Mechanical metamaterials have enabled exotic and desirable mechanical properties that are inaccessible with conventional materials owing to their properly engineered repeating microstructures. Origami, which transforms 2D materials into complex 3D structures, is able to provide a geometric design approach independent of scale and material, and hence offers a promising platform for the design of metamaterials. Thus, our laboratory focuses on the design of metamaterials depending on the multilayer origami structures.

1 Origami-inspired Mechanical Metamaterials

A systematic design theory for origami-inspired mechanical metamaterial was developed. This theory made a full use of the inherent folding behavior of origami patterns, and generated large-scale metamaterials through 3D tessellation. Based on this theory, a series of mechanical metamaterials with 3D negative Poisson’s ratio and tunable stiffness were proposed. These mechanical properties of the metamaterials can be programmed by the geometric design parameters of the origami patterns, and by controlling the material properties of the creases and facets of the origami structures.

Origami-based mechanical metamaterials with negative Poison’s ratio in three-dimensions and tunable stiffness

2 Graded Mechanical Metamaterials

A novel graded mechanical metamaterial, both two-dimensional and three-dimensional, was created to adapt to non-uniform environments based on the Miura-ori folding pattern. The geometric parameters of this metamaterial was varied using kinematic analysis to create both rigid foldable and self-locking stages in the configuration. This property gives the graded metamaterial an opportunity to achieve graded stiffness when subjected to quasi-static in-plane or out-of-plane compression, and superior energy absorption capability to uniform tessellating repeat units. Meanwhile, these mechanical responses can be tuned by changing the underlying geometric design.

Graded mechanical metamaterials

3 Waterbomb Based Mechanical Metamaterials

A combined kinematic and structural analysis framework was established to characterize not only the radial expansion/contraction motion of the tubular waterbomb origami, but also a previous unknown twist motion. It was uncovered that the tubular waterbomb could undergo a mechanism-structure-mechanism mode transition during radial folding, leading to an abrupt change in structural stiffness. When it was fully squeezed, a twist motion was followed, thereby achieving coupled compression-twist deformation. Moreover, the twist motion was also featured by a mechanism-structure transition and sharp change in stiffness. Based on the results, a series of mechanical metamaterials with programmable stiffness, shape modulation, and compression-twist mode were developed.

Waterbomb based mechanical metamaterials subjected to radial deployment (top), effects of geometric parameters on mechanism-structure-mechanism transition (middle), and variation in stiffness (bottom)

Waterbomb based mechanical metamaterials subjected to counter-clockwise and clockwise twist (top), and effects of geometric parameters on twist angle (bottom)

4 Square-twist Based Mechanical Metamaterials

The rigid foldability and kinematics of the square-twist origami patterns with four different mountain-valley assignments was systematically studied based on the kinematic motion transmission path. The explicit kinematic equations were derived for the rigidly foldable cases. Furthermore, a method to convert a non-rigid-foldable pattern into a rigid-foldable one by introducing an extra crease was proposed, based on which a theoretical model was established to characterize a non-rigid-foldable pattern by its rigid origami counterpart. Using the theoretical model, it was for the first time discovered that the non-rigid-foldable square-twist pattern type 2 and its rigid-foldable counterpart type 2M bifurcated during tension to follow a low-energy deformation path.

Kinematic analysis of the square-twist pattern with four mountain-valley assignments

Two different kinematic paths of the type 2M pattern together with six representative configurations on each path

Bifurcation and mechanical behaviors of the type 2 and type 2M square-twist patterns

5 Modular Origami Based Wave Metamaterials

A transformable mechanical metamaterial is proposed based on modular origami, realizing all seven different zero modes covering null-mode (solid state) to hexa-mode (near-gaseous state) and the reversible transformation among configurations for the first time. By importing orthogonally decoupled 3D modular origami design, the zero mode was corresponding to the motion angle of the linkages, achieving independent programmability of zero mode in various directions, obtaining subdivision zero mode configurations covering null-mode to hexa-mode. All ten configurations are able to be reversibly transformed from one state to another, which is verified by the 3D-printed Thermoplastic Polyurethanes prototypes and static experiments. dynamic experiments are conducted to validate the reprogrammable polarized wave control ability in different dimensions. The reported design methodology also provides a versatile tool to engineer flexible metamaterials in various scales and domains (such as mechanics, acoustics and photonics).

In terms of 3D penta-mode metamaterials, a novel 3D penta-mode metamaterial design is proposed based on truncated octahedron topology. The configurations of regular truncated octahedron and transformed truncated octahedron exhibit isotropic and anisotropic penta-mode property, respectively, and there are three or more orders of magnitude of broad tunable range. With the proposed transformable anisotropic penta-mode metamaterial, we demonstrate the adjustable wave velocity and impedance, which can be further harnessed for the novel 3D waveguide design.

Engineering zero modes in transformable mechanical metamaterials

Transformable anisotropic 3D penta-mode metamaterial