fig3

Figure 3. Morphing matter based on origami and kirigami. (A) An origami tessellation based on Resch’s patterns is showcased, optimizing the developable pattern while eliminating local collisions. Reproduced with permission from^[91]; Copyright 2023, Elsevier Ltd; (B) A Generalized Miura-ori obtained from constrained optimization algorithms exhibits surfaces with negative, positive, and mixed Gauss curvature, aligning well with manually folded physical paper. Reproduced with permission from^[92]; Copyright 2022, Macmillan Publishers Limited; (C) Magnetic Kresling units capable of folding/deploying and ominidirectional bending are interconnected with a robotic arm, displaying multimodal behaviors under rotating magnetic fields. Reproduced with permission from^[100]; Copyright 2022, National Academy of Sciences, U.S.A; (D) Nonperiodic modular origami structures are proposed for volumetric 3D spatial curvilinear geometries. Reproduced with permission from^[95]; Copyright 2022, Macmillan Publishers Limited; (E) Reconfigurable kirigami with optimized quadrilateral tiles can morph from an initial compact configuration to a customized deployed state and finally to another compact configuration. Reproduced with permission from^[105]; Copyright 2021, American Physical Society; (F) A computational wrapping method enables nonstretchable and even brittle materials to conform to curved surfaces. Reproduced with permission from^[106]; Copyright 2020, AAAS; (G) A quad kirigami tessellation is extended to fit curved surfaces with complex Gaussian curvature. Reproduced with permission from^[107]; Copyright 2019, Macmillan Publishers Limited; (H) Auxetic kirigami sheets, comprising spatial varying motifs, exhibit stable morphing surfaces with optimized compressive stiffness. Reproduced with permission from^[111]; Copyright 2021, Association for Computing Machinery; (I) Elastic tapered patterns are cut from a sheet to form axisymmetric structures with programmed profiles under compressive load at their edges. Reproduced with permission from^[112]; Copyright 2020, The Royal Society of Chemistry; (J) Perforated kirigami exhibits a programmed apple-shaped structure with potential applications in grippers or packaging. Reproduced with permission from^[114]; Copyright 2022, Elsevier Ltd; (K) A Cellular triangular microlattice design strategy is presented to reconstruct biomimetic surfaces resembling the blueberry flower. Reproduced with permission from^[115]; Copyright 2023, AAAS; (L) Functionally graded composites using multi-materials voxel-based 3D printing are employed to constitute the divided elastic strip for morphing structures. Reproduced with permission from^[116]; Copyright 2023, Elsevier Ltd.