Tapered elasticæ as a route for axisymmetric morphing structures
Mingchao Liu1, Lucie Domino1, Dominic Vella1
1Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK. dominic.vella@maths.ox.ac.uk.
Soft Matter
|August 4, 2020
Summary
Researchers developed a new method to create 3D shapes from 2D sheets using a tapered elastica model. This technique allows precise control over shape formation, enabling gap-free 3D structures for advanced materials.
Area of Science:
- Materials Science
- Mechanical Engineering
- Applied Mathematics
Background:
- Transforming 2D sheets into 3D structures is crucial for applications like mechanical metamaterials and flexible electronics.
- Existing methods like Kirigami involve cuts allowing planar face rotation, but some deformations involve bending.
Purpose of the Study:
- To model bending deformations in elastic strips using a tapered elastica formulation.
- To design tapering patterns for creating 2D sheets that morph into desired axisymmetric 3D shapes.
- To demonstrate the creation of 3D structures with controlled Gaussian curvatures and closed gaps.
Main Methods:
- Modeling elastic strips with tapered thickness and width (tapered elastica).
- Designing tapering patterns for specific 3D shape morphing under edge-loads.
- Utilizing numerical simulations and physical experiments for verification.
Main Results:
- A theoretical framework for designing 2D sheets that morph into desired 3D shapes was established.
- Miniature structures with positive, negative, and variable Gaussian curvatures were successfully recreated.
- Tapering sheet thickness was shown to close gaps, enabling tessellated 3D structures.
Conclusions:
- The tapered elastica model provides a powerful tool for designing complex 3D shapes from flat sheets.
- This method offers precise control over shape formation and gap closure in 3D structures.
- The findings have implications for advanced manufacturing of metamaterials and electronics.
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