Limits...
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

Sample patterns of BCHn and cellular folded metamaterials.(A) A BCH2 sheet. (B) A BCH3 sheet-adding one layer of small parallelograms to the first row reduces the DOF of the system to 1 for rigid origami behavior. (C) Combination of BCH2 and layers of large and small parallelograms with the same geometries as the ones used in BCH2. (D) Combination of BCH3 and layers of large and small parallelograms with the same geometries as the ones used in BCH3. (E) A BCH3 sheet and layers of small parallelograms with the same geometries as the ones used in BCH3. (F) A sheet composed of various BCHn and Miura-ori cells with the same angle ϕ. (G) A stacked cellular metamaterial made from seven layers of folded sheets of BCH2 with two different geometries. (H) Cellular metamaterial made from two layers of 3 × 3 sheets of BCH2 of different heights tailored for stacking and bonded along the joining fold lines. The resulting configuration is flat-foldable in one direction.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4643767&req=5

Figure 3: Sample patterns of BCHn and cellular folded metamaterials.(A) A BCH2 sheet. (B) A BCH3 sheet-adding one layer of small parallelograms to the first row reduces the DOF of the system to 1 for rigid origami behavior. (C) Combination of BCH2 and layers of large and small parallelograms with the same geometries as the ones used in BCH2. (D) Combination of BCH3 and layers of large and small parallelograms with the same geometries as the ones used in BCH3. (E) A BCH3 sheet and layers of small parallelograms with the same geometries as the ones used in BCH3. (F) A sheet composed of various BCHn and Miura-ori cells with the same angle ϕ. (G) A stacked cellular metamaterial made from seven layers of folded sheets of BCH2 with two different geometries. (H) Cellular metamaterial made from two layers of 3 × 3 sheets of BCH2 of different heights tailored for stacking and bonded along the joining fold lines. The resulting configuration is flat-foldable in one direction.

Mentions: For rigid panels connected via hinges at fold lines, the BCH with n = 2 has only one independent DOF, on the basis of the geometry of the unit cell. In general, the number of DOF for each unit cell of BCHn is 2n − 3. Using at least two consecutive rows of small parallelograms, instead of one, in BCHn (fig. S1B) decreases the DOF of BCH to 1, irrespective of the number of n (for more details, see fig. S2 and Section 7-1 in the Supplementary Materials). In addition, the patterns are rigid- and flat-foldable. Moreover, they can be folded from a flat sheet of material (that is, they are developable) (movie S1). Figure 3 presents a few configurations of the patterns.


Unraveling metamaterial properties in zigzag-base folded sheets.

Eidini M, Paulino GH - Sci Adv (2015)

Sample patterns of BCHn and cellular folded metamaterials.(A) A BCH2 sheet. (B) A BCH3 sheet-adding one layer of small parallelograms to the first row reduces the DOF of the system to 1 for rigid origami behavior. (C) Combination of BCH2 and layers of large and small parallelograms with the same geometries as the ones used in BCH2. (D) Combination of BCH3 and layers of large and small parallelograms with the same geometries as the ones used in BCH3. (E) A BCH3 sheet and layers of small parallelograms with the same geometries as the ones used in BCH3. (F) A sheet composed of various BCHn and Miura-ori cells with the same angle ϕ. (G) A stacked cellular metamaterial made from seven layers of folded sheets of BCH2 with two different geometries. (H) Cellular metamaterial made from two layers of 3 × 3 sheets of BCH2 of different heights tailored for stacking and bonded along the joining fold lines. The resulting configuration is flat-foldable in one direction.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 3: Sample patterns of BCHn and cellular folded metamaterials.(A) A BCH2 sheet. (B) A BCH3 sheet-adding one layer of small parallelograms to the first row reduces the DOF of the system to 1 for rigid origami behavior. (C) Combination of BCH2 and layers of large and small parallelograms with the same geometries as the ones used in BCH2. (D) Combination of BCH3 and layers of large and small parallelograms with the same geometries as the ones used in BCH3. (E) A BCH3 sheet and layers of small parallelograms with the same geometries as the ones used in BCH3. (F) A sheet composed of various BCHn and Miura-ori cells with the same angle ϕ. (G) A stacked cellular metamaterial made from seven layers of folded sheets of BCH2 with two different geometries. (H) Cellular metamaterial made from two layers of 3 × 3 sheets of BCH2 of different heights tailored for stacking and bonded along the joining fold lines. The resulting configuration is flat-foldable in one direction.
Mentions: For rigid panels connected via hinges at fold lines, the BCH with n = 2 has only one independent DOF, on the basis of the geometry of the unit cell. In general, the number of DOF for each unit cell of BCHn is 2n − 3. Using at least two consecutive rows of small parallelograms, instead of one, in BCHn (fig. S1B) decreases the DOF of BCH to 1, irrespective of the number of n (for more details, see fig. S2 and Section 7-1 in the Supplementary Materials). In addition, the patterns are rigid- and flat-foldable. Moreover, they can be folded from a flat sheet of material (that is, they are developable) (movie S1). Figure 3 presents a few configurations of the patterns.

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