Strain Reversal in Actuated Origami Structures

Origami in engineering is gaining interest for its potential as deployable or shape-adaptive structures. Practical systems could employ a network of actuators distributed across the structure to induce these deformations. Selecting the actuator locations requires an understanding of how the effect of a single actuator propagates spatially in an origami structure. We combine experimental results, finite element analysis, and reduced-order bar-and-hinge models to show how a localized static actuation decays elastically in Miura-ori tubes and sheets. We observe a strain reversal, before the origami structure springs back to the initial configuration further away from the point of actuation. The strain reversal is the result of bending of the facets, while the spring back requires in-plane facet deformations.

Figure 1

A localized actuation, here compressing a unit cell, at one end of a Miura-ori tube propagates along its length. The deformation elastically decays away from the source, eventually returning to the unperturbed shape. This elastic decay is a result of facet deformations, which alter the unit cell kinematics.

Figure 2

(a) Geometric parameters of a Miura-ori unit cell. Angle $\eta$ is used to characterize the unit cell deformation. (b) Physical model of Miura-ori tube used in the experiments.

Figure 3

Comparison of experimental results and numerical models. The unit cell deformation $\widehat{\eta }$ is plotted along the length of the tube. Both experimental and FEA results show a strain reversal of the unit cells ($\widehat{\eta }<0$), before springing back to the original configuration ($\widehat{\eta }=0$).

Figure 4

The nonlinear merlin2 and linear bar-and-hinge model capture the behavior accurately compared to FEA, where $k_F=0.1\mathrm{N}/\mathrm{rad}$, $k_B=1.3\mathrm{N}/\mathrm{rad}$, and $k_S=1.0\mathrm{N}/\mathrm{m}$.

Figure 5

Effect of stiffness parameters on localization of actuation in a Miura-ori tube. (a) Ratio ${\mu }_{FB}$ of fold and bending stiffness is varied for infinite in-plane stiffness ($k_S=\infty$). (b) Ratio ${\mu }_{FS}$ of fold and in-plane stiffness is varied for flat facets ($k_B=\infty$).

Figure 6

A transition from infinite to realistic in-plane facet stiffness, where ${\mu }_{FB}=0.1$ and $k_B=0.1\mathrm{N}/\mathrm{rad}$.