Programming Curvature using Origami Tessellations
arXiv:1812.08922 · doi:10.1038/nmat4540
Abstract
Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can be designed to fit target shapes. Here, starting from the simplest periodic origami pattern that yields one degree-of-freedom collapsible structures, we show that scale-independent elementary geometric constructions and constrained optimization algorithms can be used to determine spatially modulated patterns that yield approximations to given surfaces of constant or varying curvature. Paper models confirm the feasibility of our calculations. We also assess the difficulty of realizing these geometric structures by quantifying the energetic barrier that separates the metastable flat and folded states. Moreover, we characterize the trade-off between the accuracy to which the pattern conforms to the target surface, and the effort associated with creating finer folds. Our approach enables the tailoring of origami patterns to drape complex surfaces independent of absolute scale, and quantify the energetic and material cost of doing so.
16 pages
References in corpus (4)
Cited by in corpus (62)
- Bistable Auxetic Mechanical Metamaterials Inspired by Ancient Geometric Motifs
- Programming shape using kirigami tessellations
- Buckling-Induced Kirigami
- Kirigami-inspired inflatables with programmable shapes
- Critical slowing down in purely elastic `snap-through' instabilities
- A characteristic lengthscale causes anomalous size effects and boundary programmability in mechanical metamaterials
- Shape-morphing architected sheets with non-periodic cut patterns
- Learning without neurons in physical systems
- Inverse design of deployable origami structures that approximate a general surface
- The designs and deformations of rigidly and flat-foldable quadrilateral mesh origami
- Topological defects produce exotic mechanics in complex metamaterials
- Programming stiff inflatable shells from planar patterned fabrics
- Helical Miura Origami
- Continuum field theory for the deformations of planar kirigami
- An additive algorithm for origami design
- On Elastic Geodesic Grids and Their Planar to Spatial Deployment
- Volumetric-mapping-based inverse design of 3D architected materials and mobility control by topology reconstruction
- An additive framework for kirigami design
- Shaping dynamical folding and misfolding pathways in mechanical metamaterials
- Non-Euclidean Origami
- Design of pseudo-mechanisms and multistable units for mechanical metamaterials
- Generalized Deployable Elastic Geodesic Grids
- Strain compatibility and gradient elasticity in morphing origami metamaterials
- Plasticity and Aging of Folded Elastic Sheets
- Microelectronic Morphogenesis: Progress towards Artificial Organisms
- Foldable Cones as a Framework for Nonrigid Origami
- Response evolution of mechanical metamaterials under architectural transformations
- Learning to self-fold at a bifurcation
- Programming bistability in geometrically perturbed mechanical metamaterials
- Rapid Multi-Physics Simulation for Electro-Thermal Origami Systems
- Effective continuum models for the buckling of non-periodic architected sheets that display quasi-mechanism behaviors
- Origami Lattices and Folding-induced Lattice Transformations
- Topology and morphology design of spherically reconfigurable homogeneous Modular Soft Robots (MSoRos)
- Harnessing Interpretable Machine Learning for Holistic Inverse Design of Origami
- The difficulty of folding self-folding origami
- Compliant morphing structures from twisted bulk metallic glass ribbons
- Derivation of an effective plate theory for parallelogram origami from bar and hinge elasticity
- Excess Floppy Modes and Multi-Branched Mechanisms in Metamaterials with Symmetries
- Conforming nanoparticle sheets to surfaces with Gaussian curvature
- Design and Fabrication of Elastic Geodesic Grid Structures
- Plastic deformation of a permanently bonded network: stress relaxation by pleats
- Exactly solvable flat-foldable quadrilateral origami tilings
- Slender Origami with Complex 3D Folding Shapes
- Keeping it Together: Interleaved Kirigami Extension Assembly
- Folded Goursat surface and banana-shaped seedpod
- Design and Fabrication of Multi-Patch Elastic Geodesic Grid Structures
- Flexible Kokotsakis Meshes with Skew Faces: Generalization of the Orthodiagonal Involutive Type
- Emergent Nonlocal Combinatorial Design Rules for Multimodal Metamaterials
- Geometric optimization using nonlinear rotation-invariant coordinates
- A continuum geometric approach for inverse design of origami structures
- Origami of Multi-Layered Spaced Sheets
- Computing quasiconformal folds
- Lorentz transformation for the kinematics of degree-4 rigid origami vertices and compatibility of rigid-foldable polygons
- Design and Fabrication of String-driven Origami Robots
- Theorem for the design of deployable kirigami tessellations with different topologies
- Quasi-symmetric nets: A constructive approach to the equimodular elliptic type of Kokotsakis polyhedra
- Optimal face-to-face coupling for fast self-folding kirigami
- Constructing rigid-foldable generalized Miura-ori tessellations for curved surfaces
- Totimorphic assemblies from neutrally-stable units
- Explosive rigidity percolation in origami
- Metamorphs: Bistable Planar Structures
- Architected kirigami metamorphosis