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Sinha P, Mukhopadhyay T. Programmable multi-physical mechanics of mechanical metamaterials. Advances in Mechanics, in press doi: 10.6052/1000-0992-24-012
Citation: Sinha P, Mukhopadhyay T. Programmable multi-physical mechanics of mechanical metamaterials. Advances in Mechanics, in press doi: 10.6052/1000-0992-24-012

Programmable multi-physical mechanics of mechanical metamaterials

doi: 10.6052/1000-0992-24-012
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  • Mechanical metamaterials are engineered materials with unconventional mechanical behavior that originates from artificially programmed microstructures along with intrinsic material properties. With tremendous advancement in computational and manufacturing capabilities to realize complex microstructures over the last decade, the field of mechanical metamaterials has been attracting wide attention due to immense possibilities of achieving unprecedented multi-physical properties which are not attainable in naturally-occurring materials. One of the rapidly emerging trends in this field is to couple the mechanics of material behavior and the unit cell architecture with different other multi-physical aspects such as electrical or magnetic fields, and stimuli like temperature, light or chemical reactions to expand the scope of actively programming on-demand mechanical responses. In this article, we aim to abridge outcomes of the relevant literature concerning mechanical and multi-physical property modulation of metamaterials focusing on the emerging trend of bi-level design, and subsequently highlight the broad-spectrum potential of mechanical metamaterials in their critical engineering applications. The evolving trends, challenges and future roadmaps have been critically analyzed here involving the notions of real-time reconfigurability and functionality programming, 4D printing, nano-scale metamaterials, artificial intelligence and machine learning, multi-physical origami/kirigami, living matter, soft and conformal metamaterials, manufacturing complex microstructures, service-life effects and scalability.

     

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  • [1]
    Abd El-Sayed F K, Jones R, Burgess I W. 1979. A theoretical approach to the deformation of honeycomb based composite materials. Composites, 10: 209-214. doi: 10.1016/0010-4361(79)90021-1
    [2]
    Adhikari S, Mukhopadhyay T, Liu X. 2021. Broadband dynamic elastic moduli of honeycomb lattice materials: A generalized analytical approach. Mechanics of Materials, 157: 103796. doi: 10.1016/j.mechmat.2021.103796
    [3]
    Adhikari S, Mukhopadhyay T, Shaw A, Lavery N P. 2020. Apparent negative values of Young’s moduli of lattice materials under dynamic conditions. International Journal of Engineering Science, 150: 103231. doi: 10.1016/j.ijengsci.2020.103231
    [4]
    Aghighi F, Morris J, Amirkhizi A V. 2019. Low-frequency micro-structured mechanical metamaterials. Mechanics of Materials, 130: 65-75. doi: 10.1016/j.mechmat.2018.12.008
    [5]
    Alderson A, Alderson K L, Chirima G, Ravirala N, Zied K M. 2010. The in-plane linear elastic constants and out-of-plane bending of 3-coordinated ligament and cylinder-ligament honeycombs. Composites Science and Technology, Special issue on Chiral Smart Honeycombs, 70: 1034-1041.
    [6]
    Al-Mulla T, Buehler M J. 2015. Folding creases through bending. Nature Mater., 14: 366-368. doi: 10.1038/nmat4258
    [7]
    Alturki M, Burgueño R. 2019. Multistable cosine-curved dome system for elastic energy dissipation. Journal of Applied Mechanics, 86 .
    [8]
    Alù A, Engheta N. 2008. Dielectric sensing in $ \mathrm{\epsilon } $ -near-zero narrow waveguide channels. Phys. Rev. B, 78: 1098-1121.
    [9]
    Ambati M, Fang N, Sun C, Zhang X. 2007. Surface resonant states and superlensing in acoustic metamaterials. Phys. Rev. B, 75: 195447. doi: 10.1103/PhysRevB.75.195447
    [10]
    Andrews E W, Gibson L J, Ashby M F. 1999. The creep of cellular solids. Acta Materialia, 47: 2853-2863. doi: 10.1016/S1359-6454(99)00150-0
    [11]
    Ashby M F. 2005. The properties of foams and lattices. Philosophical Transactions of the Royal Society A: Mathematical. Physical and Engineering Sciences, 364: 15-30.
    [12]
    Bacquet C L, Al Ba’ba’a H, Frazier M J, Nouh M, Hussein M I. 2018. Metadamping: Dissipation emergence in elastic metamaterials. Advances in Applied Mechanics, 51: 115-164.
    [13]
    Bakhvalov N, Panasenko G. 1989. Homogenisation: Averaging processes in periodic media: Mathematical problems in the mechanics of composite materials. Netherlands, 36 .
    [14]
    Balan P M, Mertens A J, Bahubalendruni M V A R. 2023. Auxetic mechanical metamaterials and their futuristic developments: A state-of-art review. Materials Today Communications, 34: 105285. doi: 10.1016/j.mtcomm.2022.105285
    [15]
    Banerjee A, Das R, Calius E P. 2017. Frequency graded 1d metamaterials: A study on the attenuation bands. Journal of Applied Physics, 122: 075101. doi: 10.1063/1.4998446
    [16]
    Bao Y, Hong G, Chen Y, Chen J, Chen H, Song W-L, Fang D. 2020. Customized kirigami electrodes for flexible and deformable lithium-ion batteries. ACS Appl. Mater. Interfaces, 12: 780-788. doi: 10.1021/acsami.9b18232
    [17]
    Bassik N, Abebe B T, Laflin K E, Gracias D H. 2010. Photolithographically patterned smart hydrogel based bilayer actuators. Polymer, 51: 6093-6098. doi: 10.1016/j.polymer.2010.10.035
    [18]
    Bauer J, Schroer A, Schwaiger R, Kraft O. 2016. Approaching theoretical strength in glassy carbon nanolattices. Nature Mater., 15: 438-443. doi: 10.1038/nmat4561
    [19]
    Benedetti M, du Plessis A, Ritchie R O, Dallago M, Razavi N, Berto F. 2021. Architected cellular materials: A review on their mechanical properties towards fatigue-tolerant design and fabrication. Materials Science and Engineering: R: Reports, 144: 100606. doi: 10.1016/j.mser.2021.100606
    [20]
    Bertoldi K, Vitelli V, Christensen J, van Hecke M. 2017. Flexible mechanical metamaterials. Nat. Rev. Mater., 2: 1-11.
    [21]
    Bessa M A, Glowacki P, Houlder M. 2019. Bayesian machine learning in metamaterial design: Fragile becomes supercompressible. Advanced Materials, 31: 1904845. doi: 10.1002/adma.201904845
    [22]
    Bigoni D, Guenneau S, Movchan A B, Brun M. 2013. Elastic metamaterials with inertial locally resonant structures: Application to lensing and localization. Phys. Rev. B, 87: 174303. doi: 10.1103/PhysRevB.87.174303
    [23]
    Blees M K, Barnard A W, Rose P A, Roberts S P, McGill K L, Huang P Y, Ruyack A R, Kevek J W, Kobrin B, Muller D A, McEuen P L. 2015. Graphene kirigami. Nature, 524: 204-207. doi: 10.1038/nature14588
    [24]
    Boatti E, Vasios N, Bertoldi K. 2017. Origami metamaterials for tunable thermal expansion. Advanced Materials, 29: 1700360. doi: 10.1002/adma.201700360
    [25]
    Boley J W, van Rees W M, Lissandrello C, Horenstein M N, Truby R L, Kotikian A, Lewis J A, Mahadevan L. 2019. Shape-shifting structured lattices via multimaterial 4D printing. Proceedings of the National Academy of Sciences, 116: 20856-20862. doi: 10.1073/pnas.1908806116
    [26]
    Brillouin L N. 1953. Wave propagation in periodic structures: Electric filters and crystal lattices. Dover Publications.
    [27]
    Brunet T, Merlin A, Mascaro B, Zimny K, Leng J, Poncelet O, Aristégui C, Mondain-Monval O. 2015. Soft 3D acoustic metamaterial with negative index. Nature Mater., 14: 384-388. doi: 10.1038/nmat4164
    [28]
    Bückmann T, Thiel M, Kadic M, Schittny R, Wegener M. 2014. An elasto-mechanical unfeelability cloak made of pentamode metamaterials. Nat. Commun., 5: 4130. doi: 10.1038/ncomms5130
    [29]
    Buckner T L, Bilodeau R A, Kim S Y, Kramer-Bottiglio R. 2020. Roboticizing fabric by integrating functional fibers. Proceedings of the National Academy of Sciences, 117: 25360-25369. doi: 10.1073/pnas.2006211117
    [30]
    Cai R, Jin Y, Rabczuk T, Zhuang X, Djafari-Rouhani B. 2021. Propagation and attenuation of rayleigh and pseudo surface waves in viscoelastic metamaterials. Journal of Applied Physics, 129: 124903. doi: 10.1063/5.0042577
    [31]
    Cai W, Chettiar V, Kildishev A, V Shalaev. 2007. Optical cloaking with metamaterials. Nature Photon, 1: 224-227. doi: 10.1038/nphoton.2007.28
    [32]
    Carrara M, Cacan M R, Leamy M J, Ruzzene M, Erturk A. 2012. Dramatic enhancement of structure-borne wave energy harvesting using an elliptical acoustic mirror. Applied Physics Letters, 100: 204105. doi: 10.1063/1.4719098
    [33]
    Carrara M, Cacan M R, Toussaint J, Leamy M J, Ruzzene M, Erturk A. 2013. Metamaterial-inspired structures and concepts for elastoacoustic wave energy harvesting. Smart Mater. Struct., 22: 065004. doi: 10.1088/0964-1726/22/6/065004
    [34]
    Chandra Y, Adhikari S, Mukherjee S, Mukhopadhyay T. 2022. Unfolding the mechanical properties of buckypaper composites: Nano-to-macro-scale coupled atomistic-continuum simulations. Engineering with Computers, 38: 5199-5229. doi: 10.1007/s00366-021-01538-w
    [35]
    Chandra Y, Mukhopadhyay T, Adhikari S, Figiel Ł. 2020. Size-dependent dynamic characteristics of graphene based multi-layer nano hetero-structures. Nanotechnology, 31: 145705. doi: 10.1088/1361-6528/ab6231
    [36]
    Chaurha A, Malaji P V, Mukhopadhyay T. 2022. Dual functionality of vibration attenuation and energy harvesting: Effect of gradation on non-linear multi-resonator metastructures. Eur. Phys. J. Spec. Top., 231: 1403-1413. doi: 10.1140/epjs/s11734-022-00506-9
    [37]
    Che K, Yuan C, Wu J, Jerry Qi H, Meaud J. 2016. Three-dimensional-printed multistable mechanical metamaterials with a deterministic deformation sequence. Journal of Applied Mechanics, 84 .
    [38]
    Chen B G, Upadhyaya N, Vitelli V. 2014. Nonlinear conduction via solitons in a topological mechanical insulator. Proceedings of the National Academy of Sciences, 111: 13004-13009. doi: 10.1073/pnas.1405969111
    [39]
    Chen C, Lu T J, Fleck N A. 1999. Effect of imperfections on the yielding of two-dimensional foams. Journal of the Mechanics and Physics of Solids, 47: 2235-2272. doi: 10.1016/S0022-5096(99)00030-7
    [40]
    Chen D, Zheng X. 2018. Multi-material additive manufacturing of metamaterials with giant, tailorable negative poisson’s ratios. Sci. Rep., 8: 9139. doi: 10.1038/s41598-018-26980-7
    [41]
    Chen J S, Su W J, Cheng Y, Li W C, Lin C Y. 2019. A metamaterial structure capable of wave attenuation and concurrent energy harvesting. Journal of Intelligent Material Systems and Structures, 30: 2973-2981. doi: 10.1177/1045389X19880023
    [42]
    Chen S, Cao Y, Sarparast M, Yuan H, Dong L, Tan X, Cao C. 2020. Soft crawling robots: Design, actuation, and locomotion. Advanced Materials Technologies, 5: 1900837. doi: 10.1002/admt.201900837
    [43]
    Chen Y, Ai B, Wong Z J. 2020. Soft optical metamaterials. Nano Convergence, 7: 1-17. doi: 10.1186/s40580-019-0212-3
    [44]
    Chen Y, Jin L. 2018. Geometric role in designing pneumatically actuated pattern-transforming metamaterials. Extreme Mechanics Letters, 23: 55-66. doi: 10.1016/j.eml.2018.08.001
    [45]
    Chen Y, Ma Y, Yin Q, Pan F, Cui C, Zhang Z, Liu B. 2021. Advances in mechanics of hierarchical composite materials. Composites Science and Technology, 214: 108970. doi: 10.1016/j.compscitech.2021.108970
    [46]
    Chen Y, Mai Y W, Ye L. 2023. Perspectives for multiphase mechanical metamaterials. Materials Science and Engineering: R: Reports, 153: 100725. doi: 10.1016/j.mser.2023.100725
    [47]
    Cheng Y C, Lu H C, Lee X, Zeng H, Priimagi A. 2020. Kirigami-based light-induced shape-morphing and locomotion. Advanced Materials, 32: 1906233. doi: 10.1002/adma.201906233
    [48]
    Cho Y, Shin J H, Costa A, Kim T A, Kunin V, Li J, Lee S Y, Yang S, Han H N, Choi I S, Srolovitz D J. 2014. Engineering the shape and structure of materials by fractal cut. Proceedings of the National Academy of Sciences, 111: 17390-17395. doi: 10.1073/pnas.1417276111
    [49]
    Choi G P T, Dudte L H, Mahadevan L. 2019. Programming shape using kirigami tessellations. Nat. Mater., 18: 999-1004. doi: 10.1038/s41563-019-0452-y
    [50]
    Claeys C, Pluymers B, Sas P, Desmet W. 2014. Design of a resonant metamaterial based acoustic enclosure. Proceedings of the 26th International Conference on Noise and Vibration Engineering, 325 .
