دورية أكاديمية
An additive framework for kirigami design.
| العنوان: | An additive framework for kirigami design. |
|---|---|
| المؤلفون: | Dudte LH; School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA., Choi GPT; Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA., Becker KP; School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA.; Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA., Mahadevan L; School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA. lmahadev@g.harvard.edu.; Departments of Physics, and Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA. lmahadev@g.harvard.edu. |
| المصدر: | Nature computational science [Nat Comput Sci] 2023 May; Vol. 3 (5), pp. 443-454. Date of Electronic Publication: 2023 May 25. |
| نوع المنشور: | Journal Article |
| اللغة: | English |
| بيانات الدورية: | Publisher: Springer Nature Country of Publication: United States NLM ID: 101775476 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 2662-8457 (Electronic) Linking ISSN: 26628457 NLM ISO Abbreviation: Nat Comput Sci Subsets: PubMed not MEDLINE; MEDLINE |
| أسماء مطبوعة: | Original Publication: [New York, N.Y.] : Springer Nature, [2021]- |
| مستخلص: | We present an additive approach for the inverse design of kirigami-based mechanical metamaterials by focusing on the empty (negative) spaces instead of the solid tiles. By considering each negative space as a four-bar linkage, we identify a simple recursive relationship between adjacent linkages, yielding an efficient method for creating kirigami patterns. This allows us to solve the kirigami design problem using elementary linear algebra, with compatibility, reconfigurability and rigid-deployability encoded into an iterative procedure involving simple matrix multiplications. The resulting linear design strategy circumvents the solution of a non-convex global optimization problem and allows us to control the degrees of freedom in the deployment angle field, linkage offsets and boundary conditions. We demonstrate this by creating a large variety of rigid-deployable, compact, reconfigurable kirigami patterns. We then realize our kirigami designs physically using two simple but effective fabrication strategies with very different materials. Altogether, our additive approaches present routes for efficient mechanical metamaterial design and fabrication based on ori/kirigami art forms. (© 2023. The Author(s), under exclusive licence to Springer Nature America, Inc.) |
| References: | Callens, S. J. & Zadpoor, A. A. From flat sheets to curved geometries: origami and kirigami approaches. Mater. Today 21, 241–264 (2018). (PMID: 10.1016/j.mattod.2017.10.004) Zhai, Z., Wu, L. & Jiang, H. Mechanical metamaterials based on origami and kirigami. Appl. Phys. Rev. 8, 041319 (2021). (PMID: 10.1063/5.0051088) Lang, R. J. Origami Design Secrets: Mathematical Methods for an Ancient Art (CRC Press, 2012). Demaine, E. D. & O’Rourke, J. Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Cambridge Univ. Press, 2007). Hull, T. C. Origametry: Mathematical Methods in Paper Folding (Cambridge Univ. Press, 2020). Temko, F. Kirigami, The Creative Art of Paper Cutting (Platt & Munk, 1962). Borcea, C. & Streinu, I. Geometric auxetics. Proc. R. Soc. A 471, 20150033 (2015). (PMID: 10.1098/rspa.2015.0033) Chen, B. G.-g et al. Topological mechanics of origami and kirigami. Phys. Rev. Lett. 116, 135501 (2016). (PMID: 10.1103/PhysRevLett.116.135501) Bertoldi, K., Vitelli, V., Christensen, J. & Van Hecke, M. Flexible mechanical metamaterials. Nat. Rev. Mater. 2, 17066 (2017). (PMID: 10.1038/natrevmats.2017.66) Celli, P. et al. Shape-morphing architected sheets with non-periodic cut patterns. Soft Matter 14, 9744–9749 (2018). (PMID: 10.1039/C8SM02082E) Singh, N. & van Hecke, M. Design of pseudo-mechanisms and multistable units for mechanical metamaterials. Phys. Rev. Lett. 126, 248002 (2021). (PMID: 10.1103/PhysRevLett.126.248002) Zheng, Y., Niloy, I., Celli, P., Tobasco, I. & Plucinsky, P. Continuum field theory for the deformations of planar kirigami. Phys. Rev. Lett. 128, 208003 (2022). (PMID: 10.1103/PhysRevLett.128.208003) Czajkowski, M., Coulais, C., van Hecke, M. & Rocklin, D. Conformal elasticity of mechanism-based metamaterials. Nat. Commun. 13, 211 (2022). (PMID: 10.1038/s41467-021-27825-0) Konaković-Luković, M., Panetta, J., Crane, K. & Pauly, M. Rapid deployment of curved surfaces via programmable auxetics. ACM Trans. Graph. 37, 106 (2018). (PMID: 10.1145/3197517.3201373) Choi, G. P. T., Dudte, L. H. & Mahadevan, L. Programming shape using kirigami tessellations. Nat. Mater. 18, 999–1004 (2019). (PMID: 10.1038/s41563-019-0452-y) Jiang, C., Rist, F., Pottmann, H. & Wallner, J. Freeform quad-based kirigami. ACM Trans. Graph. 39, 1–11 (2020). (PMID: 10.1145/3414685.3417769) Choi, G. P. T., Dudte, L. H. & Mahadevan, L. Compact reconfigurable kirigami. Phys. Rev. Res. 3, 043030 (2021). (PMID: 10.1103/PhysRevResearch.3.043030) Dang, X., Feng, F., Duan, H. & Wang, J. Theorem for the design of deployable kirigami tessellations with different topologies. Phys. Rev. E 104, 055006 (2021). (PMID: 10.1103/PhysRevE.104.055006) Thompson, D. W. On Growth and Form (Cambridge Univ. Press, 1942). Truby, R. L. & Lewis, J. A. Printing soft matter in three dimensions. Nature 540, 371–378 (2016). (PMID: 10.1038/nature21003) Dudte, L. H., Choi, G. P. T. & Mahadevan, L. An additive algorithm for origami design. Proc. Natl Acad. Sci. USA 118, e2019241118 (2021). (PMID: 10.1073/pnas.2019241118) Dudte, L. H., Vouga, E., Tachi, T. & Mahadevan, L. Programming curvature using origami tessellations. Nat. Mater. 15, 583–588 (2016). (PMID: 10.1038/nmat4540) Lang, R. J. & Howell, L. Rigidly foldable quadrilateral meshes from angle arrays. J. Mech. Robot. 10, 021004 (2018). (PMID: 10.1115/1.4038972) Dudte, L. H., Choi, G. P. T., Becker, K. P. & Mahadevan, L. ‘Additive kirigami’. Zenodo https://doi.org/10.5281/zenodo.7763613 (2023). |
| معلومات مُعتمدة: | DMR 20-11754 National Science Foundation (NSF); DMREF 19-22321 National Science Foundation (NSF); EFRI 18-30901 National Science Foundation (NSF); DMS-2002103 National Science Foundation (NSF) |
| تواريخ الأحداث: | Date Created: 20240104 Date Completed: 20240108 Latest Revision: 20240112 |
| رمز التحديث: | 20240112 |
| DOI: | 10.1038/s43588-023-00448-9 |
| PMID: | 38177849 |
| قاعدة البيانات: | MEDLINE |
Find this article in full text from Springer Verlag. | تدمد: | 2662-8457 |
|---|---|
| DOI: | 10.1038/s43588-023-00448-9 |