Tapered elasticæ as a route for axisymmetric morphing structures
Transforming flat two-dimensional (2D) sheets into three-dimensional (3D) structures by combining carefully made cuts with applied edge-loads has emerged as an exciting manufacturing paradigm in a range of applications from mechanical metamaterials to flexible electronics. In Kirigami, patterns of c...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Royal Society of Chemistry
2020
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| _version_ | 1797056858199949312 |
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| author | Liu, M Domino, L Vella, D |
| author_facet | Liu, M Domino, L Vella, D |
| author_sort | Liu, M |
| collection | OXFORD |
| description | Transforming flat two-dimensional (2D) sheets into three-dimensional (3D) structures by combining carefully made cuts with applied edge-loads has emerged as an exciting manufacturing paradigm in a range of applications from mechanical metamaterials to flexible electronics. In Kirigami, patterns of cuts are introduced that allow solid faces to rotate about each other, deforming in three dimensions whilst remaining planar. In other scenarios, however, the solid elements bend in one direction. In this paper, we model such bending deformations using the formulation of an elastic strip whose thickness and width are tapered (the ‘tapered elastica’). We show how this framework can be exploited to design the tapering patterns required to create planar sheets that morph into desired axisymmetric 3D shapes under a combination of horizontal and vertical edge-loads. We exhibit this technique by recreating miniature structures with positive, negative, and variable apparent Gaussian curvatures. With sheets of constant thickness, the resulting morphed shapes may leave gaps between the deformed elements. However, by tapering the thickness of the sheet too, these gaps can be closed, creating tessellated three-dimensional structures. Our theoretical approaches are verified by both numerical simulations and physical experiments. |
| first_indexed | 2024-03-06T19:28:24Z |
| format | Journal article |
| id | oxford-uuid:1c975a87-c824-4ff7-942e-544c67a67fd8 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:28:24Z |
| publishDate | 2020 |
| publisher | Royal Society of Chemistry |
| record_format | dspace |
| spelling | oxford-uuid:1c975a87-c824-4ff7-942e-544c67a67fd82022-03-26T11:06:25ZTapered elasticæ as a route for axisymmetric morphing structuresJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1c975a87-c824-4ff7-942e-544c67a67fd8EnglishSymplectic ElementsRoyal Society of Chemistry2020Liu, MDomino, LVella, DTransforming flat two-dimensional (2D) sheets into three-dimensional (3D) structures by combining carefully made cuts with applied edge-loads has emerged as an exciting manufacturing paradigm in a range of applications from mechanical metamaterials to flexible electronics. In Kirigami, patterns of cuts are introduced that allow solid faces to rotate about each other, deforming in three dimensions whilst remaining planar. In other scenarios, however, the solid elements bend in one direction. In this paper, we model such bending deformations using the formulation of an elastic strip whose thickness and width are tapered (the ‘tapered elastica’). We show how this framework can be exploited to design the tapering patterns required to create planar sheets that morph into desired axisymmetric 3D shapes under a combination of horizontal and vertical edge-loads. We exhibit this technique by recreating miniature structures with positive, negative, and variable apparent Gaussian curvatures. With sheets of constant thickness, the resulting morphed shapes may leave gaps between the deformed elements. However, by tapering the thickness of the sheet too, these gaps can be closed, creating tessellated three-dimensional structures. Our theoretical approaches are verified by both numerical simulations and physical experiments. |
| spellingShingle | Liu, M Domino, L Vella, D Tapered elasticæ as a route for axisymmetric morphing structures |
| title | Tapered elasticæ as a route for axisymmetric morphing structures |
| title_full | Tapered elasticæ as a route for axisymmetric morphing structures |
| title_fullStr | Tapered elasticæ as a route for axisymmetric morphing structures |
| title_full_unstemmed | Tapered elasticæ as a route for axisymmetric morphing structures |
| title_short | Tapered elasticæ as a route for axisymmetric morphing structures |
| title_sort | tapered elasticae as a route for axisymmetric morphing structures |
| work_keys_str_mv | AT lium taperedelasticæasarouteforaxisymmetricmorphingstructures AT dominol taperedelasticæasarouteforaxisymmetricmorphingstructures AT vellad taperedelasticæasarouteforaxisymmetricmorphingstructures |