An additive framework for kirigami design

TL;DR

This paper introduces an additive, linear algebra-based method for designing kirigami patterns that ensures reconfigurability and deployability, simplifying the process and enabling diverse mechanical metamaterials.

Contribution

It presents a novel recursive and additive framework for inverse kirigami design that avoids complex optimization and facilitates physical fabrication.

Findings

Efficient linear algebra-based design method for kirigami patterns.

Ability to create reconfigurable and deployable kirigami structures.

Successful physical realization using simple fabrication strategies.

Abstract

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.