    [51]
    Compton B G, Lewis J A. 2014. 3d-printing of lightweight cellular composites. Advanced materials, 26: 5930-5935. doi: 10.1002/adma.201401804
    [52]
    Cummer S A, Christensen J, Alù A. 2016. Controlling sound with acoustic metamaterials. Nat Rev Mater., 1: 1-13.
    [53]
    Cummer S A, Schurig D. 2007. One path to acoustic cloaking. New J. Phys., 9: 45. doi: 10.1088/1367-2630/9/3/045
    [54]
    Cundy H M, Rollett A P. 1961. Mathematical Models. Oxford University Press.
    [55]
    David R H Jones, Michael F Ashby. 2011. Engineering Materials 1: An Introduction to Properties, Application and Design. Elsevier, Oxford, United Kingdom.
    [56]
    de Bruijn N G. 1981. Algebraic theory of penrose’s non-periodic tilings of the plane, kon. Nederl. Akad. Wetensch. Proc, Ser, 84: 1-7. doi: 10.1016/1385-7258(81)90013-5
    [57]
    de Loos M, Feringa B L, van Esch J H. 2005. Design and application of self-assembled low molecular weight hydrogels. European Journal of Organic Chemistry, 17: 3615-3631.
    [58]
    de Moura B, Machado M R, Mukhopadhyay T, Dey S. 2022. Dynamic and wave propagation analysis of periodic smart beams coupled with resonant shunt circuits: Passive property modulation. Eur. Phys. J. Spec. Top., 231: 1415-1431. doi: 10.1140/epjs/s11734-022-00504-x
    [59]
    Del Vescovo D, Giorgio I. 2014. Dynamic problems for metamaterials: Review of existing models and ideas for further research. International Journal of Engineering Science, 80: 153-172. doi: 10.1016/j.ijengsci.2014.02.022
    [60]
    dell’Isola F, Steigmann D, Corte A D. 2016. Synthesis of fibrous complex structures: Designing microstructure to deliver targeted macroscale response. Applied Mechanics Reviews, 67: 060804.
    [61]
    Demaine E, O’Rourke J. 2007. Geometric folding algorithms: linkages, origami, polyhedra, Cambridge university press.
    [62]
    Deshpande V S, Ashby M F, Fleck N A. 2001. Foam topology: Bending versus stretching dominated architectures. Acta Materialia, 49: 1035-1040. doi: 10.1016/S1359-6454(00)00379-7
    [63]
    Dey S, Mukhopadhyay T, Adhikari S. 2018. Uncertainty quantification in laminated composites: A meta-model based approach. CRC Press.
    [64]
    Deymier P A. 2013. Acoustic metamaterials and phononic crystals. Springer science & Business media, 173 .
    [65]
    Dima A, Bhaskarla S, Becker C, Brady M, Campbell C, Dessauw P, Hanisch R, Kattner U, Kroenlein K, Newrock M, Peskin A, Plante R, Li S Y, Rigodiat P F, Amaral G S, Trautt Z, Schmitt X, Warren J, Youssef S. 2016. Informatics infrastructure for the materials genome initiative. JOM, 68: 2053-2064. doi: 10.1007/s11837-016-2000-4
    [66]
    Ding Z, Yuan C, Peng X, Wang T, Qi H J, Dunn M L. 2017. Direct 4d printing via active composite materials. Science Advances, 3: e1602890. doi: 10.1126/sciadv.1602890
    [67]
    Dudek K K, Gatt R, Dudek M R, Grima J N. 2018. Negative and positive stiffness in auxetic magneto-mechanical metamaterials. Proceedings of the Royal Society A: Mathematical. Physical and Engineering Sciences, 474: 20180003. doi: 10.1098/rspa.2018.0003
    [68]
    Dudek K K, Gatt R, Grima J N. 2020. 3D composite metamaterial with magnetic inclusions exhibiting negative stiffness and auxetic behaviour. Materials & Design, 187: 108403.
    [69]
    Dudek, K K, Martínez, J A I, Ulliac G, Kadic M. 2022. Micro-scale auxetic hierarchical mechanical metamaterials for shape morphing. Advanced Materials, 34: 2110115. doi: 10.1002/adma.202110115
    [70]
    Dudek K K, Wolak W, Gatt R, Grima J N. 2019. Impact resistance of composite magnetic metamaterials. Sci. Rep., 9: 1-9. doi: 10.1038/s41598-018-37186-2
    [71]
    Dudek M R, Dudek K K, Wolak W, Wojciechowski K W, Grima J N. 2019. Magnetocaloric materials with ultra-small magnetic nanoparticles working at room temperature. Sci. Rep., 9: 1-10. doi: 10.1038/s41598-018-37186-2
    [72]
    Dudte L H, Vouga E, Tachi T, Mahadevan L. 2016. Programming curvature using origami tessellations. Nature Mater., 15: 583-588. doi: 10.1038/nmat4540
    [73]
    Lockwood E H, MacMillan R H, Geometric Symmetry. cambridge university press, 1978.
    [74]
    Eidini M, Paulino G H. 2015. Unraveling metamaterial properties in zigzag-base folded sheets. Science Advances, 1: e1500224. doi: 10.1126/sciadv.1500224
    [75]
    El Helou C, Buskohl P R, Tabor C E, Harne R L. 2021. Digital logic gates in soft, conductive mechanical metamaterials. Nat. Commun., 12: 1-8. doi: 10.1038/s41467-020-20314-w
    [76]
    Evans A A, Silverberg J L, Santangelo C D. 2015. Lattice mechanics of origami tessellations. Phys. Rev. E, 92: 013205. doi: 10.1103/PhysRevE.92.013205
    [77]
    Evans K E, Alderson A. 2000. Auxetic materials: Functional materials and structures from lateral thinking! Advanced Materials, 12 : 617–628.
    [78]
    F Fahy, J Walker, Advanced Applications in Acoustics, Noise and Vibration. CRC Press, 2018.
    [79]
    Fan H, Yang L, Tian Y, Wang Z. 2020. Design of metastructures with quasi-zero dynamic stiffness for vibration isolation. Composite Structures, 243: 112244. doi: 10.1016/j.compstruct.2020.112244
    [80]
    Fan Y, Collet M, Ichchou M, Li L, Bareille O, Dimitrijevic Z. 2017. Enhanced wave and finite element method for wave propagation and forced response prediction in periodic piezoelectric structures. Chinese Journal of Aeronautics, 30: 75-87. doi: 10.1016/j.cja.2016.12.011
    [81]
    Fang H, Chu S C A, Xia Y, Wang K W. 2018. Programmable self-locking origami mechanical metamaterials. Advanced Materials, 30: 1706311. doi: 10.1002/adma.201706311
    [82]
    Fang H, Li S, Ji H, Wang K W. 2016. Uncovering the deformation mechanisms of origami metamaterials by introducing generic degree-four vertices. Phys. Rev. E, 94: 043002. doi: 10.1103/PhysRevE.94.043002
    [83]
    Fang N, Lee H, Sun C, Zhang X. 2005. Sub-diffraction-limited optical imaging with a silver superlens. Science, 308: 534-537. doi: 10.1126/science.1108759
    [84]
    Fang Z, Song H, Zhang Y, Jin B, Wu J, Zhao Q, Xie T. 2020. Modular 4d printing via interfacial welding of digital light-controllable dynamic covalent polymer networks. Matter., 2: 1187-1197. doi: 10.1016/j.matt.2020.01.014
    [85]
    Fathers R K, Gattas J M, You Z. 2015. Quasi-static crushing of eggbox, cube, and modified cube foldcore sandwich structures. International Journal of Mechanical Sciences, 101: 421-428.
    [86]
    Filipov E T, Tachi T, Paulino G H. 2015. Origami tubes assembled into stiff, yet reconfigurable structures and metamaterials. Proceedings of the National Academy of Sciences, 112: 12321-12326. doi: 10.1073/pnas.1509465112
    [87]
    Fleck N A, Deshpande V S, Ashby M F. 2010. Micro-architectured materials: Past, present and future. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 466: 2495-2516. doi: 10.1098/rspa.2010.0215
    [88]
    Florijn B, Coulais C, van Hecke M. 2014. Programmable mechanical metamaterials. Phys. Rev. Lett., 113: 175503. doi: 10.1103/PhysRevLett.113.175503
    [89]
    Frenzel T, Kadic M, Wegener M. 2017. Three-dimensional mechanical metamaterials with a twist. Science, 358: 1072-1074. doi: 10.1126/science.aao4640
    [90]
    Galea R, Dudek K K, Farrugia P S, Zammit Mangion L, Grima J N, Gatt R. 2022. Reconfigurable magneto-mechanical metamaterials guided by magnetic fields. Composite Structures, 280: 114921. doi: 10.1016/j.compstruct.2021.114921
    [91]
    Gao H, Ji B, Jäger I L, Arzt E, Fratzl P. 2003. Materials become insensitive to flaws at nanoscale: Lessons from nature. Proceedings of the National Academy of Sciences, 100: 5597-5600. doi: 10.1073/pnas.0631609100
    [92]
    Gardner D F, Evans J S, Smalyukh I I. 2011. Towards reconfigurable optical metamaterials: Colloidal nanoparticle self-assembly and self-alignment in liquid crystals. Molecular Crystals and Liquid Crystals, 545: 3-1227.
    [93]
    Gatt R, Grima J N. 2008. Negative compressibility. Physica Status Solidi, 2: 236-238.
    [94]
    Gatt R, Mizzi L, Azzopardi J I, Azzopardi K M, Attard D, Casha A, Briffa J, Grima J N. 2015. Hierarchical auxetic mechanical metamaterials. Sci. Rep., 5: 8395. doi: 10.1038/srep08395
    [95]
    Ge Q, Dunn C K, Qi H J, Dunn M L. 2014. Active origami by 4D printing. Smart Mater. Struct., 23: 094007. doi: 10.1088/0964-1726/23/9/094007
    [96]
    Ge Q, Qi H J, Dunn M L. 2013. Active materials by four-dimension printing. Applied Physics Letters, 103: 131901. doi: 10.1063/1.4819837
    [97]
    Ghuku S, Mukhopadhyay T. 2023. On enhancing mode-dependent failure strength under large deformation: The concept of anti-curvature in honeycomb lattices. Composite Structures, 305: 116318. doi: 10.1016/j.compstruct.2022.116318
    [98]
    Ghuku S, Mukhopadhyay T. 2022. Anti-curvature honeycomb lattices for mode-dependent enhancement of nonlinear elastic properties under large deformation. International Journal of Non-Linear Mechanics, 140: 103887. doi: 10.1016/j.ijnonlinmec.2021.103887
    [99]
    Gibson I J, Ashby M F. 1997. The mechanics of three-dimensional cellular materials. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 382: 43-59.
    [100]
    Gibson L J. 2012. The hierarchical structure and mechanics of plant materials. Journal of The Royal Society Interface, 9: 2749-2766. doi: 10.1098/rsif.2012.0341
    [101]
    Gibson L J, Ashby M F, Schajer G S, Robertson, C I. 1997. The mechanics of two-dimensional cellular materials. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 382: 25-42.
    [102]
    Giri T R, Mailen R. 2021. Controlled snapping sequence and energy absorption in multistable mechanical metamaterial cylinders. International Journal of Mechanical Sciences, 204: 106541. doi: 10.1016/j.ijmecsci.2021.106541
    [103]
    Gleeson H. 2020. Stretching the limits. Phys. World, 33: 36.
