Multi-stability of irregular four-fold origami structures

Origami-inspired structures can manifest a range of interesting characteristics such as reconfigurability and multi-stablity. Theoretically, the energy of rigid-foldable origami structures is a result of deformations in their creases. Although the multi-stability of the classic double-corrugated origami (or the Miura-ori) has been studied extensively, the energy variation analysis of its generalized derivatives such as those with less symmetric unit fragments need to be further investigated. Here, we derive the general energy equations and study the multistability behavior of certain low-symmetry double-corrugated origami tessellations. In particular, studies on the double-corrugated origami pattern with maximally asymmetric octagonal unit fragments are extended from our previous research on the design of two-dimensional patterns to their deformation and energy analyses in the three-dimensional space. We demonstrate that a reasonable selection of initial design configuration parameters can enable the corresponding origami structure to be multi-stable, on condition that appropriate pre-stresses are introduced to the crease pattern. We also derive the energy equations of non-prestressed origami structures with the abovementioned geometric design specifications. In addition, the obtained theoretical formulas are verified by finite element models, as well as against some previously reported results for the classical Miura-ori. The findings of this study enable the precise customization of multi-stable origami design configurations and facilitate the development of more complex origami structures.