This paper presents two new types of origamiinspired mechanical metamaterials based on the Miura-derivative fold patterns that consist of nonidentical 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.

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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.

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