Inverse Kirigami Design

The basic building block of any kirigami pattern is a periodic planar motif with cuts that allow the unit cell to open or close via planar rotations. The tessellations of the plane can take many forms - quads, kagome lattices, and even Islamic tilings. Recent work has explored these geometries in the context of mechanical metamaterials, and focused primarily on the forward problem - given a topology and geometry of the kirigami pattern, how does it deploy and what are the mechanical properties of the structure. In this work, we pose and solve the inverse problem of designing the number, size, and orientation of cuts that allows us to convert a closed, compact regular kirigami tessellation of the plane into a deployment that conforms approximately to any prescribed target shape in two and three dimensions.