Elastic theory of origami-based metamaterials

Brunck, V.; Lechenault, Frédéric; Reid, Austin; Adda-Bedia, Mokhtar

doi:10.1103/physreve.93.033005

Cited by 91 publications

(60 citation statements)

References 28 publications

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“…In the standard paradigm for self-folding origami, an initially unfolded sheet is "programmed" by setting the equilibrium dihedral angle of each fold to a nonzero value [2,8,10,20]. One illustrative self-folding energy functional takes the form …”

Section: Discussionmentioning

confidence: 99%

“…III C). This phenomenon is well known in the origami community [35] and an illuminating example is the six-fold origami vertex with alternating mountain and valley folds (MVMVMV in cyclic order around the vertex) called the "waterbomb structure" [8,20]. Since the distribution of mountain and valley folds does not distinguish different branches in configuration space, and further, since it is hard to guess which MV assignments are allowed, the question remains, is there anything that does distinguish those branches from each other?…”

Section: Duplicatesmentioning

confidence: 99%

“…This attractive design paradigm suggests the use of origami as the foundation for mechanical metamaterials [9][10][11][12][13][14] and deployable structures [15,16]. Yet, flexibility is both a blessing and a curse: a single origami crease pattern can admit many different folding pathways [17][18][19] and, indeed, manipulating a nearly unfolded origami structure with one's hands (e.g., the "map-folding problem") illustrates the competition between pathways that can impede folding to a specific desired configuration [2,8,10,20].…”

Section: Introductionmentioning

confidence: 99%

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Branches of Triangulated Origami Near the Unfolded State

Chen

Santangelo

2018

Phys. Rev. X

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Origami structures are characterized by a network of folds and vertices joining unbendable plates. For applications to mechanical design and self-folding structures, it is essential to understand the interplay between the set of folds in the unfolded origami and the possible 3D folded configurations. When deforming a structure that has been folded, one can often linearize the geometric constraints, but the degeneracy of the unfolded state makes a linear approach impossible there. We derive a theory for the second-order infinitesimal rigidity of an initially unfolded triangulated origami structure and use it to study the set of nearly unfolded configurations of origami with four boundary vertices. We find that locally, this set consists of a number of distinct "branches" which intersect at the unfolded state, and that the number of these branches is exponential in the number of vertices. We find numerical and analytical evidence that suggests that the branches are characterized by choosing each internal vertex to either "pop up" or "pop down." The large number of pathways along which one can fold an initially unfolded origami structure strongly indicates that a generic structure is likely to become trapped in a "misfolded" state. Thus, new techniques for creating self-folding origami are likely necessary; controlling the popping state of the vertices may be one possibility.

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Section: Discussionmentioning

confidence: 99%

Section: Duplicatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Branches of Triangulated Origami Near the Unfolded State

Chen

Santangelo

2018

Phys. Rev. X

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“…Recently, the principle of origami and kirigami has received growing attention from the research communities of both science and engineering [7][8][9][10][11], due to their promising potentials in a wide range of applications ranging from reconfigurable architected materials [12][13][14][15], deformable batteries [16,17], microscale 3D self-assembly [18][19][20][21], energy absorption [22], topological mechanics [23] and compact deployable structures [3,[24][25][26]. In particular, the intriguing mechanical properties of origami/kirigami structures, such as auxiticity, afford significant advantages in building mechanical metamaterials [27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Patterning Curved Three-Dimensional Structures With Programmable Kirigami Designs

