Bending-active kirigami

Kirigami techniques use prescribed arrangements of cuts and fold lines to transform 2D sheet materials into complex 3D forms. These sheet transformations occur via elastic deformations, rigid folding motions, and/or pop-up mechanisms; design techniques for kirigami patterns are correspondingly based on mechanics, kinematics, and physical prototyping. This paper proposes a new family of pop-up kirigami patterns termed ‘bending-active kirigami’, which transform flat sheets into approximated double-curved surfaces using a simple 1-DOF actuation mechanism. A pattern design technique is first developed from a combination of the well-known ‘elastica’ solution for the large elastic deformation of slender rods, with the kinematic constraints imposed by a kirigami pop-up mechanism. This combination creates a rapid and intuitive design method for specification of a formed surface and its constituent kirigami pattern. An extended family of patterns are then developed based on other elastica solutions and pop-up mechanism types. Finally, a bending-active kirigami pattern is applied to the design of a deployable structure, with measurements of a physical prototype used to verify the developed design method.