    [104]
    Goldsmith B R, Esterhuizen J, Liu J X, Bartel C J, Sutton C. 2018. Machine learning for heterogeneous catalyst design and discovery. AIChE Journal, 64: 2311-2323. doi: 10.1002/aic.16198
    [105]
    Gómez L R, Turner A M, van Hecke M, Vitelli V. 2012. Shocks near Jamming. Phys. Rev. Lett., 108: 058001. doi: 10.1103/PhysRevLett.108.058001
    [106]
    Greer J R, Deshpande V S. 2019. Three-dimensional architected materials and structures: Design, fabrication, and mechanical behavior. MRS Bulletin, 44: 750-757. doi: 10.1557/mrs.2019.232
    [107]
    Grima J N, Caruana-Gauci R, Dudek M R, Wojciechowski K W, Gatt, R. 2013. Smart metamaterials with tunable auxetic and other properties. Smart Mater. Struct., 22: 084016. doi: 10.1088/0964-1726/22/8/084016
    [108]
    Grimberg R. 2013. Electromagnetic metamaterials. Materials Science and Engineering, 178: 1285-1295. doi: 10.1016/j.mseb.2013.03.022
    [109]
    Grosskopf A K, Truby R L, Kim H, Perazzo A, Lewis J A, Stone H A. 2018. Viscoplastic matrix materials for embedded 3d printing. ACS Appl. Mater. Interfaces, 10: 23353-23361. doi: 10.1021/acsami.7b19818
    [110]
    Gu G X, Chen C T, Buehler M J. 2018a. De novo composite design based on machine learning algorithm. Extreme Mechanics Letters, 18: 19-28. doi: 10.1016/j.eml.2017.10.001
    [111]
    Gu G X, Chen C T, Richmond D J, Buehler M J. 2018b. Bioinspired hierarchical composite design using machine learning: Simulation, additive manufacturing, and experiment. Mater. Horiz., 5: 939-945. doi: 10.1039/C8MH00653A
    [112]
    Gu G X, Wettermark, S, Buehler, M J. 2017. Algorithm-driven design of fracture resistant composite materials realized through additive manufacturing. Additive Manufacturing, 17: 47-54. doi: 10.1016/j.addma.2017.07.002
    [113]
    Gu H, Boehler Q, Cui H, Secchi E, Savorana G, De Marco C, Gervasoni S, Peyron Q, Huang T Y, Pane S, Hirt A M, Ahmed D, Nelson B J. 2020. Magnetic cilia carpets with programmable metachronal waves. Nat. Commun., 11: 2637. doi: 10.1038/s41467-020-16458-4
    [114]
    Guenneau S, Movchan A, Pétursson G, Ramakrishna S A. 2007. Acoustic metamaterials for sound focusing and confinement. New J. Phys., 9: 399. doi: 10.1088/1367-2630/9/11/399
    [115]
    Guo K, Yang Z, Yu C H, Buehler M J. 2021. Artificial intelligence and machine learning in design of mechanical materials. Mater. Horiz., 8: 1153-1172. doi: 10.1039/D0MH01451F
    [116]
    Gupta K, Mukhopadhyay T, Roy L, Dey S. 2022. High-velocity ballistics of twisted bilayer graphene under stochastic disorder. Adv. Nano Res, 12: 529-547.
    [117]
    Gupta K K, Roy A, Mukhopadhyay T, Roy L, Dey S. 2022. Probing the stochastic fracture behavior of twisted bilayer graphene: Efficient ann based molecular dynamics simulations for complete probabilistic characterization. Materials Today Communications, 32: 103932. doi: 10.1016/j.mtcomm.2022.103932
    [118]
    Gupta S, Mukhopadhyay T, Kushvaha V. 2023. Microstructural image based convolutional neural networks for efficient prediction of full-field stress maps in short fiber polymer composites. Defence Technology, 24: 58-82. doi: 10.1016/j.dt.2022.09.008
    [119]
    Ha C S, Lakes R S, Plesha M E. 2018. Design, fabrication, and analysis of lattice exhibiting energy absorption via snap-through behavior. Materials & Design, 141: 426-437.
    [120]
    Hahn V, Kiefer P, Frenzel T, Qu J, Blasco E, Barner-Kowollik C, Wegener M. 2020. Rapid assembly of small materials building blocks (voxels) into large functional 3d metamaterials. Advanced Functional Materials, 30: 1907795. doi: 10.1002/adfm.201907795
    [121]
    Hao X P, Xu Z, Li C Y, Hong W, Zheng Q, Wu Z L. 2020. Kirigami-design-enabled hydrogel multimorphs with application as a multistate switch. Advanced Materials, 32: 2000781. doi: 10.1002/adma.202000781
    [122]
    He L, Wen Z, Jin Y, Torrent D, Zhuang X, Rabczuk T. 2021. Inverse design of topological metaplates for flexural waves with machine learning. Materials & Design, 199: 109390.
    [123]
    Hedayati R, Leeflang A M, Zadpoor A A. 2017. Additively manufactured metallic pentamode meta-materials. Applied Physics Letters, 110: 091905. doi: 10.1063/1.4977561
    [124]
    Helma C, Cramer T, Kramer S, De Raedt L. 2004. Data mining and machine learning techniques for the identification of mutagenicity inducing substructures and structure activity relationships of noncongeneric compounds. J. Chem. Inf. Comput. Sci, 44: 1402-1411. doi: 10.1021/ci034254q
    [125]
    Hewage T A M, Alderson K L, Alderson A, Scarpa F. 2016. Double-negative mechanical metamaterials displaying simultaneous negative stiffness and negative poisson’s ratio properties. Advanced Materials, 28: 10323-10332. doi: 10.1002/adma.201603959
    [126]
    Hu N, Burgueño R. 2015. Buckling-induced smart applications: Recent advances and trends. Smart Mater. Struct, 24: 063001. doi: 10.1088/0964-1726/24/6/063001
    [127]
    Hua J, Lei H, Gao C F, Guo X, Fang D. 2020. Parameters analysis and optimization of a typical multistable mechanical metamaterial. Extreme Mechanics Letters, 35: 100640. doi: 10.1016/j.eml.2020.100640
    [128]
    Huang C, Chen L. 2016. Negative poisson’s ratio in modern functional materials. Advanced Materials, 28: 8079-8096. doi: 10.1002/adma.201601363
    [129]
    Huang J, Zhang J, Xu D, Zhang S, Tong H, Xu N. 2023. From jammed solids to mechanical metamaterials : A brief review. Current Opinion in Solid State and Materials Science, 27: 101053. doi: 10.1016/j.cossms.2022.101053
    [130]
    Hussein M I. 2009. Reduced bloch mode expansion for periodic media band structure calculations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 465: 2825-2848. doi: 10.1098/rspa.2008.0471
    [131]
    Hussein M I, Frazier M J. 2013. Metadamping: An emergent phenomenon in dissipative metamaterials. Journal of Sound and Vibration, 332: 4767-4774. doi: 10.1016/j.jsv.2013.04.041
    [132]
    Hussein M I, Leamy M J, Ruzzene M. 2014. Dynamics of phononic materials and structures: Historical origins, recent progress, and future outlook. Applied Mechanics Reviews, 66 .
    [133]
    Imre A R. 2014. Metamaterials with negative compressibility—A novel concept with a long history. Mater. Sci. -Pol., 32: 126-129. doi: 10.2478/s13536-013-0179-4
    [134]
    Inman D J. 2017. Vibration with control. John Wiley & Sons.
    [135]
    Isanaka B R, Mukhopadhyay T, Varma R K, Kushvaha V. 2022. On exploiting machine learning for failure pattern driven strength enhancement of honeycomb lattices. Acta Materialia, 239: 118226. doi: 10.1016/j.actamat.2022.118226
    [136]
    Isobe M, Okumura K. 2016. Initial rigid response and softening transition of highly stretchable kirigami sheet materials. Sci. Rep., 6: 24758. doi: 10.1038/srep24758
    [137]
    Jackson J A, Messner M C, Dudukovic N A, Smith W L, Bekker L, Moran B, Golobic A M, Pascall A J, Duoss E B, Loh K J, Spadaccini C M. 2018. Field responsive mechanical metamaterials. Science Advances, 4: eaau6419. doi: 10.1126/sciadv.aau6419
    [138]
    Jacob Z, Alekseyev L V, Narimanov E. 2006. Optical hyperlens: Far-field imaging beyond the diffraction limit. Opt. Express, 14: 8247. doi: 10.1364/OE.14.008247
    [139]
    Jain A, Ong S P, Hautier G, Chen W, Richards W D, Dacek S, Cholia S, Gunter D, Skinner D, Ceder G, Persson K A. 2013. Commentary: The materials project: A materials genome approach to accelerating materials innovation. APL Materials, 1: 011002. doi: 10.1063/1.4812323
    [140]
    Jakšić Z, Jakšić O, Djurić Z, Kment C. 2007. A consideration of the use of metamaterials for sensing applications: Field fluctuations and ultimate performance. J. Opt. A: Pure Appl. Opt., 9: S377. doi: 10.1088/1464-4258/9/9/S16
    [141]
    Janbaz S, Bobbert F S L, Mirzaali M J, Zadpoor A A. 2019. Ultra-programmable buckling-driven soft cellular mechanisms. Mater. Horiz., 6: 1138-1147. doi: 10.1039/C9MH00125E
    [142]
    Janbaz S, Noordzij N, Widyaratih D S, Hagen C W, Fratila-Apachitei L E, Zadpoor A A. 2017. Origami lattices with free-form surface ornaments. Science Advances, 3: eaao1595. doi: 10.1126/sciadv.aao1595
    [143]
    Jang D, Greer J R. 2010. Transition from a strong-yet-brittle to a stronger-and-ductile state by size reduction of metallic glasses. Nature Mater., 9: 215-219. doi: 10.1038/nmat2622
    [144]
    Jena D P, Panigrahi S N, Kumar R. 2013. Gear fault identification and localization using analytic wavelet transform of vibration signal. Measurement, 46: 1115-1124. doi: 10.1016/j.measurement.2012.11.010
    [145]
    Jenett B, Cameron C, Tourlomousis F, Rubio A P, Ochalek M, Gershenfeld N. 2020. Discretely assembled mechanical metamaterials. Science Advances, 6: eabc9943. doi: 10.1126/sciadv.abc9943
    [146]
    Ji X, Deng L, Zhang J, Luan Y, Duan Y. 2022. Energy absorption characteristics of 3d lattice structure filled with periodic inner core based on 3d printing. J. of Materi Eng and Perform, 31: 6784-6794. doi: 10.1007/s11665-022-06692-w
    [147]
    Jia H, Gu S Y, Chang K. 2018. 3D printed self-expandable vascular stents from biodegradable shape memory polymer. Advances in Polymer Technology, 37: 3222-3228. doi: 10.1002/adv.22091
    [148]
    Jiang C, Rist F, Wang H, Wallner J, Pottmann H. 2022. Shape-morphing mechanical metamaterials. Computer-Aided Design, 143: 103146. doi: 10.1016/j.cad.2021.103146
    [149]
    Jikov V V, Kozlov S M, Oleinik O A. 1994. Homogenization of differential operators and integral functionals. Springer Science & Business Media.
    [150]
    Jin L, Forte A E, Deng B, Rafsanjani A, Bertoldi K. 2020. Kirigami-inspired inflatables with programmable shapes. Advanced Materials, 32: 2001863. doi: 10.1002/adma.202001863
    [151]
    Jin Y, He L, Wen Z, Mortazavi B, Hongwei G, Torrent D, Djafari-Rouhani B, Rabczuk T, Zhuang X, Li Y. 2022. Intelligent on-demand design of phononic metamaterials. Nanophotonics, 11: 439-460. doi: 10.1515/nanoph-2021-0639
    [152]
    Kadic M, Bückmann T, Stenger N, Thiel M, Wegener M. 2012. On the practicability of pentamode mechanical metamaterials. Applied Physics Letters, 100: 191901. doi: 10.1063/1.4709436
    [153]
    Kadic M, Milton G W, van Hecke M, Wegener M. 2019. 3d metamaterials. Nat Rev Phys, 1: 198-210. doi: 10.1038/s42254-018-0018-y
    [154]
    Kaur M, Yun T G, Han S M, Thomas E L, Kim W S. 2017. 3D printed stretching-dominated micro-trusses. Materials & Design, 134: 272-280.
