Limits...
Origami-based cellular metamaterial with auxetic, bistable, and self-locking properties

View Article: PubMed Central - PubMed

ABSTRACT

We present a novel cellular metamaterial constructed from Origami building blocks based on Miura-ori fold. The proposed cellular metamaterial exhibits unusual properties some of which stemming from the inherent properties of its Origami building blocks, and others manifesting due to its unique geometrical construction and architecture. These properties include foldability with two fully-folded configurations, auxeticity (i.e., negative Poisson’s ratio), bistability, and self-locking of Origami building blocks to construct load-bearing cellular metamaterials. The kinematics and force response of the cellular metamaterial during folding were studied to investigate the underlying mechanisms resulting in its unique properties using analytical modeling and experiments.

No MeSH data available.


Related in: MedlinePlus

(a) (left image) The Miura-ori can be described by constant angle of α and the single degree of freedom (DOF) which can be defined in terms of dihedral angles, θ, and ξ, and the angle between mountain and front valley folding lines, β. (middle image) Two Miura-ori units are first positioned in a zigzag pattern, then mirrored to form a symmetric structure. (right image) ‘First-order element’, used in developing the Origami-based cellular metamaterial. (b) First-order elements are attached together in three different ways to make a ‘second-order element’ with internal angles, γ1, γ2, and γ3. (c) From all possible closed-loop elements, formed by using second-order elements, only one arrangement leads to a rigid-foldable geometry while the other are all rigid.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC5384242&req=5

f1: (a) (left image) The Miura-ori can be described by constant angle of α and the single degree of freedom (DOF) which can be defined in terms of dihedral angles, θ, and ξ, and the angle between mountain and front valley folding lines, β. (middle image) Two Miura-ori units are first positioned in a zigzag pattern, then mirrored to form a symmetric structure. (right image) ‘First-order element’, used in developing the Origami-based cellular metamaterial. (b) First-order elements are attached together in three different ways to make a ‘second-order element’ with internal angles, γ1, γ2, and γ3. (c) From all possible closed-loop elements, formed by using second-order elements, only one arrangement leads to a rigid-foldable geometry while the other are all rigid.

Mentions: Although an Origami construction relies on a mechanically simple folding operation, discovering the exact sequence of folds for a desired behavior is a combinatorically intractable problem232425. In this context, simplification is possible through an intricate coupling of topology and mechanical compatibility to design periodic fold sequence that can be repeated to create such Origami2627. An example is the pioneering work of Tachi and Miura13, who introduced a type of rigid Origami based on the previously-proposed Miura-ori fold28. Miura-ori is a single degree of freedom (DOF) rigid-foldable Origami shown in Fig. 1(a) – left image. The four crease lines of Miura-ori which result in one mountain and three valley folds define four identical parallelograms with adjacent sides defining an acute angle, α [shown in Fig. 1(a) – left image]. As the flat sheet deforms, these parallelograms become inclined to each other which can be quantified in terms of dihedral angles, , , or the angle between the mountain and front valley folding lines, . Due to the geometrical constraints, only one of these angles (θ, ξ, or β) is independent and can then be used to represent the single DOF of the system in analysis. For example, β and ξ can be expressed in terms of θ, and the constant angle, α, using the following relationships [see Supporting Information for details]:


Origami-based cellular metamaterial with auxetic, bistable, and self-locking properties
(a) (left image) The Miura-ori can be described by constant angle of α and the single degree of freedom (DOF) which can be defined in terms of dihedral angles, θ, and ξ, and the angle between mountain and front valley folding lines, β. (middle image) Two Miura-ori units are first positioned in a zigzag pattern, then mirrored to form a symmetric structure. (right image) ‘First-order element’, used in developing the Origami-based cellular metamaterial. (b) First-order elements are attached together in three different ways to make a ‘second-order element’ with internal angles, γ1, γ2, and γ3. (c) From all possible closed-loop elements, formed by using second-order elements, only one arrangement leads to a rigid-foldable geometry while the other are all rigid.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5384242&req=5

f1: (a) (left image) The Miura-ori can be described by constant angle of α and the single degree of freedom (DOF) which can be defined in terms of dihedral angles, θ, and ξ, and the angle between mountain and front valley folding lines, β. (middle image) Two Miura-ori units are first positioned in a zigzag pattern, then mirrored to form a symmetric structure. (right image) ‘First-order element’, used in developing the Origami-based cellular metamaterial. (b) First-order elements are attached together in three different ways to make a ‘second-order element’ with internal angles, γ1, γ2, and γ3. (c) From all possible closed-loop elements, formed by using second-order elements, only one arrangement leads to a rigid-foldable geometry while the other are all rigid.
Mentions: Although an Origami construction relies on a mechanically simple folding operation, discovering the exact sequence of folds for a desired behavior is a combinatorically intractable problem232425. In this context, simplification is possible through an intricate coupling of topology and mechanical compatibility to design periodic fold sequence that can be repeated to create such Origami2627. An example is the pioneering work of Tachi and Miura13, who introduced a type of rigid Origami based on the previously-proposed Miura-ori fold28. Miura-ori is a single degree of freedom (DOF) rigid-foldable Origami shown in Fig. 1(a) – left image. The four crease lines of Miura-ori which result in one mountain and three valley folds define four identical parallelograms with adjacent sides defining an acute angle, α [shown in Fig. 1(a) – left image]. As the flat sheet deforms, these parallelograms become inclined to each other which can be quantified in terms of dihedral angles, , , or the angle between the mountain and front valley folding lines, . Due to the geometrical constraints, only one of these angles (θ, ξ, or β) is independent and can then be used to represent the single DOF of the system in analysis. For example, β and ξ can be expressed in terms of θ, and the constant angle, α, using the following relationships [see Supporting Information for details]:

View Article: PubMed Central - PubMed

ABSTRACT

We present a novel cellular metamaterial constructed from Origami building blocks based on Miura-ori fold. The proposed cellular metamaterial exhibits unusual properties some of which stemming from the inherent properties of its Origami building blocks, and others manifesting due to its unique geometrical construction and architecture. These properties include foldability with two fully-folded configurations, auxeticity (i.e., negative Poisson’s ratio), bistability, and self-locking of Origami building blocks to construct load-bearing cellular metamaterials. The kinematics and force response of the cellular metamaterial during folding were studied to investigate the underlying mechanisms resulting in its unique properties using analytical modeling and experiments.

No MeSH data available.


Related in: MedlinePlus