Fig. 1 The mainstream research fields and topics of origami: ( a ) the main research field of origami in recent years, ( b ) research topics on origami systems retrieved from the Web of Science from 2018 to 2023, and ( c ) numerous articles were published in several top journals from 2018 to 2023 More about this image found in The mainstream research fields and topics of origami: ( a ) the main resear...

Fig. 2 Geometric definitions of origami: ( a ) single vertex Miura-ori crease pattern, ( b ) rigidly foldable origami (Reproduced with permission from Ref. [ 102 ]. Copyright 2020 by ASME), ( c ) flat-foldable origami, and ( d ) developable and nondevelopable origami (Adapted with permission from ... More about this image found in Geometric definitions of origami: ( a ) single vertex Miura-ori crease patt...

Fig. 3 Classical origami patterns and corresponding tessellation/stacked structures: ( a ) Miura-ori pattern, ( b ) Tachi–Miura and stacked Miura structures, ( c ) waterbomb origami patterns, ( d ) waterbomb tube (Adapted with permission from Ref. [ 82 ]. Copyright 2020 by Elsevier), ( e ) Kreslin... More about this image found in Classical origami patterns and corresponding tessellation/stacked structure...

Fig. 4 Equivalent mechanical model for origami: ( a ) bar-and-hinge model for the rigidly foldable and nonrigidly foldable origami, ( b ) the particle-bar-spring model is combined with the finite particle method for Miura-ori, ( c ) the energy conversion of the Miura-ori tessellated foldable struc... More about this image found in Equivalent mechanical model for origami: ( a ) bar-and-hinge model for the ...

Fig. 5 Truss model for Kresling origami: ( a ) bar-and-hinge model for the Kresling origami [ 9 ], ( b ) strain energy landscapes along minimum energy deployment paths for Kresling modules with varying stress-free orientations δ 0 (Figs. 5( a ) and 5( b ) are adapted with permission from Re... More about this image found in Truss model for Kresling origami: ( a ) bar-and-hinge model for the Kreslin...

Fig. 6 Tunable stiffness of the Miura-ori: ( a ) origami-inspired metamaterials can alter their stiffness (Reproduced with permission from Ref. [ 150 ]. Copyright 2020, The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science), ( b ) origami-inspire... More about this image found in Tunable stiffness of the Miura-ori: ( a ) origami-inspired metamaterials ca...

Fig. 7 Tunable stiffness of Kresling origami. ( a ) Coupled Kresling modular origami-inspired structure, and ( b )tunable stiffness of coupled Kresling modular structure by tuning the initial geometrical parameters (Figs. 7( a ) and 7( b ) are adapted with permission from Ref. [ 153 ]. Copyrig... More about this image found in Tunable stiffness of Kresling origami. ( a ) Coupled Kresling modular origa...

Fig. 8 Bistable origami: ( a ) bistable states of the Miura-ori, ( b ) bistable states of the waterbomb origami, ( c )bistable states of the Kresling origami, ( d ) multistable waterbomb origami structures, and ( e ) multistable Kresling origami structures (Figs. 8( a ) – 8( e ) are reproduced w... More about this image found in Bistable origami: ( a ) bistable states of the Miura-ori, ( b ) bistable st...

Fig. 9 Multistable properties of the Miura-ori. ( a ) Stacked Miura-ori unit, ( b ) nested-in (up) and bulged-out (below) configuration, and ( c ) three-dimensional expansion ability (Figs. 9( a ) – 9( c ) are adapted with permission from Ref. [ 158 ]. Copyright 2017, The Authors, published by t... More about this image found in Multistable properties of the Miura-ori. ( a ) Stacked Miura-ori unit, ( b ...

Fig. 10 Multistable properties of the waterbomb origami: ( a ) multimode, multidirectional waterbomb-based origami grippers (Adapted with permission from Ref. [ 163 ]. Copyright 2022, The Authors, published by the Royal Society), ( b )vertex height corresponds to changes in loading force under dif... More about this image found in Multistable properties of the waterbomb origami: ( a ) multimode, multidire...

Fig. 11 Multistable properties of the Kresling origami: ( a ) deformation modes of the structures (Adapted with permission from Ref. [ 166 ]. Copyright 2022 by Wiley‐VCH GmbH), ( b ) three stable states of the Kresling origami (Reproduced with permission from Ref. [ 91 ]. Copyright 2023 by Elsevie... More about this image found in Multistable properties of the Kresling origami: ( a ) deformation modes of ...

Fig. 12 Bistable and multistable properties of the other origami. ( a ) Two stable states of the hyperbolic paraboloid origami, and ( b ) unique stable states of the hyperbolic paraboloid origami structure (Figs. 12( a ) and 12( b ) are adapted with permission from Ref. [ 169 ]. Copyright 2019... More about this image found in Bistable and multistable properties of the other origami. ( a ) Two stable ...

Fig. 13 OTFMs based on Miura-ori: ( a ) negative Poisson's ratio for in-plane deformations of Miura OTFMs (Adapted with permission from Ref. [ 121 ]. Copyright 2013, The Authors, published by National Academy of Sciences), ( b ) the in-plane expansion coefficient of the Miura OTFMs (Reproduced wit... More about this image found in OTFMs based on Miura-ori: ( a ) negative Poisson's ratio for in-plane defor...

Fig. 14 OTFMs based on Ron Resch origami. ( a ) Ron Resch origami patterns (Adapted with permission from Ref. [ 190 ]. Copyright 2013 by ASME). ( b ) Normalized axial compressive force versus axial strain for the Ron Resch origami tubular foldable metamaterials, and ( c ) load-bearing capability o... More about this image found in OTFMs based on Ron Resch origami. ( a ) Ron Resch origami patterns (Adapted...