials for trapping energy Extreme Mech. Lett. 28 8–21
[130] Melancon D, Gorissen B, García-Mora C J, Hoberman C and Bertoldi K 2021 Multistable inflatable origami structures at the metre scale Nature 592 545–50
[131] Korpas L M, Yin R, Yasuda H and Raney J R 2021 Temperature-responsive multistable metamaterials ACS Appl. Mater. Interfaces 13 31163–70
[132] Follador M, Conn A T and Rossiter J 2015 Bistable minimum energy structures (BiMES) for binary robotics Smart Mater. Struct. 24 065037
[133] Faber J A, Arrieta A F and Studart A R 2018 Bioinspired spring origami Science 359 1386–91
[134] Novelino L S, Ze Q, Wu S, Paulino G H and Zhao R K 2020 Untethered control of functional origami microrobots with distributed actuation Proc. Natl Acad. Sci. USA 117 24096–101
[135] Treml B, Gillman A, Buskohl P and Vaia R 2018 Origami mechanologic Proc. Natl Acad. Sci. USA 115 6916–21
[136] Vangelatos Z, Gu G X and Grigoropoulos C P 2019 Architected metamaterials with tailored 3D buckling mechanisms at the microscale Extreme Mech. Lett. 33 100580
[137] Jennings A T, Burek M J and Greer J R 2010 Microstructure versus size: mechanical properties of electroplated single crystalline Cu nanopillars Phys. Rev. Lett. 104 135503
[138] Greer J R, Oliver W C and Nix W D 2005 Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients Acta Mater. 53 1821–30
[139] Banerjee A et al 2018 Ultralarge elastic deformation of nanoscale diamond Science 360 300–2
[140] Arzt E 1998 Size effects in materials due to microstructural and dimensional constraints: a comparative review Acta Mater. 46 5611–26
[141] Gao H J, Ji B H, J.ger I L, Arzt E and Fratzl P 2003 Materials become insensitive to flaws at nanoscale: lessons from nature Proc. Natl Acad. Sci. USA 100 5597–600
[142] Rus D and Tolley M T 2015 Design, fabrication and control of soft robots Nature 521 467–75
[143] Rafsanjani A, Bertoldi K and Studart A R 2019 Programming soft robots with flexible mechanical metamaterials Sci. Robot. 4 eaav7874
[144] Wang H B, Totaro M and Beccai L 2018 Toward perceptive soft robots: progress and challenges Adv. Sci. 5 1800541
[145] Sachyani Keneth E, Kamyshny A, Totaro M, Beccai L and Magdassi S 2021 3D printing materials for soft robotics Adv. Mater. 33 2003387
[146] Ze Q, Wu S, Dai J Z, Leanza S, Ikeda G, Yang P C, Iaccarino G and Zhao R R 2022 Spinning-enabled wireless amphibious origami millirobot Nat. Commun. 13 3118
[147] Wang Y Z, Gupta U, Parulekar N and Zhu J 2019 A soft gripper of fast speed and low energy consumption Sci. China Technol. Sci. 62 31–38
[148] Chen T, Bilal O R, Shea K and Daraio C 2018 Harnessing bistability for directional propulsion of soft, untethered robots Proc. Natl Acad. Sci. USA 115 5698–702
[149] Wang J X, Gao D C and Lee P S 2021 Recent progress in artificial muscles for interactive soft robotics Adv. Mater. 33 2003088
[150] Wu MX,ZhengXW, LiuRS,HouNZ,AfridiWH, Afridi RH, Guo X, Wu J N,WangC and Xie G M2022 Glowing sucker octopus (Stauroteuthis syrtensis)-inspired soft robotic gripper for underwater self-adaptive grasping and sensing Adv. Sci. 9 2104382
[151] Theis T N and Horn P M 2003 Basic research in the information technology industry Phys. Today 56 44–49
[152] Kam H, Liu T-J K, Stojanovi′c V, Markovi′c D and Alon E 2011 Design, optimization, and scaling of MEM relays for ultra-low-power digital logic IEEE Trans. Electron Devices 58 236–50
[153] Yan W Z, Li S G, Deguchi M, Zheng Z L, Rus D and Mehta A 2023 Origami-based integration of robots that sense, decide, and respond Nat. Commun. 14 1553
[154] Yasuda H, Johnson K, Arroyos V, Yamaguchi K, Raney J R and Yang J 2022 Leaf-like origami with bistability for self-adaptive grasping motions Soft Robot. 9 938–47
[155] Yasuda H, Buskohl P R, Gillman A, Murphey T D, Stepney S, Vaia R A and Raney J R 2021 Mechanical computing Nature 598 39–48
[156] Pagano A, Yan T X, Chien B, Wissa A and Tawfick S 2017 A crawling robot driven by multi-stable origami Smart Mater. Struct. 26 094007
[157] El Helou C, Grossmann B, Tabor C E, Buskohl P R and Harne R L 2022 Mechanical integrated circuit materials Nature 608 699–703
[158] Reid S R 1993 Plastic deformation mechanisms in axially compressed metal tubes used as impact energy absorbers Int. J. Mech. Sci. 35 1035–52
[159] Tattersall H G and Tappin G 1966 The work of fracture and its measurement in metals, ceramics and other materials J. Mater. Sci. 1 296–301
