Experimental realization of tunable Poisson’s ratio in deployable origami metamaterials

Misseroni, D.; Pratapa, Phanisri P.; Liu, Ke; Paulino, Gláucio H.

doi:10.1016/j.eml.2022.101685

Cited by 31 publications

(8 citation statements)

References 45 publications

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“…According to the Saint-Venant principle [33], extra zones near the boundary of a tested sample must be excluded when evaluating the properties of the material, which leads to a need for large enough samples in conventional mechanical testing to ensure a uniform deformation in the central portion of the sample. We demonstrate that the Saint-Venant setup alleviates the influence of unwanted boundary effects, leading to precise and reliable measurements on relatively small samples that represent the physics of the parent periodic system [34]. We further observe that the Trimorph metamaterial displays equal but opposite Poisson's ratio under stretching and bending by our generalized lattice-based definition (this was previously observed in standard origami metamaterials only when their lattice and principal Poisson's ratios coincide, i.e.…”

Section: Introductionsupporting

confidence: 68%

Triclinic Metamaterials by Tristable Origami with Reprogrammable Frustration

et al. 2022

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Geometrical‐frustration‐induced anisotropy and inhomogeneity are explored to achieve unique properties of metamaterials that set them apart from conventional materials. According to Neumann's principle, to achieve anisotropic responses, the material unit cell should possess less symmetry. Based on such guidelines, a triclinic metamaterial system of minimal symmetry is presented, which originates from a Trimorph origami pattern with a simple and insightful geometry: a basic unit cell with four tilted panels and four corresponding creases. The intrinsic geometry of the Trimorph origami, with its changing tilting angles, dictates a folding motion that varies the primitive vectors of the unit cell, couples the shear and normal strains of its extrinsic bulk, and leads to an unusual Poisson effect. Such an effect, associated with reversible auxeticity in the changing triclinic frame, is observed experimentally, and predicted theoretically by elegant mathematical formulae. The nonlinearities of the folding motions allow the unit cell to display three robust stable states, connected through snapping instabilities. When the tristable unit cells are tessellated, phenomena that resemble linear and point defects emerge as a result of geometric frustration. The frustration is reprogrammable into distinct stable and inhomogeneous states by arbitrarily selecting the location of a single or multiple point defects. The Trimorph origami demonstrates the possibility of creating origami metamaterials with symmetries that are hitherto nonexistent, leading to triclinic metamaterials with tunable anisotropy for potential applications such as wave propagation control and compliant microrobots.

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Section: Introductionsupporting

confidence: 68%

Triclinic Metamaterials by Tristable Origami with Reprogrammable Frustration

et al. 2022

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“…Future work could verify the in-plane Poisson’s ratio experimentally in a similar manner to [19] and compare with theoretical and numerical results. Poisson’s ratio in bending could also be analytically determined as has been done with the Miura-ori [22], eggbox [23], morph [14] and other tessellated patterns [24,25].…”

Section: Discussionmentioning

confidence: 92%

“…The load was applied in the +y-direction at each top vertex. The boundary conditions were chosen to resemble an experimental set-up using the Saint–Venant Fixture described in [19] to experimentally verify Poisson’s ratio of origami metamaterials. Poisson’s ratio was calculated by tracking the position and displacement of the top right vertex highlighted in blue in figure 7.…”

Section: Morph and Hybrid Patternsmentioning

confidence: 99%

Geometric mechanics of hybrid origami assemblies combining developable and non-developable patterns

Liu,

Paulino

2024

Proc. R. Soc. A.

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Origami provides a method to transform a flat surface into complex three-dimensional geometries, which has applications in deployable structures, meta-materials, robotics and beyond. The Miura-ori and the eggbox are two fundamental planar origami patterns. Both patterns have been studied closely, and have become the basis for many engineering applications and derivative origami patterns. Here, we study the hybrid structure formed by combining unit cells of the Miura-ori and eggbox patterns. We find the compatibility constraints required to form the hybrid structure and derive properties of its kinematics such as self-locking and Poisson’s ratio. We then compare the aforementioned properties of the Miura-eggbox hybrid with those of the morph pattern, another generalization of the Miura-ori and eggbox patterns. In addition, we study the structure formed by combining all three unit cells of the Miura-ori, eggbox and morph. Our results show that such patterns have tunable self-locking states and Poisson’s ratio beyond their constituent components. Hybrid patterns formed by combining different origami patterns are an avenue to derive more functionality from simple constituents for engineering applications.

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“…While this article was under review, calculations for the in-plane Poisson’s ratio of the Morph subfamily were experimentally verified in ref. 84 and the equal-and-opposite property of generic four-parallelogram origami sheets was computed via an alternative calculation in ref. 85 .…”

Section: Note Added In Proofmentioning

confidence: 99%

Discrete symmetries control geometric mechanics in parallelogram-based origami

McInerney

Paulino

Rocklin

2022

Proc. Natl. Acad. Sci. U.S.A.

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Geometric compatibility constraints dictate the mechanical response of soft systems that can be utilized for the design of mechanical metamaterials such as the negative Poisson’s ratio Miura-ori origami crease pattern. Here, we develop a formalism for linear compatibility that enables explicit investigation of the interplay between geometric symmetries and functionality in origami crease patterns. We apply this formalism to a particular class of periodic crease patterns with unit cells composed of four arbitrary parallelogram faces and establish that their mechanical response is characterized by an anticommuting symmetry. In particular, we show that the modes are eigenstates of this symmetry operator and that these modes are simultaneously diagonalizable with the symmetric strain operator and the antisymmetric curvature operator. This feature reveals that the anticommuting symmetry defines an equivalence class of crease pattern geometries that possess equal and opposite in-plane and out-of-plane Poisson’s ratios. Finally, we show that such Poisson’s ratios generically change sign as the crease pattern rigidly folds between degenerate ground states and we determine subfamilies that possess strictly negative in-plane or out-of-plane Poisson’s ratios throughout all configurations.

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Experimental realization of tunable Poisson’s ratio in deployable origami metamaterials

Cited by 31 publications

References 45 publications

Triclinic Metamaterials by Tristable Origami with Reprogrammable Frustration

Triclinic Metamaterials by Tristable Origami with Reprogrammable Frustration

Geometric mechanics of hybrid origami assemblies combining developable and non-developable patterns

Discrete symmetries control geometric mechanics in parallelogram-based origami

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