This paper presents two new types of origami-inspired mechanical metamaterials based on the Miura-derivative fold patterns that consist of non-identical parallelogram facets. The analytical models to predict dimension changes and deformation kinematics of the proposed metamaterials are developed. Furthermore, by modelling the creases as revolute hinges with certain rotational spring constants, we derived analytical models for stretching and bulk moduli. The analytical models are validated through finite-element simulation results. Numerical examples reveal that the proposed metamaterials possess some intriguing properties, including negative Poisson’s ratios and bulk modulus. The work presented in this paper can provide a highly flexible framework for the design of versatile tunable mechanical metamaterials.

The recent development of modular origami structures has ushered in an era for active metamaterials with multiple degrees of freedom (multi-DOF). Notably, no systematic inverse design approach for 3D curvilinear modular origami structures has been reported. Moreover, very few modular origami topologies have been studied to design active metamaterials with multi-DOF. Herein, we develop an inverse design method for constructing 3D reconfigurable architected structures — we synthesize modular origami structures whose unit cells can be volumetrically mapped into a prescribed 3D curvilinear shape followed by volumetric shrinkage to construct modules. After modification of the tubular geometry, we search through all the possible geometric and topological combinations of the modular origami structures to attain the target mobility using a topological reconstruction of modules. Our inverse design using geometric and topological reconstructions can provide an effective solution to construct 3D curvilinear reconfigurable structures with multi-DOF. Our work opens a path toward 3D reconfigurable systems based on volumetric inverse design, such as 3D active metamaterials and 3D morphing devices for automotive, aerospace, and biomedical engineering applications.

Origami geometric design is fundamental to many engineering applications of origami structures. This paper presents a new method for the design of three-dimensional (3D) origami structures suitable for engineering use. Using input point sets specified, respectively, in the x − z and y − z planes of a Cartesian coordinate system, the proposed method generates the coordinates of the vertices of a folded origami structure, whose fold lines are then defined by straight line segments each connecting two adjacent vertices. It is mathematically guaranteed that the origami structures obtained by this method are developable. Moreover, an algorithm to simulate the unfolding process from designed 3D configurations to planar crease patterns is provided. The validity and versatility of the proposed method are demonstrated through several numerical examples ranging from Miura-Ori to cylinder and curved-crease designs. Furthermore, it is shown that the proposed method can be used to design origami structures to support two given surfaces.

This paper presents a mathematical framework for the design of rigid-foldable doubly curved origami tessellations based on trapezoidal crease patterns that can simultaneously fit two target surfaces with rotational symmetry about a common axis. The geometric parameters of the crease pattern and the folding angles of the target folded state are determined through a set of combined geometric and constraint equations. An algorithm to simulate the folding motion of the designed crease pattern is provided. Furthermore, the conditions and procedures to design folded ring structures that are both developable and flat-foldable and stacked folded structures consisting of two layers that can fold independently or compatibly are discussed. The proposed framework has potential applications in designing engineering doubly curved structures such as deployable domes and folded cores for doubly curved sandwich structures on the aircraft.

Cellular mechanical metamaterials based on origami folded structures have attracted much attention due to their high designability in the mechanical properties. While origami cellular metamaterials (OCMs) made of plastics via 3 D printing have been studied extensively, those fabricated by metallic 3 D printing are relatively rare. This article presents a systematical experimental and numerical study on the quasi-static mechanical properties of 3 D-printed metallic OCMs based on various origami configurations and revealed the relationship between their key design parameters and mechanical performance. First, the OCM specimens based on the Miura pattern were fabricated using a metallic 3 D printing method, and compression tests were carried out to obtain their mechanical responses. The experiment results showed that the OCM specimens made from stainless steel exhibited large elastoplastic deformation, whereas early fracture of the material occurred in the aluminum alloy and titanium alloy specimens, and those with smaller cell size and wall thickness showed enhanced mechanical performance. Second, the FE modeling method for the metallic OCMs was developed and validated with the experiment data. Parametric studies on the compressive behaviors of metallic OCM models based on the two-stage Miura, perforated Miura, graded Miura, and cube pipe structures were then conducted. The relationships between the key geometric parameters and mechanical performance of various OCM models were disclosed. This work can provide a practical guide for the design and fabrication of 3 D-printed metallic OCMs.