[160] Dixit P M and Dixit U S 2015 Plasticity: Fundamentals and Applications (CRC Press) pp 1–40
[161] LiQQ,LiE,ChenT, Wu L,WangGQandHeZC 2021 Improve the frontal crashworthiness of vehicle through the design of front rail Thin Walled Struct. 162 107588
[162] SunSJ,LiHY, ZhuCH,MeiKH,JiangH,SunYMand Huang H Z 2021 Study on the anti-collision performance of basalt fiber reinforced polymer beam-column guardrail Compos. Struct. 276 114588
[163] Xie M W 2021 Discussion on the design and performance of the whole packaging box of environmentally friendly packaging materials Adv. Mater. Sci. Eng. 2021 4779965
[164] Liang X D, Fu H B and Crosby A J 2022 Phase-transforming metamaterial with magnetic interactions Proc. Natl Acad. Sci. USA 119 e2118161119
[165] QinQH,ChenSJ,LiKK,JiangMQ,CuiTNand Zhang J X 2020 Structural impact damage of metal honeycomb sandwich plates Compos. Struct. 252 112719
[166] Zhang J X and Guo H Y 2022 Large deflection of rectangular sandwich tubes with metal foam core Compos. Struct. 293 115745
[167] LiX,YahyaMY, NiaAB,WangZH,YangJLandLuGX 2017 Dynamic failure of basalt/epoxy laminates under blast—experimental observation Int. J. Impact Eng. 102 16–26
[168] Cherkaev A and Leelavanichkul S 2012 An impact protective structure with bistable links Int. J. Damage Mech. 21 697–711
[169] Zareei A, Deng B L and Bertoldi K 2020 Harnessing transition waves to realize deployable structures Proc. Natl Acad. Sci. USA 117 4015–20
[170] Yasuda H, Korpas L M and Raney J R 2020 Transition waves and formation of domain walls in multistable mechanical metamaterials Phys. Rev. Appl. 13 054067
[171] Nadkarni N, Arrieta A F, Chong C, Kochmann D M and Daraio C 2016 Unidirectional transition waves in bistable lattices Phys. Rev. Lett. 116 244501
[172] Shen C, Xie Y B, Li J F, Cummer S A and Jing Y 2016 Asymmetric acoustic transmission through near-zero-index and gradient-index metasurfaces Appl. Phys. Lett. 108 223502
[173] Su X S and Norris A N 2016 Focusing, refraction, and asymmetric transmission of elastic waves in solid metamaterials with aligned parallel gaps J. Acoust. Soc. Am. 139 3386–94
[174] Lu Z C and Norris A N 2020 Non-reciprocal wave transmission in a bilinear spring-mass system J. Vib. Acoust. 142 021006
[175] ZhangX,MaJY, LiMY, You Z,WangXY, LuoY, MaKX and Chen Y 2022 Kirigami-based metastructures with programmable multistability Proc. Natl Acad. Sci. USA 119 e2117649119
[176] Tan X J, Chen S, Wang B, Tang J, Wang L C, Zhu S W, Yao K L and Xu P F 2020 Real-time tunable negative stiffness mechanical metamaterial Extreme Mech. Lett. 41 100990
[177] Benichou I and Givli S 2020 Force-sensitive metamaterials for vibration mitigation and mechanical protection Extreme Mech. Lett. 40 100932
[178] Yang N, Chen C-W, Yang J and Silverberg J L 2020 Emergent reconfigurable mechanical metamaterial tessellations with an exponentially large number of discrete configurations Mater. Des. 196 109143
[179] Peretz O, Ben Abu E, Zigelman A, Givli S and Gat A D 2022 A metafluid with multistable density and internal energy states Nat. Commun. 13 1810
[180] Wang L-C, Song W-L, Zhang Y-J, Qu M-J, Zhao Z A, Chen M J, YangYZ, Chen H S and Fang D N2020 Active reconfigurable tristable square-twist origami Adv. Funct. Mater. 30 1909087
[181] Cecchini L, Mariani S, Ronzan M, Mondini A, Pugno N M and Mazzolai B 2023 4D printing of humidity-driven seed inspired soft robots Adv. Sci. 10 2205146
[182] Wu L L, Liu L, Wang Y, Zhai Z R, Zhuang H L, Krishnaraju D, Wang Q X and Jiang H Q 2020 A machine learning-based method to design modular metamaterials Extreme Mech. Lett. 36 100657
[183] Van Mastrigt R, Dijkstra M, Van Hecke M and Coulais C 2022 Machine learning of implicit combinatorial rules in mechanical metamaterials Phys. Rev. Lett. 129 198003
[184] Liu F, Jiang X H, Wang X T and Wang L F 2020 Machine learning-based design and optimization of curved beams for multistable structures and metamaterials Extreme Mech. Lett. 41 101002
[185] Pal A and Sitti M 2023 Programmable mechanical devices through magnetically tunable bistable elements Proc. Natl Acad. Sci. USA 120 e2212489120
[186] Preston D J, Rothemund P, Jiang H J, Nemitz M P, Rawson J, Suo Z G and Whitesides G M 2019 Digital logic for soft devices Proc. Natl Acad. Sci. USA 116 7750–9
[187] Yang T, Zhou S X, Fang S T, Qin W Y and Inman D J 2021 Nonlinear vibration energy harvesting and vibration suppression technologies: designs, analysis, and applications Appl. Phys. Rev. 8 031317
