# An additive framework for kirigami design

arXiv: https://arxiv.org/abs/2207.01810 · HTML: https://mlsanity.com/paper/2207.01810/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jul 2022.

## Built on by (most cited first, 2 of 2)

- [A cyclical route linking fundamental mechanism and AI algorithm: An example from tuning Poisson's ratio in amorphous networks](https://mlsanity.com/paper/2312.03404/) (2023)
- [Reinforcement learning for inverse silhouette design and rapid laser cutting of compact parallelogram quad kirigami prototypes](https://mlsanity.com/paper/2605.08098/) (2026)

## Abstract (arXiv)

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