The Tessellation Rule and Properties Programming of Origami Metasheets Built with a Mixture of Rigid and Non-Rigid Square-Twist Patterns

Bertoldi, 2017, Flexible mechanical metamaterials, Nat Rev Mater, 2, 17066, 10.1038/natrevmats.2017.66 Kadic, 2019, 3D metamaterials, Nat Rev Phys, 1, 198, 10.1038/s42254-018-0018-y Liu, 2015, Metamaterials: reshape and rethink, Engineering, 1, 179, 10.15302/J-ENG-2015036 Zhang, 2008, One-step nanoscale assembly of complex structures via harnessing of an elastic instability, Nano Lett, 8, 1192, 10.1021/nl0801531 Matsumoto, 2009, Elastic-instability triggered pattern formation, Phys Rev E, 80, 021604, 10.1103/PhysRevE.80.021604 Bertoldi, 2010, Negative Poisson’s ratio behavior induced by an elastic instability, Adv Mater, 22, 361, 10.1002/adma.200901956 Matsumoto, 2012, Patterns on a roll: a method of continuous feed nanoprinting, Soft Matter, 8, 11038, 10.1039/c2sm26516h Brunck, 2016, Elastic theory of origami-based metamaterials, Phys Rev E, 93, 033005, 10.1103/PhysRevE.93.033005 Kamrava, 2017, Origami-based cellular metamaterial with auxetic, bistable, and self-locking properties, Sci Rep, 7, 46046, 10.1038/srep46046 Sengupta, 2018, Harnessing the anisotropic multistability of stacked-origami mechanical metamaterials for effective modulus programming, J Intell Mater Syst Struct, 29, 2933, 10.1177/1045389X18781040 Waitukaitis, 2015, Origami multistability: from single vertices to metasheets, Phys Rev Lett, 114, 055503, 10.1103/PhysRevLett.114.055503 Boatti, 2017, Origami metamaterials for tunable thermal expansion, Adv Mater, 29, 1700360, 10.1002/adma.201700360 Ni, 2019, 2D mechanical metamaterials with widely tunable unusual modes of thermal expansion, Adv Mater, 31, 1905405, 10.1002/adma.201905405 Zhang, 2020, Effects of structural parameters on the Poisson’s ratio and compressive modulus of 2D pentamode structures fabricated by selective laser melting, Engineering, 6, 56, 10.1016/j.eng.2019.06.009 Zheng, 2014, Ultralight, ultrastiff mechanical metamaterials, Science, 344, 1373, 10.1126/science.1252291 Berger, 2017, Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness, Nature, 543, 533, 10.1038/nature21075 Silverberg, 2014, Using origami design principles to fold reprogrammable mechanical metamaterials, Science, 345, 647, 10.1126/science.1252876 Zhai, 2018, Origami-inspired, on-demand deployable and collapsible mechanical metamaterials with tunable stiffness, Proc Natl Acad Sci USA, 115, 2032, 10.1073/pnas.1720171115 Zhai, 2020, In situ stiffness manipulation using elegant curved origami, Sci Adv, 6, eabe2000, 10.1126/sciadv.abe2000 Schenk, 2013, Geometry of Miura-folded metamaterials, Proc Natl Acad Sci USA, 110, 3276, 10.1073/pnas.1217998110 Zhou, 2016, Origami mechanical metamaterials based on the Miura-derivative fold patterns, Proc Math Phys Eng Sci, 472, 20160361 Eidini, 2015, Unraveling metamaterial properties in zigzag-base folded sheets, Sci Adv, 1, e1500224, 10.1126/sciadv.1500224 Ma, 2018, An origami-inspired structure with graded stiffness, Int J Mech Sci, 136, 134, 10.1016/j.ijmecsci.2017.12.026 Liu, 2020, Big influence of small random imperfections in origami-based metamaterials, Proc Math Phys Eng Sci, 476, 20200236 Yuan, 2020, The behavior of a functionally graded origami structure subjected to quasi-static compression, Mater Des, 189, 108494, 10.1016/j.matdes.2020.108494 Kidambi, 2020, Dynamics of Kresling origami deployment, Phys Rev E, 101, 063003, 10.1103/PhysRevE.101.063003 Lv, 2014, Origami based mechanical metamaterials, Sci Rep, 4, 5979, 10.1038/srep05979 Chen, 2019, Ron Resch origami pattern inspired energy absorption structures, J Appl Mech, 86, 011005, 10.1115/1.4041415 Dieleman, 2020, Jigsaw puzzle design of pluripotent origami, Nat Phys, 16, 63, 10.1038/s41567-019-0677-3 Silverberg JL, Na JH, Evans AA, Liu B, Hull TC, Santangelo CD, et al. Origami structures with a critical transition to bistability arising from hidden degrees of freedom. Nat Mater 2015;14(4):389–93. Corrigendum in: Nat Mater 2015;14:540. Wang, 2019, Twistable origami and kirigami: from structure-guided smartness to mechanical energy storage, ACS Appl Mater Interfaces, 11, 3450, 10.1021/acsami.8b17776 Wang, 2020, Active reconfigurable twistable square-twist origami, Adv Funct Mater, 30, 1909087, 10.1002/adfm.201909087 Peng, 2018, The effect of mountain-valley folds on the rigid foldability of double corrugated pattern, Mechanism Mach Theory, 128, 461, 10.1016/j.mechmachtheory.2018.06.012 Chen, 2020, Assigning mountain-valley fold lines of flat-foldable origami patterns based on graph theory and mixed-integer linear programming, Comput Strucy, 239, 106328, 10.1016/j.compstruc.2020.106328 Chen, 2021, Particle swarm optimization-based metaheuristic design generation of non-trivial flat-foldable origami tessellations with degree-4 vertices, J Mech Des, 143, 011703, 10.1115/1.4047437 Feng, 2020, Rigid foldability and mountain-valley crease assignments of square-twist origami pattern, Mechanism Mach Theory, 152, 103947, 10.1016/j.mechmachtheory.2020.103947 Zang S, Ma J, Chen Y. Deformation characteristics and mechanical properties of a non-rigid square-twist origami structure with rotational symmetry. 2021. arXiv:2109.12488. Ma, 2021, Theoretical characterization of a non-rigid-foldable square-twist origami for property programmability, Int J Mech Sci, 189, 105981, 10.1016/j.ijmecsci.2020.105981 Lyu, 2021, Origami-based cellular mechanical metamaterials with tunable Poisson’s ratio: construction and analysis, Int J Mech Sci, 212, 106791, 10.1016/j.ijmecsci.2021.106791 Jha, 2013, A critical review of recent research on functionally graded plates, Compos Struct, 96, 833, 10.1016/j.compstruct.2012.09.001