Recoverable and Programmable Collapse from Folding Pressurized Origami Cellular Solids

We report a unique collapse mechanism by exploiting the negative stiffness observed in the folding of an origami solid, which consists of pressurized cells made by stacking origami sheets. Such a collapse mechanism is recoverable, since it only involves rigid folding of the origami sheets and it is programmable by pressure control and the custom design of the crease pattern. The collapse mechanism features many attractive characteristics for applications such as energy absorption. The reported results also suggest a new branch of origami study focused on its nonlinear mechanics associated with folding.

Figure 1

Recoverable collapse from an example of a pressurized origami cellular solid. (a) Stacking origami sheets into a cellular solid with naturally embedded tubular channels. (b) A 3D printed channel prototype based on the Miura-Ori crease for a pressure-induced stiffness and collapse test. (c) The force-deformation relationships. Solid and dashed curves are analytical results; squares and diamonds are averaged experimental results. To-scale geometries of the Miura-Ori solids are illustrated at different important configurations: (0) flat sheet, (1) maximum volume configuration, (2) collapsing point, and (3) fully folded configuration.

Figure 2

Adopting single collinear vertices to program the collapse behavior. (a) A single collinear rigid-foldable origami sheet, where the elementary vertex unit is highlighted. (b) Identical origami sheets can be stacked into a cellular solid, where the equivalent vertices are labeled on both sheets to illustrate the stacking arrangement. (c) Force-displacement relationship based on an example design: ${\gamma }_1=60°$, ${\gamma }_2=75°$, $a_1=38\mathrm{mm}$, $a_2=57\mathrm{mm}$, $b_1=38\mathrm{mm}$, and $b_2=19\mathrm{mm}$. Notice that the negative stiffness region stops before the origami is fully folded to $L=0$. (d) To-scale geometry of the origami cellular solids, with the unit cell being highlighted.

Figure 3

The collapse performance based on different origami designs. (a) Normalized force-deformation curves of flat-foldable origami. (b) The lengths of a flat-foldable origami unit cell at different important configurations. The inset is the solution of Eq. (6). (c)–(h) Normalized collapse performance corresponding to generic single collinear creases, where the insets in (f) and (g) are achievable ranges of combinations of ${\widehat{L}}^m$, ${\widehat{L}}^c$, and ${\widehat{L}}^l$. $\beta =1$ in these figures, and figures with $\beta =2$ and 0.5 are in Appendix Sec. V [30].

Figure 4

Integrating different cells into a solid. (a) Two different sheets that meet specific geometric constraints can be stacked seamlessly together and form a foldable solid with three types of cells (b). (c) A 3D printed tricell prototype for concept testing, in this design: ${\gamma }_1^A={\gamma }_1^B=70°$, $\beta =1$, and $a^B=1.35a^A$. (d) Normalized collapse performance of the prototype design. The solid points are the corresponding averaged experimental results. (e) Normalized collapse performances from a generic single collinear design: ${\gamma }_1^A=45°$, ${\gamma }_1^B=70°$, $\beta =1$, and $a^B=1.25a^A$.