A Kirigami Approach to Forming a Synthetic Buckliball

The shape transformation of some biological systems inspires scientists to create sophisticated structures at the nano- and macro- scales. However, to be useful in engineering, the mechanics of governing such a spontaneous, parallel and large deformation must be well understood. In this study, a kirigami approach is used to fold a bilayer planar sheet featuring a specific pattern into a buckliball under a certain thermal stimulus. Importantly, this prescribed spherical object can retract into a much smaller sphere due to constructive buckling caused by radially inward displacement. By minimizing the potential strain energy, we obtain a critical temperature, below which the patterned sheet exhibits identical principal curvatures everywhere in the self-folding procedure and above which buckling occurs. The applicability of the theoretical analysis to the self-folding of sheets with a diversity of patterns is verified by the finite element method.