    [155]
    Kim D, Ferretto I, Leinenbach C, Lee W. 2022. 3d and 4d printing of complex structures of Fe-mn-Si-based shape memory alloy using laser powder bed fusion. Advanced Materials Interfaces, 9: 2200171. doi: 10.1002/admi.202200171
    [156]
    Kim W, Byun J, Kim J K, Choi W Y, Jakobsen K, Jakobsen J, Lee D Y, Cho K J. 2019. Bioinspired dual-morphing stretchable origami. Science Robotics, 4: eaay3493. doi: 10.1126/scirobotics.aay3493
    [157]
    Kim Y, Parada G A, Liu S, Zhao X. 2019. Ferromagnetic soft continuum robots. Science Robotics, 4: eaax7329. doi: 10.1126/scirobotics.aax7329
    [158]
    Kim Y, Yuk H, Zhao R, Chester S A, Zhao X. 2018. Printing ferromagnetic domains for untethered fast-transforming soft materials. Nature, 558: 274-279. doi: 10.1038/s41586-018-0185-0
    [159]
    Kirklin S, Saal J E, Meredig B, Thompson A, Doak J W, Aykol M, Rühl S, Wolverton C. 2015. The open quantum materials database (oqmd): Assessing the accuracy of dft formation energies. npj Comput Mater., 1: 1-15.
    [160]
    Kokkinis D, Bouville F, Studart A R. 2018. 3d printing of materials with tunable failure via bioinspired mechanical gradients. Advanced Materials, 30: 1705808. doi: 10.1002/adma.201705808
    [161]
    Kokkinis D, Schaffner M, Studart A R. 2015. Multimaterial magnetically assisted 3d printing of composite materials. Nat. Commun., 6: 8643. doi: 10.1038/ncomms9643
    [162]
    Kozin V K, Shelykh I A, Nalitov A V, Iorsh I V. 2018. Topological metamaterials based on polariton rings. Phys. Rev. B, 98: 125115. doi: 10.1103/PhysRevB.98.125115
    [163]
    Krishnamoorthy H N S, Jacob Z, Narimanov E, Kretzschmar I, Menon V M. 2012. Topological transitions in metamaterials. Science, 336: 205-209. doi: 10.1126/science.1219171
    [164]
    Krödel S, Thomé N, Daraio C. 2015. Wide band-gap seismic metastructures. Extreme Mechanics Letters, 4: 111-117. doi: 10.1016/j.eml.2015.05.004
    [165]
    Kruk S S, Wong Z J, Pshenay-Severin E, O’Brien K, Neshev D N, Kivshar Y S, Zhang X. 2016. Magnetic hyperbolic optical metamaterials. Nat. Commun., 7: 11329. doi: 10.1038/ncomms11329
    [166]
    Kruth J P, Froyen L, Van Vaerenbergh J, Mercelis P, Rombouts M, Lauwers B. 2004. Selective laser melting of iron-based powder. Journal of Materials Processing Technology, 149: 616-622. doi: 10.1016/j.jmatprotec.2003.11.051
    [167]
    Kuang X, Roach D J, Wu J, Hamel C M, Ding Z, Wang T, Dunn M L, Qi H J. 2019a. Advances in 4d printing: Materials and applications. Advanced Functional Materials, 29: 1805290. doi: 10.1002/adfm.201805290
    [168]
    Kuang X, Wu J, Chen K, Zhao Z, Ding Z, Hu F, Fang D, Qi H J. 2019. Grayscale digital light processing 3D printing for highly functionally graded materials. Science Advances, 5: eaav5790. doi: 10.1126/sciadv.aav5790
    [169]
    Kundu D, Ghuku S, Naskar S, Mukhopadhyay T. 2023. Extreme specific stiffness through interactive cellular networks in bi-level micro-topology architected metamaterials. Advanced Engineering Materials, 25: 2201407. doi: 10.1002/adem.202201407
    [170]
    Kuribayashi K, Tsuchiya K, You Z, Tomus D, Umemoto M, Ito T, Sasaki M. 2006. Self-deployable origami stent grafts as a biomedical application of Ni-rich TiNi shape memory alloy foil. Materials Science and Engineering: A, 419: 131-137. doi: 10.1016/j.msea.2005.12.016
    [171]
    Lakes R. 1993. Advances in negative Poisson’s ratio materials. Advanced Materials, 5: 293-296. doi: 10.1002/adma.19930050416
    [172]
    Lakes R. 1987. Foam structures with a negative Poisson’s ratio. Science, 235: 1038-1040. doi: 10.1126/science.235.4792.1038
    [173]
    Lakes R, Wojciechowski K W. 2008. Negative compressibility, negative Poisson’s ratio, and stability. Physica Status Solidi, 245: 545-551. doi: 10.1002/pssb.200777708
    [174]
    Lakes R S, Lee T, Bersie A, Wang Y C. 2001. Extreme damping in composite materials with negative-stiffness inclusions. Nature, 410: 565-567. doi: 10.1038/35069035
    [175]
    Lamoureux A, Lee K, Shlian M, Forrest S R, Shtein M. 2015. Dynamic kirigami structures for integrated solar tracking. Nat. Commun., 6: 8092. doi: 10.1038/ncomms9092
    [176]
    Lang J P, Jiang W, Teng X C, Zhang X G, Han D, Hao J, Xu H H, Ni X H, Xie Y M, Qin Q H, Yang J, Ren X. 2023. Assembled mechanical metamaterials with transformable shape and auxeticity. Construction and Building Materials, 378: 131181. doi: 10.1016/j.conbuildmat.2023.131181
    [177]
    Lang R J. 2012. Origami design secrets: Mathematical methods for an ancient art. CRC Press.
    [178]
    Lee D Y, Kim J S, Kim S R, Koh J S, Cho K J. 2014. The deformable wheel robot using magic-ball origami structure. International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 55942.
    [179]
    Lee H J, Yook J G. 2008. Biosensing using split-ring resonators at microwave regime. Applied Physics Letters, 92: 254103. doi: 10.1063/1.2946656
    [180]
    Lee J H, Singer J P, Thomas E L. 2012. Micro-/nanostructured mechanical metamaterials. Advanced Materials, 24: 4782-4810. doi: 10.1002/adma.201201644
    [181]
    Lee N, Yoon B, Kim T, Bae J Y, Lim J S, Chang I, Cho H H. 2020. Multiple resonance metamaterial emitter for deception of infrared emission with enhanced energy dissipation. ACS Appl. Mater. Interfaces, 12: 8862-8869. doi: 10.1021/acsami.9b21030
    [182]
    Lee S H, Park C M, Seo Y M, Wang Z G, Kim C K. 2009a. Acoustic metamaterial with negative density. Physics Letters A, 373: 4464-4469. doi: 10.1016/j.physleta.2009.10.013
    [183]
    Lee S H, Park C M, Seo Y M, Wang Z G, Kim C K. 2009b. Acoustic metamaterial with negative modulus. J. Phys: Condens. Matter, 21: 175704. doi: 10.1088/0953-8984/21/17/175704
    [184]
    Lei M, Hamel C M, Yuan C, Lu H, Qi H J. 2018. 3d printed two-dimensional periodic structures with tailored in-plane dynamic responses and fracture behaviors. Composites Science and Technology, 159: 189-198. doi: 10.1016/j.compscitech.2018.02.024
    [185]
    Lei M, Hong W, Zhao Z, Hamel C, Chen M, Lu H, Qi H J. 2019. 3d printing of auxetic metamaterials with digitally reprogrammable shape. ACS Appl. Mater. Interfaces, 11: 22768-22776. doi: 10.1021/acsami.9b06081
    [186]
    Levine D J, Turner K T, Pikul J H. 2021. Materials with electroprogrammable stiffness. Advanced Materials, 33: 2007952. doi: 10.1002/adma.202007952
    [187]
    Li J, Chan C T. 2004. Double-negative acoustic metamaterial. Phys. Rev. E, 70: 055602. doi: 10.1103/PhysRevE.70.055602
    [188]
    Li K, Cheng X, Zhu F, Li L Z, Xie Z, Luan H, Wang Z, Ji Z, Wang H, Liu F, Xue Y, Jiang C, Feng X, Li L M, Rogers J A, Huang Y, Zhang Y. 2019. A generic soft encapsulation strategy for stretchable electronics. Advanced Functional Materials, 29: 1806630. doi: 10.1002/adfm.201806630
    [189]
    Li S, Stampfli J J, Xu H J, Malkin E, Diaz E V, Rus D, Wood R J. 2019. A vacuum-driven origami “magic-ball” soft gripper. 2019 International Conference on Robotics and Automation (ICRA), 7401–7408.
    [190]
    Li S, Wang K W. 2015. Fluidic origami: A plant-inspired adaptive structure with shape morphing and stiffness tuning. Smart Mater. Struct., 24: 105031. doi: 10.1088/0964-1726/24/10/105031
    [191]
    Li T, Wang J, Zhang L, Yang J, Yang M, Zhu D, Zhou X H, Handschuh-Wang S, Liu Y, Zhou X C. 2017. “Freezing”, morphing, and folding of stretchy tough hydrogels. J. Mater. Chem. B, 5: 5726-5732. doi: 10.1039/C7TB01265A
    [192]
    Li W, Matsuhisa N, Liu Z Y, Wang M, Luo Y, Cai P, Chen G, Zhang F, Li C, Liu Z H, Lv Z, Zhang W, Chen X. 2021. An on-demand plant-based actuator created using conformable electrodes. Nat. Electron., 4: 134-142. doi: 10.1038/s41928-020-00530-4
    [193]
    Libonati F, Buehler M J. 2017. Advanced structural materials by bioinspiration. Advanced Engineering Materials, 19: 1600787. doi: 10.1002/adem.201600787
    [194]
    Lier E, Shaw R K. 2008. Design and simulation of metamaterial-based hybrid-mode horn antennas. Electronics Letters, 44: 1444-1445. doi: 10.1049/el:20082639
    [195]
    Lier E, Werner D H, Scarborough C P, Wu Q, Bossard J A. 2011. An octave-bandwidth negligible-loss radiofrequency metamaterial. Nat. Mater., 10: 216-222. doi: 10.1038/nmat2950
    [196]
    Ligon S C, Liska R, Stampfl J, Gurr M, Mülhaupt R. 2017. Polymers for 3d printing and customized additive manufacturing. Chem. Rev., 117: 10212-10290. doi: 10.1021/acs.chemrev.7b00074
    [197]
    Lim T C. 2015. Auxetic materials and structures. Engineering Materials.
    [198]
    Liu J, Gu T, Shan S, Kang S H, Weaver J C, Bertoldi K. 2016. Harnessing buckling to design architected materials that exhibit effective negative swelling. Advanced Materials, 28: 6619-6624. doi: 10.1002/adma.201600812
    [199]
    Liu Q, Wang W, Reynolds M F, Cao M C, Miskin M Z, Arias T A, Muller D A, McEuen P L, Cohen I. 2021. Micrometer-sized electrically programmable shape-memory actuators for low-power microrobotics. Science Robotics, 6: eabe6663. doi: 10.1126/scirobotics.abe6663
    [200]
    Liu R, Yabansu Y C, Yang Z, Choudhary A N, Kalidindi S R, Agrawal A. 2017. Context aware machine learning approaches for modeling elastic localization in three-dimensional composite microstructures. Integr Mater Manuf Innov, 6: 160-171. doi: 10.1007/s40192-017-0094-3
    [201]
    Liu S, Azad A I, Burgueño R. 2019. Architected materials for tailorable shear behavior with energy dissipation. Extreme Mechanics Letters, 28: 1-7 doi: 10.1016/j.eml.2019.01.010
    [202]
    Liu X N, Hu G K, Huang G L, Sun C T. 2011. An elastic metamaterial with simultaneously negative mass density and bulk modulus. Applied Physics Letters, 98: 251907. doi: 10.1063/1.3597651
    [203]
    Liu Y, Shaw B, Dickey M D, Genzer J. 2017. Sequential self-folding of polymer sheets. Science Advances, 3: e1602417. doi: 10.1126/sciadv.1602417
    [204]
    Liu Y, Wang H, Ho J, Ng R C, Ng R J H, Hall-Chen V H, Koay E H H, Dong Z, Liu H, Qiu C W, Greer J R, Yang J K W. 2019. Structural color three-dimensional printing by shrinking photonic crystals. Nat. Commun., 10: 4340. doi: 10.1038/s41467-019-12360-w
    [205]
    Liu Z, Du H, Li J, Lu L, Li Z Y, Fang N X. 2018. Nano-kirigami with giant optical chirality. Science Advances, 4: eaat4436. doi: 10.1126/sciadv.aat4436
    [206]
    Liu Z, Zhang X, Mao Y, Zhu Y Y, Yang Z, Chan C T, Sheng P. 2000. Locally resonant sonic materials. Science, 289: 1734-1736. doi: 10.1126/science.289.5485.1734
    [207]
    Lorna J Gibson, Michael F Ashby. 1999. Cellular solids structure and properties. Cambridge University Press.
    [208]
    Lu M H, Feng L, Chen Y F. 2009. Phononic crystals and acoustic metamaterials. Materials Today, 12: 34-42.
