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Updated: Sep 2, 2025
14:52
Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding
Published on: September 23, 2018
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Discrete symmetries control geometric mechanics in parallelogram-based origami
James McInerney1,2, Glaucio H Paulino3,4,5,6, D Zeb Rocklin1
1School of Physics, Georgia Institute of Technology, Atlanta, GA 30332.
Summary
We developed a new method to analyze origami mechanical metamaterials, revealing how geometric symmetries control their unique negative Poisson
Area of Science:
- Soft Matter Physics
- Mechanical Engineering
- Materials Science
Background:
- Geometric compatibility is crucial for soft system mechanics.
- Origami crease patterns, like Miura-ori, are key to designing mechanical metamaterials with tunable properties, such as negative Poisson's ratio.
Purpose of the Study:
- To develop a formalism for linear compatibility in origami crease patterns.
- To investigate the relationship between geometric symmetries and mechanical functionality.
- To analyze periodic crease patterns with parallelogram faces.
Main Methods:
- Developed a formalism for linear compatibility analysis.
- Applied the formalism to periodic crease patterns with four parallelogram faces.
- Analyzed symmetry properties and their relation to mechanical response (Poisson's ratio).
Main Results:
- Established that the mechanical response of these patterns is governed by an anticommuting symmetry.
- Showed that modes are simultaneous eigenstates of the symmetry, strain, and curvature operators.
- Identified an equivalence class of geometries with equal and opposite in-plane and out-of-plane Poisson's ratios.
Conclusions:
- The anticommuting symmetry dictates the mechanical behavior and Poisson's ratios.
- Poisson's ratios change sign during folding between ground states.
- Identified specific subfamilies with strictly negative Poisson's ratios across all configurations.
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