Circular kirigami structures: from linear elasticity to geometrical limits

Traditionally used for decorative objects, Kirigami structures are currently found in technological applications such as stretchable electronics. Relevant cutting designs indeed promote the apparent stretching of a stiff sheet through the actual bending of the structure at the scale of the cuts. However large-scale deformations are not limited to in-plane stretching. We show how out-of-plane 3D shapes are obtained by cutting alternate arcs in a 2D sheet. Within the limit of linear deformations, we rationalize the appropriate design of the axisymmetric cutting patterns leading to cone, bowl, trumpet or more complex shapes. We also track the geometrical limit corresponding to a full stretching of the structure. Is it possible to maximize the extension or the volume of the 3D structure? What is the range of 3D topographies obtained with such kirigami process?