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Unraveling metamaterial properties in zigzag-base folded sheets.

Eidini M, Paulino GH - Sci Adv (2015)

Bottom Line: We show that our class of patterns, by expanding on the design space of Miura-ori, is appropriate for a wide range of applications from mechanical metamaterials to deployable structures at small and large scales.We further show that, depending on the geometry, these materials exhibit either negative or positive in-plane Poisson's ratios.By introducing a class of zigzag-base materials in the current study, we unify the concept of in-plane Poisson's ratio for similar materials in the literature and extend it to the class of zigzag-base folded sheet materials.

View Article: PubMed Central - PubMed

Affiliation: Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 North Mathews Avenue, Urbana, IL 61801, USA.

ABSTRACT
Creating complex spatial objects from a flat sheet of material using origami folding techniques has attracted attention in science and engineering. In the present work, we use the geometric properties of partially folded zigzag strips to better describe the kinematics of known zigzag/herringbone-base folded sheet metamaterials such as Miura-ori. Inspired by the kinematics of a one-degree of freedom zigzag strip, we introduce a class of cellular folded mechanical metamaterials comprising different scales of zigzag strips. This class of patterns combines origami folding techniques with kirigami. Using analytical and numerical models, we study the key mechanical properties of the folded materials. We show that our class of patterns, by expanding on the design space of Miura-ori, is appropriate for a wide range of applications from mechanical metamaterials to deployable structures at small and large scales. We further show that, depending on the geometry, these materials exhibit either negative or positive in-plane Poisson's ratios. By introducing a class of zigzag-base materials in the current study, we unify the concept of in-plane Poisson's ratio for similar materials in the literature and extend it to the class of zigzag-base folded sheet materials.

No MeSH data available.


Related in: MedlinePlus

Behavior of a BCH2 sheet upon bending and results of the eigenvalue analysis of a 3 × 3 BCH2 pattern.(A) A BCH2 sheet deforms into a saddle shape upon bending (that is, a typical behavior seen in materials with a positive out-of-plane Poisson’s ratio). (B) Twisting deformation, (C) saddle-shaped deformation, and (D) rigid origami behavior (planar mechanism) of a 3 × 3 pattern of BCH2 (a = 1, b = 2, and α = 60°). Twisting and saddle-shaped deformations are the softest modes observed for a wide range of material properties and geometries. For large values of Kfacet/Kfold, rigid origami behavior (planar mechanism) is simulated.
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Figure 7: Behavior of a BCH2 sheet upon bending and results of the eigenvalue analysis of a 3 × 3 BCH2 pattern.(A) A BCH2 sheet deforms into a saddle shape upon bending (that is, a typical behavior seen in materials with a positive out-of-plane Poisson’s ratio). (B) Twisting deformation, (C) saddle-shaped deformation, and (D) rigid origami behavior (planar mechanism) of a 3 × 3 pattern of BCH2 (a = 1, b = 2, and α = 60°). Twisting and saddle-shaped deformations are the softest modes observed for a wide range of material properties and geometries. For large values of Kfacet/Kfold, rigid origami behavior (planar mechanism) is simulated.

Mentions: Simple experimental observations show that these folded sheets exhibit, similarly to the Miura-ori pattern, an anticlastic (saddle-shaped) curvature upon bending (Fig. 7A, figs. S6 to S8, and movie S3), which is a curvature adopted by conventional materials with positive out-of-plane Poisson’s ratio (29). This positional semiauxetic behavior has been observed in “antitrichiral” honeycomb (33), auxetic composite laminates (34), and other patterns of folded sheets made of conventional materials (1, 3, 28).


Unraveling metamaterial properties in zigzag-base folded sheets.

Eidini M, Paulino GH - Sci Adv (2015)

Behavior of a BCH2 sheet upon bending and results of the eigenvalue analysis of a 3 × 3 BCH2 pattern.(A) A BCH2 sheet deforms into a saddle shape upon bending (that is, a typical behavior seen in materials with a positive out-of-plane Poisson’s ratio). (B) Twisting deformation, (C) saddle-shaped deformation, and (D) rigid origami behavior (planar mechanism) of a 3 × 3 pattern of BCH2 (a = 1, b = 2, and α = 60°). Twisting and saddle-shaped deformations are the softest modes observed for a wide range of material properties and geometries. For large values of Kfacet/Kfold, rigid origami behavior (planar mechanism) is simulated.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4643767&req=5

Figure 7: Behavior of a BCH2 sheet upon bending and results of the eigenvalue analysis of a 3 × 3 BCH2 pattern.(A) A BCH2 sheet deforms into a saddle shape upon bending (that is, a typical behavior seen in materials with a positive out-of-plane Poisson’s ratio). (B) Twisting deformation, (C) saddle-shaped deformation, and (D) rigid origami behavior (planar mechanism) of a 3 × 3 pattern of BCH2 (a = 1, b = 2, and α = 60°). Twisting and saddle-shaped deformations are the softest modes observed for a wide range of material properties and geometries. For large values of Kfacet/Kfold, rigid origami behavior (planar mechanism) is simulated.
Mentions: Simple experimental observations show that these folded sheets exhibit, similarly to the Miura-ori pattern, an anticlastic (saddle-shaped) curvature upon bending (Fig. 7A, figs. S6 to S8, and movie S3), which is a curvature adopted by conventional materials with positive out-of-plane Poisson’s ratio (29). This positional semiauxetic behavior has been observed in “antitrichiral” honeycomb (33), auxetic composite laminates (34), and other patterns of folded sheets made of conventional materials (1, 3, 28).

Bottom Line: We show that our class of patterns, by expanding on the design space of Miura-ori, is appropriate for a wide range of applications from mechanical metamaterials to deployable structures at small and large scales.We further show that, depending on the geometry, these materials exhibit either negative or positive in-plane Poisson's ratios.By introducing a class of zigzag-base materials in the current study, we unify the concept of in-plane Poisson's ratio for similar materials in the literature and extend it to the class of zigzag-base folded sheet materials.

View Article: PubMed Central - PubMed

Affiliation: Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 North Mathews Avenue, Urbana, IL 61801, USA.

ABSTRACT
Creating complex spatial objects from a flat sheet of material using origami folding techniques has attracted attention in science and engineering. In the present work, we use the geometric properties of partially folded zigzag strips to better describe the kinematics of known zigzag/herringbone-base folded sheet metamaterials such as Miura-ori. Inspired by the kinematics of a one-degree of freedom zigzag strip, we introduce a class of cellular folded mechanical metamaterials comprising different scales of zigzag strips. This class of patterns combines origami folding techniques with kirigami. Using analytical and numerical models, we study the key mechanical properties of the folded materials. We show that our class of patterns, by expanding on the design space of Miura-ori, is appropriate for a wide range of applications from mechanical metamaterials to deployable structures at small and large scales. We further show that, depending on the geometry, these materials exhibit either negative or positive in-plane Poisson's ratios. By introducing a class of zigzag-base materials in the current study, we unify the concept of in-plane Poisson's ratio for similar materials in the literature and extend it to the class of zigzag-base folded sheet materials.

No MeSH data available.


Related in: MedlinePlus