Here, to enable design practitioners and researchers alike to explore the potential of origami for the design of metamaterials without restrictions to facet or vertex types, we present a computational approach for the design of origami mechanisms and tessellations of arbitrary size and complexity. Recent publications attempt to make the computational design process more efficient and intuitive by subsequentially extending a crease pattern with primitives, but are limited to quadrilateral patterns 24 and discrete sector angles 25 leaving most origami patterns inaccessible for possible applications in the design of metamaterials. Despite their successes, these approaches either solely address shape matching without guaranteeing rigid foldability 18 or target artistic origami 19, are limited to a set of well-studied patterns and vertex degrees 20, 21, 22, or incur considerable computational costs 23. In response, literature reports on a series of efforts to develop computational approaches to ease the design of crease patterns. While origami provided essential principles to realize these applications, the complex relations between crease pattern geometry and folding kinematics make the intuitive design of crease patterns difficult and confined to a set of well-studied patterns 17. Possible applications range across many scientific and engineering domains, involving metamaterials with negative Poisson’s ratios 4, 5, metamaterials with bistable and self-locking properties 5, 6, 7, 8, stacked 9, 10, 11 and multistable metamaterial sheets 8, 12, reconfigurable prismatic metamaterials 13, 14 and origami-inspired tube assemblages 15, 16. ![]() The special property of origami to fold into almost any shape renders their application in the design of metamaterials a conceptually promising direction in which advanced mechanical and physical properties can be configured based on the specific geometries a structure exhibits during the folding motion. An emerging direction to design mechanical metamaterials for new functionalities and complex behavior is in the application of origami. These properties can be controlled by changing the topology and geometry of the unit cell resulting in the purposeful design of cellular structures with advanced macroscopic mechanical and physical properties 1, 2, 3. The properties of mechanical metamaterials strongly depend on the spatial arrangement of their constituent base materials. ![]() Due to its versatility, the approach provides an inexhaustible source of foldable patterns to inspire the design of metamaterials for a wide range of applications. ![]() The versatility of the approach is demonstrated by its capability to not only generate, analyze and optimize regular origami patterns, but also generate and analyze kirigami, generic three-dimensional panel-hinge assemblages and their tessellations. ![]() We build on generalized conditions for rigid foldability of degree- n vertices to design origami patterns of arbitrary size and complexity. Here, we present a generalized approach for the algorithmic design of rigidly-foldable origami structures exhibiting a single kinematic degree of freedom. Although this makes origami a conceptually attractive source of inspiration when designing foldable structures and reconfigurable metamaterials for multiple functionalities, their designs are still based on a set of well-studied patterns leaving the full potential of origami inaccessible for design practitioners and researchers. Origami, the ancient art of paper folding, embodies techniques for transforming a flat sheet of paper into shapes of arbitrary complexity.
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