Bistable morphology analysis of the flexible single-vertex origami unit cell

Abstract

In origami structures, it is necessary to study the novel properties of the single-vertex origami unit cell first, which is the basic unit that could be assembled into a large-scale origami tessellation with complex patterns. When the elasticity of the sheet and the kinematics of the crease are combined, nearly all single-vertex origami unit cells with an arbitrary crease pattern are foldable and bistable. In this case, the stable morphology of the unit cell is dominated by both the crease rotation and the shell deformation. In this work, two models are proposed for the solution of the bistability of the flexible origami unit cell. First, a flexible boundary conical shell model is proposed, by introducing crease mechanics based on the previous work. This linear model can be easily solved for flexible f-cones with arbitrary crease patterns by a certain assembly scheme. Moreover, to consider the nonlinearity, the discrete creased model (DCM) is further developed for the stable state solution of the arbitrary origami unit cell. Thereafter, the results obtained by the two models are verified with the corresponding FE simulations. Based on the normalized crease stiffness, the coupling effect between the crease and the shell is analyzed. The core deformation mechanism of flexible origami unit cells is classified into three cases: the crease-dominated case, the crease-shell coupled case, and the shell-dominated case. Additionally, the energy ratio of crease rotation to shell bending at the snapping state is found to be approximately proportional to the normalized crease stiffness.