Programming Shape Using Kirigami Tessellations

Abstract

Kirigami tessellations are regular planar patterns formed by cutting flat, thin sheets that morph into structures with rich geometries and unusual material properties. However, geometric constraints make the development of such materials challenging. Here we describe and solve the inverse problem of designing the number, size, and orientation of cuts that enables the conversion of a closed, compact regular kirigami tessellation into a deployment that conforms approximately to any prescribed target shape in two- and three-dimensions. We identify the constraints on the lengths and angles of generalized kirigami tessellations that guarantee that their reconfigured face geometries can be contracted from a non-trivial deployed shape to a novel planar cut pattern. We then encode these conditions into a flexible constrained optimization framework to obtain general, geometrically deformed kirigami patterns that deploy to a wide variety of prescribed boundary target shapes. Fabricated models validate this inverse design approach, illustrating the potential of kirigami tessellations as flexible mechanical metamaterials.