On local kirigami mechanics I: Isometric conical solutions

Over the past decade, kirigami--the Japanese art of paper cutting--has been playing an increasing role in emerging field mechanical metamaterials and a myriad other applications. Nonetheless, deep understanding mathematics mechanics kirigami structures is yet to be achieved order unlock their full potential pioneer more advanced applications field. In this work, we study most fundamental geometric building block kirigami: thin sheet with single cut. We consider reduced two-dimensional plate model circular disk radial slit investigate its deformation following opening rotation lips. isometric limit--as thickness approaches zero--the elastic energy has no stretching contribution takes conical shape known as e-cone. solve post-buckling problem for e-cone geometrically nonlinear setting assuming Saint Venant-Kirchhoff constitutive model; find closed-form expressions stress fields show geometry governed by spherical elastica problem. This allows us fully map out space solutions stability post-buckled mirror symmetric boundary conditions on lips open slit.