Kirigami patterns generate non-trivial three dimensional behavior from perforated sheets, and so offer a promising means for developing mechanical metamaterials. To create a generic account of the mechanical behavior of kirigami, we study the unit cell of a typical kirigami structure: an isolated frame. The mechanical behavior of the entire sheet may then be understood in terms of the coupling of many individual frames.
Recent developments in a geometric formulation of elasticity theory paved the way for a mathematical description of such isolated frames using the concept of “geometric charges". In this approach the mechanical problem of Kirigami and coupled frames is transformed to a simpler problem of interacting geometric charges.
In this talk I will present experimental and theoretical results on the relation between Kirigami, the geometric approach to elasticity, and geometric charges. I will show how these results provide simple rules for designing nontrivial Kirigami patterns.