    [209]
    Lum G Z, Ye Z, Dong X, Marvi H, Erin O, Hu W, Sitti M. 2016. Shape-programmable magnetic soft matter. Proceedings of the National Academy of Sciences, 113(41): E6007-E6015.
    [210]
    Luo C, Ning S, Liu Z, Zhuang Z. 2020. Interactive inverse design of layered phononic crystals based on reinforcement learning. Extreme Mechanics Letters, 36: 100651. doi: 10.1016/j.eml.2020.100651
    [211]
    Lv H, Tian X, Wang M Y, Li, D. 2013. Vibration energy harvesting using a phononic crystal with point defect states. Applied Physics Letters, 102: 034103. doi: 10.1063/1.4788810
    [212]
    Ma G, Yang M, Xiao S, Yang Z, Sheng P. 2014. Acoustic metasurface with hybrid resonances. Nat. Mater., 13: 873-878. doi: 10.1038/nmat3994
    [213]
    Ma H, Wang K, Zhao H, Shi W, Xue J, Zhou Y, Li Q, Wang G, Yan B. 2022. Energy dissipation and shock isolation using novel metamaterials. International Journal of Mechanical Sciences, 228: 107464. doi: 10.1016/j.ijmecsci.2022.107464
    [214]
    Ma H S, Prévost J H, Jullien R, Scherer G W. 2001. Computer simulation of mechanical structure–property relationship of aerogels. Journal of Non-Crystalline Solids, 285: 216-221. doi: 10.1016/S0022-3093(01)00456-2
    [215]
    Ma W, Cheng F, Liu Y. 2018. Deep-learning-enabled on-demand design of chiral metamaterials. ACS Nano, 12: 6326-6334. doi: 10.1021/acsnano.8b03569
    [216]
    Machado M R, Moura B B, Dey S, Mukhopadhyay T. 2022. Bandgap manipulation of single and multi-frequency smart metastructures with random impedance disorder. Smart Mater. Struct., 31: 105020. doi: 10.1088/1361-665X/ac8ef9
    [217]
    Mahata A, Mukhopadhyay T. 2018. Probing the chirality-dependent elastic properties and crack propagation behavior of single and bilayer stanene. Phys. Chem. Chem. Phys., 20: 22768-22782. doi: 10.1039/C8CP03892A
    [218]
    Malek S, Gibson L. 2015. Effective elastic properties of periodic hexagonal honeycombs. Mechanics of Materials, 91: 226-240. doi: 10.1016/j.mechmat.2015.07.008
    [219]
    Mao M, He J, Li X, Zhang B, Lei Q, Liu Y, Li D. 2017. The emerging frontiers and applications of high-resolution 3d printing. Micromachines, 8: 113. doi: 10.3390/mi8040113
    [220]
    Mao Y, He Q, Zhao X. 2020. Designing complex architectured materials with generative adversarial networks. Science Advances, 6: eaaz4169. doi: 10.1126/sciadv.aaz4169
    [221]
    Mead D M. 1996. Wave propagation in continuous periodic structures: Research contributions from southampton, 1964–1995. Journal of Sound and Vibration, 190: 495-524. doi: 10.1006/jsvi.1996.0076
    [222]
    Meeussen A S, Paulose J, Vitelli V. 2016. Geared topological metamaterials with tunable mechanical stability. Phys. Rev. X, 6: 041029.
    [223]
    Meza L R, Das S, Greer J R. 2014. Strong, lightweight, and recoverable three-dimensional ceramic nanolattices. Science, 345: 1322-1326. doi: 10.1126/science.1255908
    [224]
    Milton G W. 2015. New examples of three-dimensional dilational materials. Physica Status Solidi, 252: 1426-1430. doi: 10.1002/pssb.201552297
    [225]
    Milton G W, Cherkaev A V. 1995. Which elasticity tensors are realizable. Journal of Engineering Materials and Technology, 117: 483-493. doi: 10.1115/1.2804743
    [226]
    Mirzaali M J, Caracciolo A, Pahlavani H, Janbaz S, Vergani L, Zadpoor A A. 2018. Multi-material 3d printed mechanical metamaterials: rational design of elastic properties through spatial distribution of hard and soft phases. Applied Physics Letters, 113: 241903. doi: 10.1063/1.5064864
    [227]
    Mirzaali M J, Ghorbani A, Nakatani K, Nouri-Goushki M, Tümer N, Callens S J P, Janbaz S, Accardo A, Bico J, Habibi M, Zadpoor A A. 2021. Curvature induced by deflection in thick meta-plates. Advanced Materials, 33: 2008082. doi: 10.1002/adma.202008082
    [228]
    Mishin Y. 2021. Machine-learning interatomic potentials for materials science. Acta Materialia, 214: 116980. doi: 10.1016/j.actamat.2021.116980
    [229]
    Mishra A K, Wallin T J, Pan W, Xu A, Wang K, Giannelis E P, Mazzolai B, Shepherd R F. 2020. Autonomic perspiration in 3d-printed hydrogel actuators. Science Robotics, 5: eaaz3918. doi: 10.1126/scirobotics.aaz3918
    [230]
    Montgomery S M, Wu S, Kuang X, Armstrong C D, Zemelka C, Ze Q, Zhang R, Zhao R, Qi H J. 2021. Magneto-mechanical metamaterials with widely tunable mechanical properties and acoustic bandgaps. Advanced Functional Materials, 31: 2005319. doi: 10.1002/adfm.202005319
    [231]
    Mortazavi B, Zhuang X, Rabczuk T, Shapeev A V. 2023. Atomistic modeling of the mechanical properties: The rise of machine learning interatomic potentials. Mater. Horiz., 10: 1956-1968. doi: 10.1039/D3MH00125C
    [232]
    Moruzzi M C, Cinefra M, Bagassi S. 2021. Vibroacoustic analysis of an innovative windowless cabin with metamaterial trim panels in regional turboprops. Mechanics of Advanced Materials and Structures, 28: 1509-1521. doi: 10.1080/15376494.2019.1682729
    [233]
    Mousanezhad D, Haghpanah B, Ghosh R, Hamouda A M, Nayeb-Hashemi H, Vaziri A. 2016. Elastic properties of chiral, anti-chiral, and hierarchical honeycombs: A simple energy-based approach. Theoretical and Applied Mechanics Letters, 6: 81-96. doi: 10.1016/j.taml.2016.02.004
    [234]
    Mueller T, Hernandez A, Wang C. 2020. Machine learning for interatomic potential models. The Journal of Chemical Physics, 152: 050902. doi: 10.1063/1.5126336
    [235]
    Mukhopadhyay T, Adhikari S. 2017. Effective in-plane elastic moduli of quasi-random spatially irregular hexagonal lattices. International Journal of Engineering Science, 119: 142-179. doi: 10.1016/j.ijengsci.2017.06.004
    [236]
    Mukhopadhyay T, Adhikari S. 2017. Stochastic mechanics of metamaterials. Composite Structures, 162: 85-97. doi: 10.1016/j.compstruct.2016.11.080
    [237]
    Mukhopadhyay T, Adhikari S. 2016a. Effective in-plane elastic properties of auxetic honeycombs with spatial irregularity. Mechanics of Materials, 95: 204-222. doi: 10.1016/j.mechmat.2016.01.009
    [238]
    Mukhopadhyay T, Adhikari S. 2016b. Free-vibration analysis of sandwich panels with randomly irregular honeycomb core. Journal of Engineering Mechanics, 142: 06016008.
    [239]
    Mukhopadhyay T, Adhikari S. 2016c. Equivalent in-plane elastic properties of irregular honeycombs: An analytical approach. International Journal of Solids and Structures, 91: 169-184. doi: 10.1016/j.ijsolstr.2015.12.006
    [240]
    Mukhopadhyay T, Adhikari S, Alu A. 2019a. Probing the frequency-dependent elastic moduli of lattice materials. Acta Materialia, 165: 654-665. doi: 10.1016/j.actamat.2018.11.012
    [241]
    Mukhopadhyay T, Adhikari S, Alu A. 2019b. Theoretical limits for negative elastic moduli in subacoustic lattice materials. Phys. Rev. B, 99: 094108. doi: 10.1103/PhysRevB.99.094108
    [242]
    Mukhopadhyay T, Adhikari S, Batou A. 2019c. Frequency domain homogenization for the viscoelastic properties of spatially correlated quasi-periodic lattices. International Journal of Mechanical Sciences, 150: 784-806. doi: 10.1016/j.ijmecsci.2017.09.004
    [243]
    Mukhopadhyay T, Kundu D. 2022. Mixed-mode multidirectional Poisson’s ratio modulation in auxetic 3D lattice metamaterials. Advanced Engineering Materials, 24: 2101183. doi: 10.1002/adem.202101183
    [244]
    Mukhopadhyay Tanmoy, Ma J, Feng H, Hou D, Gattas J M, Chen Y, You Z. 2020. Programmable stiffness and shape modulation in origami materials: Emergence of a distant actuation feature. Applied Materials Today, 19: 100537. doi: 10.1016/j.apmt.2019.100537
    [245]
    Mukhopadhyay T, Mahata A, Adhikari S, Zaeem M A. 2018. Probing the shear modulus of two-dimensional multiplanar nanostructures and heterostructures. Nanoscale, 10: 5280-5294. doi: 10.1039/C7NR07261A
    [246]
    Mukhopadhyay T, Mahata A, Adhikari S, Zaeem M A. 2017. Effective elastic properties of two dimensional multiplanar hexagonal nanostructures. 2D Mater., 4: 025006. doi: 10.1088/2053-1583/aa551c
    [247]
    Mukhopadhyay T, Mahata A, Adhikari S, Zaeem M A. 2017. Effective mechanical properties of multilayer nano-heterostructures. Sci. Rep., 7: 15818. doi: 10.1038/s41598-017-15664-3
    [248]
    Mukhopadhyay T, Mahata A, Naskar S, Adhikari S. 2020. Probing the effective Young’s modulus of ‘magic angle’ inspired multi-functional twisted nano-heterostructures. Advanced Theory and Simulations, 3: 2000129. doi: 10.1002/adts.202000129
    [249]
    Mukhopadhyay T, Naskar S, Adhikari S. 2020b. Anisotropy tailoring in geometrically isotropic multi-material lattices. Extreme Mechanics Letters, 40: 100934. doi: 10.1016/j.eml.2020.100934
    [250]
    Mukhopadhyay T, Naskar S, Chakraborty S, Karsh P K, Choudhury R, Dey S. 2021. Stochastic oblique impact on composite laminates: A concise review and characterization of the essence of hybrid machine learning algorithms. Arch Computat Methods Eng, 28: 1731-1760. doi: 10.1007/s11831-020-09438-w
    [251]
    Münchinger A, Hsu L Y, Fürniß F, Blasco E, Wegener M. 2022. 3D optomechanical metamaterials. Materials Today, 59: 9-17. doi: 10.1016/j.mattod.2022.08.020
    [252]
    Nabian M A, Meidani H. 2018. Deep learning for accelerated seismic reliability analysis of transportation networks. Computer-Aided Civil and Infrastructure Engineering, 33: 443-458. doi: 10.1111/mice.12359
    [253]
    Narang Y S, Vlassak J J, Howe R D. 2018. Mechanically versatile soft machines through Laminar Jamming. Advanced Functional Materials, 28: 1707136. doi: 10.1002/adfm.201707136
    [254]
    Nash L M, Kleckner D, Read A, Vitelli V, Turner A M, Irvine W T M. 2015. Topological mechanics of gyroscopic metamaterials. Proceedings of the National Academy of Sciences, 112: 14495-14500. doi: 10.1073/pnas.1507413112
    [255]
    Neelakantan S, Bosbach W, Woodhouse J, Markaki A E. 2014. Characterization and deformation response of orthotropic fibre networks with auxetic out-of-plane behaviour. Acta Materialia, 66: 326-339. doi: 10.1016/j.actamat.2013.11.020
    [256]
    Ngo T D, Kashani A, Imbalzano G, Nguyen K T Q, Hui D. 2018. Additive manufacturing (3D printing): A review of materials, methods, applications and challenges. Composites Part B: Engineering, 143: 172-196. doi: 10.1016/j.compositesb.2018.02.012
    [257]
    Nguyen C, Zhuang X, Chamoin L, Zhao X, Nguyen-Xuan H, Rabczuk T. 2020. Three-dimensional topology optimization of auxetic metamaterial using isogeometric analysis and model order reduction. Computer Methods in Applied Mechanics and Engineering, 371: 113306. doi: 10.1016/j.cma.2020.113306
    [258]
    Nick Z H, Tabor C E, Harne R L. 2020. Liquid metal microchannels as digital sensors in mechanical metamaterials. Extreme Mechanics Letters, 40: 100871. doi: 10.1016/j.eml.2020.100871
    [259]
    Nicolaou Z G, Motter A E. 2012. Mechanical metamaterials with negative compressibility transitions. Nature Mater., 11: 608-613. doi: 10.1038/nmat3331
    [260]
    Ning X, Wang X, Zhang Y, Yu X, Choi D, Zheng N, Kim D S, Huang Y, Zhang Y H, Rogers, J A. 2018. Assembly of advanced materials into 3d functional structures by methods inspired by origami and kirigami: A review. Advanced Materials Interfaces, 5: 1800284. doi: 10.1002/admi.201800284
    [261]
    Nouh M, Aldraihem O, Baz A. 2014. Vibration characteristics of metamaterial beams with periodic local resonances. Journal of Vibration and Acoustics, 136 .
