Additive Design of Origami and Kirigami

Origami and kirigami, the traditional paper folding and cutting arts, have become a paradigm for mechanical metamaterials in recent years. Previous studies on the design of origami- and kirigami-based structures have primarily focused on simple geometric constructions for limited spaces of origami and kirigami tessellations or global constrained optimization frameworks that are difficult to solve computationally. In this work, we present a novel additive approach for designing origami and kirigami structures. We begin with the smallest building block of origami and kirigami patterns and identify the geometric conditions for the compatibility of adjacent cells, and then move on to strips and finally surfaces. This simple marching construction allows us to create shape-morphing structures from flat sheets at any scale efficiently, and further enables the characterization of the entire design space of generic quad origami and kirigami patterns. Overall, our work opens up a new way for the computational design of shape-shifting structures.