Reconfigurable force–displacement profiles of the square-twist origami

Origami structures with reconfigurable mechanical properties are increasingly in demand in engineering applications. The Square-Twist (S-T) origami, featured with excellent reconfigurability and torsional bistability, has a broad application prospect. However, there are relatively few reports on the abundant mechanical properties of S-T origami, especially for those uncommon configurations. In this paper, to analyze the kinematics and mechanics of the unfolding motion, an equivalent theoretical model of the S-T origami is established, which could effectively solve the challenging issues of facet bending, self-contact, and diverse loading directions. With systematic finite element analyses and experimental tests of the S-T origami structures, the effectiveness of the theoretical model along with the optimization-based numerical approach is verified. During the unfolding process, significant distinctions in the potential energy profile and the force–displacement relations among the four different configurations of the S-T origami structure are uncovered. The effects of the design geometry and the material property on the constitutive relations of the S-T origami structure are comprehensively elucidated. Finally, we demonstrate that through folding reconfiguration, an S-T origami structure could exhibit five types of force–displacement relation that are qualitatively different, including bi-stable and mono-stable profiles.