Wang

Guo

et al. 2017

Journal of Applied Mechanics

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Originated from the art of paper cutting and folding, kirigami and origami have shown promising applications in a broad range of scientific and engineering fields. Developments of kirigami-inspired inverse design methods that map target three-dimensional (3D) geometries into two dimensional (2D) patterns of cuts and creases are desired to serve as guidelines for practical applications. In this paper, using programmed kirigami tessellations, we propose two design methods to approximate the geometries of developable surfaces and non-zero Gauss curvature surfaces with rotational symmetry. In the first method, a periodic array of kirigami pattern with spatially varying geometric parameters is obtained, allowing formation of developable surfaces of desired curvature distribution and thickness, through controlled shrinkage and bending deformations. In the second method, another type of kirigami tessellations, in combination with Miura origami, is proposed to approximate non-developable surfaces with rotational symmetry. Both methods are validated by experiments of folding patterned thin copper films into desired 3D structures. The mechanical behaviors of the kirigami designs are investigated using analytical modeling and finite element simulations. The proposed methods extend the design space of mechanical metamaterials, and are expected to be useful for kirigami-inspired applications.

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“…In this case, self-avoidance and kinematic constrains impose relations between the different crease angles of a given origami structure [10,23] that constraint the corresponding degrees of freedom. While this model is fine for origami-like systems with rigid structure such as solar panels or dome constructions [24], it fails to describe either the deformation of faces in folded membranes [11] or the "snapping" of peculiar bistable origami systems [12,[25][26][27]. For that, one should take into account both the flexibility of the faces and the mechanical properties of the crease.…”

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confidence: 99%

Local mechanical description of an elastic fold

2019

Self Cite

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To go beyond the simple model for the fold as two flexible surfaces or faces linked by a crease that behaves as an elastic hinge, we carefully shape and anneal a crease within a polymer sheet and study its mechanical response. First, we carry out an experimental study that consists on recording both the shape of the fold in various loading configurations and the associated force needed to deform it. Then, an elastic model of the fold is built upon a continuous description of both the faces and the crease as a thin sheet with a non flat reference configuration. The comparison between the model and experiments yields the local fold properties and explains the significant differences we observe between tensile and compression regimes. Furthermore, an asymptotic study of the fold deformation enables us to determine the local shape of the crease and identify the origin of its mechanical behaviour.The process of folding solves the necessity to reduce the space occupied by a large slender object, while keeping the possibility to recover its original shape. Examples of this mechanism are common in nature such as leaves which grow folded inside buds before blooming [1][2][3] or insects that fold their wings inside shells on ground and deploy them on flight [4][5][6]. To add to their mandatory use, folds allow for shaping on demand three-dimensional structures starting from a two-dimensional thin plate [7].Two extreme examples of such objects are crumpled paper [8,9] and origami. The latter is literally the art of folding paper with a specific pattern into sculptures such as the famous paper crane. While origami can be pleasing to the eye, the selection of specific folding patterns generates original properties for the resulting object such as an apparent negative Poisson ratio [10]. When coupled with the elasticity of the constituent material, origami-based metamaterials are able to generate structures with a wide scope of programmable mechanical properties [11][12][13][14] and shapes [15][16][17]. The apparent scalability of origami allows for applications that range from small scales with the folding of DNA strands [18] or tunable microscopic origami machines [19] to large scales with biological systems [20,21] or the transport of deployable structures in space [22].Before studying origami patterns made of a complex network of folds, one should first decipher the behaviour of their most fundamental element: a single fold. Frequently, a fold is defined as two planar surfaces linked by a hinge-like crease setting an angular discontinuity in the structure. From there, different assumptions are made on its properties. If one considers a pure geometrical approach, the faces are assumed to be rigid panels while the crease angle is a degree of freedom of the system. In this case, self-avoidance and kinematic constrains impose relations between the different crease angles of a given origami structure [10,23] that constraint the corresponding degrees of freedom. While this model is fine for origami-like systems with rigid struct...

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Elastic theory of origami-based metamaterials

Cited by 91 publications

References 28 publications

Branches of Triangulated Origami Near the Unfolded State

Branches of Triangulated Origami Near the Unfolded State

Patterning Curved Three-Dimensional Structures With Programmable Kirigami Designs

Local mechanical description of an elastic fold

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