An additive framework for kirigami design

We present an additive approach for the inverse design of kirigami-based mechanical metamaterials by focusing on empty (negative) spaces instead solid tiles. By considering each negative space as a four-bar linkage, we identify simple recursive relationship between adjacent linkages, yielding efficient method creating kirigami patterns. This allows us to solve problem using elementary linear algebra, with compatibility, reconfigurability and rigid-deployability encoded into iterative procedure involving matrix multiplications. The resulting strategy circumvents solution non-convex global optimization control degrees freedom in deployment angle field, linkage offsets boundary conditions. demonstrate this large variety rigid-deployable, compact, reconfigurable then realize our designs physically two but effective fabrication strategies very different materials. Altogether, approaches routes metamaterial based ori/kirigami art forms.