Gradient Origami Metamaterials for Programming Out‐of‐Plane Curvatures

Abstract

Designer materials, where rationally designed geometry at the small scale gives rise to unusual materials properties at the macro-scale, are often called metamaterials. [1][2][3][4][5][6] Origami structures are a traditional Japanese art, which have recently found their way into metamaterials research due to their powerful capability to transform flat 2D structures into complex 3D structures along their creases. [7] Particularly, Miuraori origami, also known as herringbone geometry (Figure 1a,b), has been proposed as an origami-based mechanical metamaterial. [8] This design was first invented to pack solar panels efficiently, but it is relevant to note that this pattern also occurs in natural structures such as leaves, embryonic intestines, [9] and vertebrate guts. [10] The mathematical richness and tunability of Miura-ori geometry allow using it in different scales from the nanometric level to architecture. [11] The suitability of Miura-ori for engineering applications lies in its four spectacular characteristics: being able to be folded rigidly, having only one degree of freedom, having negative Poisson's ratio, and being flat-foldable. [11] 3D exotic materials with negative Poisson's ratio (known as auxetics metamaterials) offer extreme mechanical properties such as high shear resistance, energy absorption, indentation resistance, and toughness. [12] When used in 2D setting, a structure with spatially incompatible auxetic properties can create various 3D shapes through out-of-plane buckling. [13] Given the richness of the Miura-ori origami, the question that arises here is whether or not it is possible to create basic wellknown Euclidean and non-Euclidean 3D curvatures using Miura-ori metamaterials upon application of an external stimulus such as mechanical load. There have been a few studies that have used origami tessellations to create preprogrammed (not necessarily 3D) curvatures. [8,11,14] In a recent study, [15] homogenization-type two-scale asymptotic method was suggested to reconstruct arbitrary smooth surfaces that can be fitted by a given periodic truss that satisfy a known set of partial differential equations. Two recent studies presented optimization-based method procedures to produce Miura-ori tessellations [11,16] programmed to create 3D geometries with some approximations. Despite attempts to create Miura-ori tessellations which would lead to desired curvatures with some approximations, no study has been carried out on how linearly varying gradient distributions of Miura-ori unit cells (see Figure 1c) can be used to create various well-known 3D curvatures. Linearly varying Miura-ori distributions (rather than nonuniform ones created by numerical models) have the advantages of being easy to understand and thus easy to implement for practical problems, for example as building blocks for complex actuators.

Graded in-plane Miura origami as crawling robots and grippers

“…17 It is recently known that the introduction of the graded patterns on Miura-ori can be exploited as a method to pre-program the out-of-plane curvatures. 18 Although the folding motion of the graded Miura-ori gets blocked when the panels are not allowed to deform, we found that a further folding results in a global in-plane bending and the panels undergo a nonrigid deformation. To the best of our knowledge, such deformation behaviors have not been reported so far.…”

Active Acoustic Metamaterial Based on Helmholtz Resonators to Absorb Broadband Low-Frequency Noise

“…A metamaterial is an artificially engineered material built up of unit cell entities that have physical properties that are beyond those of the constituent material itself [1,2]. Even though there is no exact definition for this class of materials, they exhibit unique physical properties on a macroscopic level, such as negative permittivity [3,4], negative magnetic permeability [5], negative Poisson's ratio [6][7][8][9], negative bulk modulus [10], negative density [10], etc. [11][12][13].…”

Effects of Slit Edge Notches on Mechanical Properties of 3D-Printed PA12 Nylon Kirigami Specimens

“…Due to the significant potential for engineering design applications, researchers have recently explored the mechanical properties of kirigami-inspired structures. Similar to origami structures that fold the planar materials [ 25 ], kirigami-inspired structures are also capable of undergoing out-of-plane deformations. Isobe et al [ 1 ] investigated the mechanical response of the Kent paper and examined the relationship between the geometrical parameters of cuts and the resulting mechanical behavior.…”