    [262]
    Novelino L S, Ze Q, Wu S, Paulino G H, Zhao R. 2020. Untethered control of functional origami microrobots with distributed actuation. Proceedings of the National Academy of Sciences, 117: 24096-24101. doi: 10.1073/pnas.2013292117
    [263]
    O’Brien K, Suchowski H, Rho J, Salandrino A, Kante B, Yin X, Zhang X. 2015. Predicting nonlinear properties of metamaterials from the linear response. Nat. Mater., 14: 379-383. doi: 10.1038/nmat4214
    [264]
    O’Connor H J, Dickson A N, Dowling D P. 2018. Evaluation of the mechanical performance of polymer parts fabricated using a production scale multi jet fusion printing process. Additive Manufacturing, 22: 381-387. doi: 10.1016/j.addma.2018.05.035
    [265]
    Oh J H, Seung H M, Kim Y Y. 2016. Adjoining of negative stiffness and negative density bands in an elastic metamaterial. Applied Physics Letters, 108: 093501. doi: 10.1063/1.4943095
    [266]
    Ongaro F. 2018. Estimation of the effective properties of two-dimensional cellular materials: A review. Theoretical and Applied Mechanics Letters, 8: 209-230. doi: 10.1016/j.taml.2018.04.010
    [267]
    Overvelde J T B, de Jong T A, Shevchenko Y, Becerra S A, Whitesides G M, Weaver J C, Hoberman C, Bertoldi K. 2016. A three-dimensional actuated origami-inspired transformable metamaterial with multiple degrees of freedom. Nat. Commun., 7: 1-8.
    [268]
    P Sinha, D Kundu, T Mukhopadhyay. 2023. Effective in-plane and out-of-plane elastic properties of 3d lattice materials with intrinsic stresses: an analytical approach. In press.
    [269]
    P Sinha, T Mukhopadhyay. 2023. Elastostatics of inflatable lattices: realization of extreme specific stiffness along with multi-functionality in active modulation and deployability. In press.
    [270]
    Pahlavani H, Amani M, Saldívar M C, Zhou J, Mirzaali M J, Zadpoor A A. 2022. Deep learning for the rare-event rational design of 3D printed multi-material mechanical metamaterials. Commun Mater., 3: 1-11. doi: 10.1038/s43246-021-00223-1
    [271]
    Palermo A, Marzani A. 2016. Extended bloch mode synthesis: Ultrafast method for the computation of complex band structures in phononic media. International Journal of Solids and Structures, 100: 29-40.
    [272]
    Palleau E, Morales D, Dickey M D, Velev O D. 2013. Reversible patterning and actuation of hydrogels by electrically assisted ionoprinting. Nat. Commun., 4: 2257. doi: 10.1038/ncomms3257
    [273]
    Pan Q, Chen S, Chen F, Zhu X. 2020. Programmable soft bending actuators with auxetic metamaterials. Sci. China Technol. Sci., 63: 2518-2526. doi: 10.1007/s11431-020-1741-2
    [274]
    Parthasarathy J, Starly B, Raman S, Christensen A. 2010. Mechanical evaluation of porous titanium (Ti6Al4V) structures with electron beam melting (EBM). Journal of the Mechanical Behavior of Biomedical Materials, 3: 249-259. doi: 10.1016/j.jmbbm.2009.10.006
    [275]
    Paulose J, Chen B G, Vitelli V. 2015. Topological modes bound to dislocations in mechanical metamaterials. Nature Phys, 11: 153-156. doi: 10.1038/nphys3185
    [276]
    Pendry J B. 2000. Negative refraction makes a perfect lens. Phys. Rev. Lett., 85: 3966-3969. doi: 10.1103/PhysRevLett.85.3966
    [277]
    Peng X, Li Y, Zhang Q, Shang C, Bai Q W, Wang H. 2016. Tough hydrogels with programmable and complex shape deformations by ion dip-dyeing and transfer printing. Advanced Functional Materials, 26: 4491-4500. doi: 10.1002/adfm.201601389
    [278]
    Poddubny A, Iorsh I, Belov P, Kivshar Y. 2013. Hyperbolic metamaterials. Nature Photon, 7: 948-957. doi: 10.1038/nphoton.2013.243
    [279]
    Podolskiy V A, Kuhta N A, Milton G W. 2005. Optimizing the superlens: Manipulating geometry to enhance the resolution. Applied Physics Letters, 87: 231113. doi: 10.1063/1.2139620
    [280]
    Prajwal P, Ghuku S, Mukhopadhyay T. 2022. Large-deformation mechanics of anti-curvature lattice materials for mode-dependent enhancement of non-linear shear modulus. Mechanics of Materials, 171: 104337. doi: 10.1016/j.mechmat.2022.104337
    [281]
    Prall D, Lakes R S. 1997. Properties of a chiral honeycomb with a Poisson’s ratio of −1. International Journal of Mechanical Sciences, 39: 305-314. doi: 10.1016/S0020-7403(96)00025-2
    [282]
    Pratapa P P, Suryanarayana P, Paulino G H. 2018. Bloch wave framework for structures with nonlocal interactions: Application to the design of origami acoustic metamaterials. Journal of the Mechanics and Physics of Solids, 118: 115-132. doi: 10.1016/j.jmps.2018.05.012
    [283]
    Qi S, Oudich M, Li Y, Assouar, B. 2016. Acoustic energy harvesting based on a planar acoustic metamaterial. Applied Physics Letters, 108: 263501. doi: 10.1063/1.4954987
    [284]
    Rafi H K, Karthik N V, Gong H, Starr T L, Stucker B E. 2013. Microstructures and mechanical properties of Ti6Al4V parts fabricated by selective laser melting and electron beam melting. J. of Materi Eng and Perform, 22: 3872-3883. doi: 10.1007/s11665-013-0658-0
    [285]
    Rafsanjani A, Bertoldi K. 2017. Buckling-induced kirigami. Phys. Rev. Lett., 118: 084301. doi: 10.1103/PhysRevLett.118.084301
    [286]
    Rafsanjani A, Jin L, Deng B, Bertoldi K. 2019. Propagation of pop ups in kirigami shells. Proceedings of the National Academy of Sciences, 116: 8200-8205. doi: 10.1073/pnas.1817763116
    [287]
    Raghunath G, Flatau A B. 2015. Study of magnetic domain evolution in an auxetic plane of Galfenol using kerr microscopy. Journal of Applied Physics, 117: 17E704. doi: 10.1063/1.4913727
    [288]
    Reid D R, Pashine N, Bowen A S, Nagel S R, Pablo J J de. 2019. Ideal isotropic auxetic networks from random networks. Soft Matter, 15: 8084-8091. doi: 10.1039/C9SM01241A
    [289]
    Ren Z, Hu W, Dong X, Sitti M. 2019. Multi-functional soft-bodied jellyfish-like swimming. Nat. Commun., 10: 2703. doi: 10.1038/s41467-019-10549-7
    [290]
    Roach D, Hamel C, Dunn C, Johnson M, Kuang X, Qi H. 2019. The m4 3d printer: A multi-material multi-method additive manufacturing platform for future 3d printed structures. Additive Manufacturing, 29: 100819. doi: 10.1016/j.addma.2019.100819
    [291]
    Robertson I D, Yourdkhani M, Centellas P J, Aw J E, Ivanoff D G, Goli E, Lloyd E M, Dean L M, Sottos N R, Geubelle P H, Moore J S, White S R. 2018. Rapid energy-efficient manufacturing of polymers and composites via frontal polymerization. Nature, 557: 223-227. doi: 10.1038/s41586-018-0054-x
    [292]
    Rogers J, Huang Y, Schmidt O G, Gracias D H. 2016. Origami mems and nems. MRS Bulletin, 41: 123-129. doi: 10.1557/mrs.2016.2
    [293]
    Rothemund P W K. 2006. Folding DNA to create nanoscale shapes and patterns. Nature, 440: 297-302. doi: 10.1038/nature04586
    [294]
    Rozvany G I N. 2009. A critical review of established methods of structural topology optimization. Struct Multidisc Optim, 37: 217-237. doi: 10.1007/s00158-007-0217-0
    [295]
    Scarpa F, Bullough W A, Lumley P. 2004. Trends in acoustic properties of iron particle seeded auxetic polyurethane foam. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 218: 241-244. doi: 10.1243/095440604322887099
    [296]
    Scarpa F, Panayiotou P, Tomlinson G. 2000. Numerical and experimental uniaxial loading on in-plane auxetic honeycombs. The Journal of Strain Analysis for Engineering Design, 35: 383-388. doi: 10.1243/0309324001514152
    [297]
    Scarpa F, Smith F C. 2004. Passive and mr fluid-coated auxetic pu foam–mechanical, acoustic, and electromagnetic properties. Journal of Intelligent Material Systems and Structures, 15: 973-979. doi: 10.1177/1045389X04046610
    [298]
    Schaedler T A, Carter W B. 2016. Architected cellular materials. Annual Review of Materials Research, 46: 187-210. doi: 10.1146/annurev-matsci-070115-031624
    [299]
    Schaedler T A, Jacobsen A J, Torrents A, Sorensen A E, Lian J, Greer J R, Valdevit L, Carter W B. 2011. Ultralight metallic microlattices. Science, 334: 962-965. doi: 10.1126/science.1211649
    [300]
    Schaeffer Marshall, Ruzzene M. 2015. Homogenization of 1d and 2d magnetoelastic lattices. EPJ Applied Metamaterials, 2: 13. doi: 10.1051/epjam/2015013
    [301]
    Schaeffer M, Ruzzene M. 2015. Wave propagation in multistable magneto-elastic lattices. International Journal of Solids and Structures, 56: 78-95.
    [302]
    Schenk M, Guest S D. 2013. Geometry of miura-folded metamaterials. Proceedings of the National Academy of Sciences, 110: 3276-3281. doi: 10.1073/pnas.1217998110
    [303]
    Schurig D, Mock J J, Justice B J, Cummer S A, Pendry J B, Starr A F, Smith D R. 2006. Metamaterial electromagnetic cloak at microwave frequencies. Science, 314: 977-980. doi: 10.1126/science.1133628
    [304]
    Serbin J, Ovsianikov A, Chichkov B. 2004. Fabrication of woodpile structures by two-photon polymerization and investigation of their optical properties. Opt. Express, 12: 5221-5228. doi: 10.1364/OPEX.12.005221
    [305]
    Shadrivov I V. 2010. Nonlinear metamaterials. Nonlinearities in Periodic Structures and Metamaterials, Springer, pp: 241-257.
    [306]
    Shalaev V M. 2007. Optical negative-index metamaterials. Nat. Photoics, 1: 41-48. doi: 10.1038/nphoton.2006.49
    [307]
    Shalaev V M, Cai W, Chettiar U K, Yuan H K, Sarychev A K, Drachev V P, Kildishev A V. 2005. Negative index of refraction in optical metamaterials. Opt. Lett, 30: 3356-3358. doi: 10.1364/OL.30.003356
    [308]
    Shan S, Kang S H, Raney J R, Wang P, Fang L, Candido F, Lewis J A, Bertoldi K. 2015. Multistable architected materials for trapping elastic strain energy. Advanced Materials, 27: 4296-4301. doi: 10.1002/adma.201501708
    [309]
    Sharma A, Mukhopadhyay T, Rangappa S M, Siengchin S, Kushvaha V. 2022. Advances in computational intelligence of polymer composite materials: Machine learning assisted modeling, analysis and design. Arch Computat Methods Eng, 29: 3341-3385. doi: 10.1007/s11831-021-09700-9
    [310]
    Shelby R A, Smith D R, Schultz S. 2001. Experimental verification of a negative index of refraction. Science, 292: 77-79. doi: 10.1126/science.1058847
    [311]
    Silva M J, Hayes W C, Gibson L J. 1995. The effects of non-periodic microstructure on the elastic properties of two-dimensional cellular solids. International Journal of Mechanical Sciences, 37: 1161-1177. doi: 10.1016/0020-7403(94)00018-F
    [312]
    Silverberg J L, Evans A A, McLeod L, Hayward R C, Hull T, Santangelo C D, Cohen I. 2014. Using origami design principles to fold reprogrammable mechanical metamaterials. Science, 345: 647-650. doi: 10.1126/science.1252876
    [313]
    Silverberg J L, Na J H, Evans A A, Liu B, Hull T C, Santangelo C D, Lang R J, Hayward R C, Cohen I. 2015. Origami structures with a critical transition to bistability arising from hidden degrees of freedom. Nat. Mater., 14: 389-393. doi: 10.1038/nmat4232
    [314]
    Singh A, Mukhopadhyay T, Adhikari S, Bhattacharya B. 2022a. Extreme on-demand contactless modulation of elastic properties in magnetostrictive lattices. Smart Mater. Struct., 31: 125005. doi: 10.1088/1361-665X/ac9cac
    [315]
    Singh A, Mukhopadhyay T, Adhikari S, Bhattacharya B. 2022b. Active multi-physical modulation of Poisson’s ratios in composite piezoelectric lattices: On-demand sign reversal. Composite Structures, 280: 114857. doi: 10.1016/j.compstruct.2021.114857
    [316]
    Singh A, Mukhopadhyay T, Adhikari S, Bhattacharya B. 2021. Voltage-dependent modulation of elastic moduli in lattice metamaterials: Emergence of a programmable state-transition capability. International Journal of Solids and Structures, 208: 31-48.
