Multi-stability of irregular four-fold origami structures

Origami inspired structures can be reconfigurable and multi-stable. Theoretically, the energy of origami structures based on four-fold rigid origami comes from the deformation of the creases. Although the multi-stability of the Miura origami structures has been indicated, the energy variation of the generalized or irregular four-fold origami structures need to be further investigated. Here, we derive the general energy expressions for both generalized four-fold origami and irregular four-fold origami, and study their multi-stability behavior. Studies on irregular four-fold origami structures are promoted from the previous two-dimensional creases design to the performance analysis of three-dimensional space. We find a reasonable selection of the initial configuration can allow the corresponding origami structure to be multi-stable, on condition that proper pre-stresses are introduced along the creases. Subsequently, we investigate the configuration parameters to make the structures multi-stable. We also derive the expression of the true energy for non-prestressed origami structures. In addition, the corresponding theoretical formulas are verified by the finite element models and the reported results of the classical Miura origami. This facilitates the precise customization of multi-stable configurations and further promotes the development of origami structures.