    [317]
    Singh K, Tipton C R, Han E, Mullin T. 2013. Magneto-elastic buckling of an Euler beam. Proc. R. Soc. A., 469: 20130111. doi: 10.1098/rspa.2013.0111
    [318]
    Sinha A, Mukhopadhyay T. 2022. Kirigami-inspired metamaterials for programming constitutive laws: Mixed-mode multidirectional auxeticity and contact-induced stiffness modulation. iScience, 25: 105656. doi: 10.1016/j.isci.2022.105656
    [319]
    Sinha P, Mukhopadhyay T. 2023. On-demand contactless programming of nonlinear elastic moduli in hard magnetic soft beam based broadband active lattice materials. Smart Mater. Struct., 32: 055021. doi: 10.1088/1361-665X/acc43b
    [320]
    Sinha P, Mukhopadhyay T. 2022. Effective elastic properties of lattice materials with intrinsic stresses. Thin-Walled Structures, 173: 108950. doi: 10.1016/j.tws.2022.108950
    [321]
    Sinha P, Walker M G, Mukhopadhyay T. 2023. Non-invariant elastic moduli of bi-level architected lattice materials through programmed domain discontinuity. Mechanics of Materials, 184: 104691. doi: 10.1016/j.mechmat.2023.104691
    [322]
    Slesarenko V. 2020. Planar mechanical metamaterials with embedded permanent magnets. Materials, 13: 1313. doi: 10.3390/ma13061313
    [323]
    Smith D R, Pendry J B, Wiltshire M C K. 2004. Metamaterials and negative refractive index. Science, 305: 788-792. doi: 10.1126/science.1096796
    [324]
    Song J, Gao L, Cao K, Zhang H, Xu S, Jiang C, Surjadi J U, Xu Y, Lu Y. 2018. Metal-coated hybrid meso-lattice composites and their mechanical characterizations. Composite Structures, 203: 750-763. doi: 10.1016/j.compstruct.2018.07.074
    [325]
    Song Z, Ma T, Tang R, Cheng Q, Wang X, Krishnaraju D, Panat R, Chan C K, Yu H, Jiang H. 2014. Origami lithium-ion batteries. Nat. Commun., 5: 3140. doi: 10.1038/ncomms4140
    [326]
    Soukoulis C M, Wegener M. 2010. Optical metamaterials—More bulky and less lossy. Science, 330: 1633-1634. doi: 10.1126/science.1198858
    [327]
    Spadoni A, Ruzzene M. 2007. Numerical and experimental analysis of the static compliance of chiral truss-core airfoils. Journal Of Mechanics Of Materials And Structures, 2: 965-981. doi: 10.2140/jomms.2007.2.965
    [328]
    Sugino C, Leadenham S, Ruzzene M, Erturk A. 2016. On the mechanism of bandgap formation in locally resonant finite elastic metamaterials. Journal of Applied Physics, 120: 134501. doi: 10.1063/1.4963648
    [329]
    Sundararaghavan V, Zabaras N. 2005. Classification and reconstruction of three-dimensional microstructures using support vector machines. Computational Materials Science, 32: 223-239. doi: 10.1016/j.commatsci.2004.07.004
    [330]
    Surjadi J U, Gao L, Du H, Li X, Xiong X, Fang N X, Lu Y. 2019. Mechanical metamaterials and their engineering applications. Advanced Engineering Materials, 21: 1800864. doi: 10.1002/adem.201800864
    [331]
    Sussman D M, Cho Y, Castle T, Gong X, Jung E, Yang S, Kamien R D. 2015. Algorithmic lattice kirigami: A route to pluripotent materials. Proceedings of the National Academy of Sciences, 112: 7449-7453. doi: 10.1073/pnas.1506048112
    [332]
    Tan X, Chen S, Wang B, Tang J, Wang L, Zhu S, Yao K, Xu P. 2020. Real-time tunable negative stiffness mechanical metamaterial. Extreme Mechanics Letters, 41: 100990. doi: 10.1016/j.eml.2020.100990
    [333]
    Tan X, Wang B, Zhu S, Chen S, Yao K, Xu P, Wu L, Sun Y. 2019. Novel multidirectional negative stiffness mechanical metamaterials. Smart Materials and Structures, 29 .
    [334]
    Tang Y, Li Y, Hong Y, Yang S, Yin J. 2019. Programmable active kirigami metasheets with more freedom of actuation. Proceedings of the National Academy of Sciences, 116: 26407-26413. doi: 10.1073/pnas.1906435116
    [335]
    Tao R, Ji L, Li Y, Wan Z, Hu W, Wu W, Liao B, Ma L, Fang D. 2020. 4D printed origami metamaterials with tunable compression twist behavior and stress-strain curves. Composites Part B: Engineering, 201: 108344. doi: 10.1016/j.compositesb.2020.108344
    [336]
    Tee Y L, Peng C, Pille P, Leary M, Tran P. 2020. Polyjet 3d printing of composite materials: Experimental and modelling approach. JOM, 72: 1105-1117. doi: 10.1007/s11837-020-04014-w
    [337]
    Thijs L, Verhaeghe F, Craeghs T, Humbeeck J V, Kruth J P. 2010. A study of the microstructural evolution during selective laser melting of Ti–6Al–4V. Acta Materialia, 58: 3303-3312. doi: 10.1016/j.actamat.2010.02.004
    [338]
    Thomson B K, William. 2010. Baltimore lectures on molecular dynamics and the wave theory of light, cambridge library collection-physical sciences. Cambridge University Press, Cambridge.
    [339]
    Tian Y, Shen Y. 2020. Selective guided wave mode transmission enabled by elastic metamaterials. Journal of Sound and Vibration, 485: 115566. doi: 10.1016/j.jsv.2020.115566
    [340]
    Tipton C R, Han E, Mullin T. 2012. Magneto-elastic buckling of a soft cellular solid. Soft Matter, 8: 6880-6883. doi: 10.1039/c2sm25965f
    [341]
    Tiwari P, Naskar S, Mukhopadhyay T. 2023. Programmed out-of-plane curvature to enhance multimodal stiffness of bending-dominated composite lattices. AIAA Journal, 61: 1820-1838. doi: 10.2514/1.J062573
    [342]
    Vaishali Mukhopadhyay T, Naskar S, Dey S. 2023. On machine learning assisted data-driven bridging of fsdt and hozt for high-fidelity uncertainty quantification of laminated composite and sandwich plates. Composite Structures, 304: 116276. doi: 10.1016/j.compstruct.2022.116276
    [343]
    Valentine J, Zhang S, Zentgraf T, Ulin-Avila E, Genov D A, Bartal G, Zhang X. 2008. Three-dimensional optical metamaterial with a negative refractive index. Nature, 455: 376-379. doi: 10.1038/nature07247
    [344]
    Valipour A, Kargozarfard M H, Rakhshi M, Yaghootian A, Sedighi H M. 2022. Metamaterials and their applications: An overview. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 236: 2171-2210. doi: 10.1177/1464420721995858
    [345]
    van Manen T, Janbaz S, Ganjian M, Zadpoor A A. 2020. Kirigami-enabled self-folding origami. Materials Today, 32: 59-67. doi: 10.1016/j.mattod.2019.08.001
    [346]
    Vangelatos Z, Gu G X, Grigoropoulos C P. 2019. Architected metamaterials with tailored 3d buckling mechanisms at the microscale. Extreme Mechanics Letters, 33: 100580. doi: 10.1016/j.eml.2019.100580
    [347]
    Vyatskikh A, Delalande S, Kudo A, Zhang X, Portela C M, Greer J R. 2018. Additive manufacturing of 3D nano-architected metals. Nat. Commun., 9: 593. doi: 10.1038/s41467-018-03071-9
    [348]
    Waheed U, Myant C W, Dobson S N. 2020. Boolean and/or mechanical logic using multi-plane mechanical metamaterials. Extreme Mechanics Letters, 40: 100865. doi: 10.1016/j.eml.2020.100865
    [349]
    Waitukaitis S, Menaut R, Chen B G, van Hecke M. 2015. Origami multistability: From single vertices to metasheets. Phys. Rev. Lett., 114: 055503. doi: 10.1103/PhysRevLett.114.055503
    [350]
    Wang A J, McDowell D L. 2003. Effects of defects on in-plane properties of periodic metal honeycombs. International Journal of Mechanical Sciences, 45: 1799-1813. doi: 10.1016/j.ijmecsci.2003.12.007
    [351]
    Wang C, Tan X P, Tor S B, Lim C S. 2020. Machine learning in additive manufacturing: State-of-the-art and perspectives. Additive Manufacturing, 36: 101538. doi: 10.1016/j.addma.2020.101538
    [352]
    Wang H, Zhao D, Jin Y, Wang M, Mukhopadhyay T, You Z. 2020. Modulation of multi-directional auxeticity in hybrid origami metamaterials. Applied Materials Today, 20: 100715. doi: 10.1016/j.apmt.2020.100715
    [353]
    Wang L C, Song W L, Zhang Y J, Qu M J, Zhao Z, Chen M, Yang Y, Chen H, Fang D. 2020. Active reconfigurable tristable square-twist origami. Advanced Functional Materials, 30: 1909087. doi: 10.1002/adfm.201909087
    [354]
    Wang P, Shim J, Bertoldi K. 2013. Effects of geometric and material nonlinearities on tunable band gaps and low-frequency directionality of phononic crystals. Phys. Rev. B, 88: 014304. doi: 10.1103/PhysRevB.88.014304
    [355]
    Wang S, Shen Z A, Shen Z Y, Dong Y, Li Y, Cao Y, Zhang Y, Guo S, Shuai J, Yang Y, Lin C, Chen X, Zhang X, Huang Q. 2021. Machine-learning micropattern manufacturing. Nano Today, 38: 101152. doi: 10.1016/j.nantod.2021.101152
    [356]
    Wang W, Lu H, Liu Y, Leng J. 2014. Sodium dodecyl sulfate/epoxy composite: Water-induced shape memory effect and its mechanism. J. Mater. Chem. A, 2: 5441-5449. doi: 10.1039/c3ta15204a
    [357]
    Wang X Q, Chan K H, Cheng Y, Ding T, Li T, Achavananthadith S, Ahmet S, Ho J S, Ho G W. 2020. Somatosensory, light-driven, thin-film robots capable of integrated perception and motility. Advanced Materials, 32: 2000351. doi: 10.1002/adma.202000351
    [358]
    Wang Z, Li K, He Q, Cai S. 2019. A light-powered ultralight tensegrity robot with high deformability and load capacity. Advanced Materials, 31: 1806849. doi: 10.1002/adma.201806849
    [359]
    Wang Z J, Zhu C N, Hong W, Wu Z L, Zheng Q. 2017. Cooperative deformations of periodically patterned hydrogels. Science Advances, 3: e1700348. doi: 10.1126/sciadv.1700348
    [360]
    Ward L, Agrawal A, Choudhary A, Wolverton C. 2016. A general-purpose machine learning framework for predicting properties of inorganic materials. npj Comput Mater., 2: 1-7. doi: 10.1038/s41524-016-0001-z
    [361]
    Wei Y L, Yang Q S, Ma L H, Tao R, Shang J J. 2020. Design and analysis of 2d/3d negative hydration expansion metamaterial driven by hydrogel. Materials & Design, 196: 109084.
    [362]
    Wilt J K, Yang C, Gu G X. 2020. Accelerating auxetic metamaterial design with deep learning. Advanced Engineering Materials, 22: 2070018. doi: 10.1002/adem.202070018
    [363]
    Wu L, Liu L, Wang Y, Zhai Z, Zhuang H, Krishnaraju D, Wang Q, Jiang H. 2020. A machine learning-based method to design modular metamaterials. Extreme Mechanics Letters, 36: 100657. doi: 10.1016/j.eml.2020.100657
    [364]
    Wu R, Roberts P C E, Lyu S, Zheng F, Soutis C, Diver C, Zhou D, Li L, Deng Z. 2021. Lightweight self-forming super-elastic mechanical metamaterials with adaptive stiffness. Advanced Functional Materials, 31: 2008252. doi: 10.1002/adfm.202008252
    [365]
    Wu W, Tao Y, Xia Y, Chen J, Lei H, Sun L, Fang D. 2017. Mechanical properties of hierarchical anti-tetrachiral metastructures. Extreme Mechanics Letters, 16: 18-32. doi: 10.1016/j.eml.2017.08.004
    [366]
    Wu X, Jin Y, Khelif A, Zhuang X, Rabczuk T, Djafari-Rouhani B. 2022. Topological surface wave metamaterials for robust vibration attenuation and energy harvesting. Mechanics of Advanced Materials and Structures, 29: 4759-4767. doi: 10.1080/15376494.2021.1937758
    [367]
    Wyart M, Liang H, Kabla A, Mahadevan L. 2008. Elasticity of floppy and stiff random networks. Phys. Rev. Lett., 101: 215501. doi: 10.1103/PhysRevLett.101.215501
    [368]
    Xia X, Afshar A, Yang H, Portela C M, Kochmann D M, Di Leo C V, Greer J R. 2019. Electrochemically reconfigurable architected materials. Nature, 573: 205-213. doi: 10.1038/s41586-019-1538-z
    [369]
    Xia X, Spadaccini C M, Greer J R. 2022. Responsive materials architected in space and time. Nat. Rev. Mater., 7: 683-701. doi: 10.1038/s41578-022-00450-z
    [370]
    Xiang X M, Lu G, You Z. 2020. Energy absorption of origami inspired structures and materials. Thin-Walled Structures, 157: 107130. doi: 10.1016/j.tws.2020.107130
    [371]
    Xin X, Liu L, Liu Y, Leng J. 2020. Origami-inspired self-deployment 4d printed honeycomb sandwich structure with large shape transformation. Smart Mater. Struct., 29: 065015. doi: 10.1088/1361-665X/ab85a4
    [372]
    Xu C, Quinn B, L’Espérance G, Lebel L, Daniel T. 2019. Multi-material direct ink writing (DIW) for complex 3d metallic structures with removable supports. ACS Applied Materials & Interfaces, 11: 8499-8506.
    [373]
    Xu L, Wang X, Kim Y, Shyu T C, Lyu J, Kotov N A. 2016. Kirigami nanocomposites as wide-angle diffraction gratings. Acs Nano, 10: 6156-6162. doi: 10.1021/acsnano.6b02096
    [374]
    Yang C, Boorugu M, Dopp A, Ren J, Martin R, Han D, Choi W, Lee H. 2019. 4d printing reconfigurable, deployable and mechanically tunable metamaterials. Mater. Horiz., 6: 1244-1250. doi: 10.1039/C9MH00302A
    [375]
    Yang H, D’Ambrosio N, Liu P, Pasini D, Ma L. 2023. Shape memory mechanical metamaterials. Materials Today, 66: 36-49. doi: 10.1016/j.mattod.2023.04.003
    [376]
    Yang H, Ma L. 2020. 1d to 3d multi-stable architected materials with zero Poisson’s ratio and controllable thermal expansion. Materials & Design, 188: 108430.
    [377]
    Yang H, Ma L. 2019. Multi-stable mechanical metamaterials by elastic buckling instability. J Mater Sci, 54: 3509-3526. doi: 10.1007/s10853-018-3065-y
    [378]
    Yang L, Harrysson O, Cormier D, West H, Gong H, Stucker B. 2015. Additive manufacturing of metal cellular structures: Design and fabrication. JOM, 67: 608-615. doi: 10.1007/s11837-015-1322-y
    [379]
    Yang Y, You Z. 2020. A Modular Origami-inspired Mechanical Metamaterial.
    [380]
    Yao J, Sun R, Scarpa F, Remillat C, Gao Y, Su Y. 2021. Two-dimensional graded metamaterials with auxetic rectangular perforations. Composite Structures, 261: 113313. doi: 10.1016/j.compstruct.2020.113313
    [381]
    Yu K, Du H, Xin A, Lee K H, Feng Z, Masri S F, Chen Y, Huang G, Wang Q. 2020. Healable, memorizable, and transformable lattice structures made of stiff polymers. NPG Asia Mater., 12: 1-16. doi: 10.1038/s41427-019-0187-x
    [382]
    Yu X, Zhou J, Liang H, Jiang Z, Wu L. 2018. Mechanical metamaterials associated with stiffness, rigidity and compressibility: A brief review. Progress in Materials Science, 94: 114-173. doi: 10.1016/j.pmatsci.2017.12.003
    [383]
    Zadpoor A A. 2016. Mechanical meta-materials. Mater. Horiz., 3: 371-381. doi: 10.1039/C6MH00065G
    [384]
    Zeng C, Liu L, Bian W, Leng J, Liu Y. 2022. Temperature-dependent mechanical response of 4d printed composite lattice structures reinforced by continuous fiber. Composite Structures, 280: 114952. doi: 10.1016/j.compstruct.2021.114952
    [385]
    Zeng H, Wani O M, Wasylczyk P, Priimagi A. 2018. Light-driven, caterpillar-inspired miniature inching robot. Macromolecular Rapid Communications, 39: 1700224. doi: 10.1002/marc.201700224
    [386]
    Zhai Z, Wang Y, Jiang H. 2018. Origami-inspired, on-demand deployable and collapsible mechanical metamaterials with tunable stiffness. Proceedings of the National Academy of Sciences, 115: 2032-2037. doi: 10.1073/pnas.1720171115
    [387]
    Zhai Z, Wang Y, Lin K, Wu L, Jiang H. 2020. In situ stiffness manipulation using elegant curved origami. Science Advances, 6: eabe2000. doi: 10.1126/sciadv.abe2000
    [388]
    Zhai Z, Wu L, Jiang H. 2021. Mechanical metamaterials based on origami and kirigami. Applied Physics Reviews, 8: 041319. doi: 10.1063/5.0051088
    [389]
    Zhang J, Ashby M F. 1992. The out-of-plane properties of honeycombs. International Journal of Mechanical Sciences, 34: 475-489. doi: 10.1016/0020-7403(92)90013-7
    [390]
    Zhang J, Lu G, You Z. 2020. Large deformation and energy absorption of additively manufactured auxetic materials and structures: A review. Composites Part B: Engineering, 201: 108340. doi: 10.1016/j.compositesb.2020.108340
    [391]
    Zhang K, Chermprayong P, Xiao F, Tzoumanikas D, Dams B, Kay S, Kocer B B, Burns A, Orr L, Choi C, Darekar D D, Li W, Hirschmann S, Soana V, Ngah S A, Sareh S, Choubey A, Margheri L, Pawar V M, Ball R J, Williams C, Shepherd P, Leutenegger S, Stuart-Smith R, Kovac M. 2022. Aerial additive manufacturing with multiple autonomous robots. Nature, 609: 709-717. doi: 10.1038/s41586-022-04988-4
    [392]
    Zhang Q, Barri K, Jiao P, Lu W, Luo J, Meng W, Wang J, Hong L, Mueller J, Lin Wang Z, Alavi A H. 2023. Meta-mechanotronics for self-powered computation. Materials Today, 65: 78-89. doi: 10.1016/j.mattod.2023.03.026
    [393]
    Zhang Q, Kuang X, Weng S, Zhao Z, Chen H, Fang D, Qi H J. 2020. Rapid volatilization induced mechanically robust shape-morphing structures toward 4d printing. ACS Appl. Mater. Interfaces, 12: 17979-17987. doi: 10.1021/acsami.0c02038
    [394]
    Zhang Q, Wommer J, O’Rourke C, Teitelman J, Tang Y, Robison J, Lin G, Yin J. 2017. Origami and kirigami inspired self-folding for programming three-dimensional shape shifting of polymer sheets with light. Extreme Mechanics Letters, 11: 111-120. doi: 10.1016/j.eml.2016.08.004
    [395]
    Zhang S, Yin L, Fang N. 2009. Focusing ultrasound with an acoustic metamaterial network. Phys. Rev. Lett., 102: 194301. doi: 10.1103/PhysRevLett.102.194301
    [396]
    Zhang X, Liu Z. 2008. Superlenses to overcome the diffraction limit. Nature Mater., 7: 435-441. doi: 10.1038/nmat2141
    [397]
    Zhang Y, Wang Q, Tichem M, van Keulen F. 2020. Design and characterization of multi-stable mechanical metastructures with level and tilted stable configurations. Extreme Mechanics Letters, 34: 100593. doi: 10.1016/j.eml.2019.100593
    [398]
    Zhang Y, Yan Z, Nan K, Xiao D, Liu Y, Luan H, Fu H, Wang X, Yang Q, Wang J C, Ren W, Si H, Liu F, Yang L, Li H, Wang J T, Guo X, Luo H, Wang L, Huang Y, Rogers J A. 2015. A mechanically driven form of kirigami as a route to 3d mesostructures in micro/nanomembranes. Proceedings of the National Academy of Sciences, 112: 11757-11764. doi: 10.1073/pnas.1515602112
    [399]
    Zhang Z, Dou J, He J, Xiao C, Shen L, Yang J, Wang Y, Zhou Z. 2017. Electrically/infrared actuated shape memory composites based on a bio-based polyester blend and graphene nanoplatelets and their excellent self-driven ability. J. Mater. Chem. C, 5: 4145-4158. doi: 10.1039/C7TC00828G
    [400]
    Zhang Z, Krushynska A O. 2022. Programmable shape morphing of rose mechanical metamaterials. APL Mater., 10: 080701. doi: 10.1063/5.0099323
    [401]
    Zhang Z, Scarpa F, Bednarcyk B A, Chen Y. 2021. Harnessing fractal cuts to design robust lattice metamaterials for energy dissipation. Additive Manufacturing, 46: 102126. doi: 10.1016/j.addma.2021.102126
    [402]
    Zhao Z, Wu J, Mu X, Chen H, Qi H J, Fang D. 2017. Origami by frontal photopolymerization. Science Advances, 3: e1602326. doi: 10.1126/sciadv.1602326
    [403]
    Zheng X, Lee H, Weisgraber T H, Shusteff M, DeOtte J, Duoss E B, Kuntz J D, Biener M M, Ge Q, Jackson J A, Kucheyev S O, Fang N X, Spadaccini C M. 2014. Ultralight, ultrastiff mechanical metamaterials. Science, 344: 1373-1377. doi: 10.1126/science.1252291
    [404]
    Zhong H, Song T, Li C, Das R, Gu J, Qian M. 2023. The gibson-ashby model for additively manufactured metal lattice materials: Its theoretical basis, limitations and new insights from remedies. Current Opinion in Solid State and Materials Science, 27: 101081. doi: 10.1016/j.cossms.2023.101081
    [405]
    Zhou X H, Li T, Wang J, Chen F, Zhou D, Liu Q, Li B, Cheng J, Zhou X C, Zheng B. 2018. Mechanochemical regulated origami with tough hydrogels by ion transfer printing. ACS Appl. Mater. Interfaces, 10: 9077-9084. doi: 10.1021/acsami.8b01610
    [406]
    Zhu H X, Hobdell J R, Windle A H. 2001. Effects of cell irregularity on the elastic properties of 2d voronoi honeycombs. Journal of the Mechanics and Physics of Solids, 49: 857-870. doi: 10.1016/S0022-5096(00)00046-6
    [407]
    Zhu R, Huang G L, Huang H H, Sun C T. 2011. Experimental and numerical study of guided wave propagation in a thin metamaterial plate. Physics Letters A, 375: 2863-2867. doi: 10.1016/j.physleta.2011.06.006
    [408]
    Zhu S, Wang B, Tan X, Hu J, Wang L, Zhou Z, Chen S. 2021. A novel bi-material negative stiffness metamaterial in sleeve-type via combining rigidity with softness. Composite Structures, 262: 113381. doi: 10.1016/j.compstruct.2020.113381
    [409]
    Zhu Y, Birla M, Oldham K R, Filipov E T. 2020. Elastically and plastically foldable electrothermal micro-origami for controllable and rapid shape morphing. Advanced Functional Materials, 30: 2003741. doi: 10.1002/adfm.202003741
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