Soft Deployable Structures via Core-Shell Inflatables

Deployable structures capable of significant geometric reconfigurations are ubiquitous in nature. While engineering contraptions typically comprise articulated rigid elements, soft structures that experience material growth for deployment mostly remain the handiwork of biology, e.g., when winged insects deploy their wings during metamorphosis. Here we perform experiments and develop formal models to rationalize the previously unexplored physics of soft deployable structures using core-shell inflatables. We first derive a Maxwell construction to model the expansion of a hyperelastic cylindrical core constrained by a rigid shell. Based on these results, we identify a strategy to obtain synchronized deployment in soft networks. We then show that a single actuated element behaves as an elastic beam with a pressure-dependent bending stiffness which allows us to model complex deployed networks and demonstrate the ability to reconfigure their final shape. Finally, we generalize our results to obtain three-dimensional elastic gridshells, demonstrating our approach’s applicability to assemble complex structures using core-shell inflatables as building blocks. Our results leverage material and geometric nonlinearities to create a low-energy pathway to growth and reconfiguration for soft deployable structures.

Figure 1

Veinlike deployable structure. (a) Images of a cicada deploying its wings following molting its exoskeleton (Tacio Philip Sansonovski/Shutterstock.com). (b) Sequence of images showing a winglike structure that expands synchronously in a plane as pressure increases (scale bar, 15 cm). The prediction of the shape by elastic beams is drawn in red.

Figure 2

Inflation of core-shell balloons. (a) Representative pressure curves of the tubes during inflation. The solid lines represent wrinkled shells, the dashed lines represent straight shells, and the dotted line is no shell. Color represents the core-shell radius ratio [see the color bar in (c)]. The inset shows typical images of core-shell inflation (scale bar, 30 cm). (b) Schematic for the Maxwell construction for the bulging of a cylindrical balloon and a core-shell balloon. (c) Plot of the pressure drop against the core-shell radius ratio. Markers represent experiments (circles: $R=3.7\mathrm{mm}$, squares: $R=7.3\mathrm{mm}$) and finite element simulations (diamonds). The line is the Maxwell construction model (see SM [35] Section 1). The error bars represent the range of the pressure measurements in the plateaued region following the bulging instability. (d) Plot of the accumulated length for a balloon system and core-shell system during inflation. Inset shows schematic of experiment.

Figure 3

Mechanics of inflated core-shell structures. (a) Force displacement curves of core-shell inflatables undergoing three point bending tests at different pressures. Color represents pressure [see color bar (b)]. (b) The effective bending stiffness $B_{\mathrm{eq}}$ plotted against the pressure difference $P$. Error bars show the local stiffness’s standard deviation for the deflection range measured. (c) Images of an inflatable network where the pressures $P$ of the inner and outer beams are controlled independently (scale bar, 30 cm) compared to our model. (d) Amplitude of the inner beam deflection from (c) plotted against the outer beam stiffness: inner beam stiffness ratio. Markers are experimental data [triangle markers represent images in (c)]. The lines are the predicted amplitudes from our model. Error bars are smaller than the markers.

Figure 4

Deployable elastic gridshells. (a) Design process for a deployable elastic gridshell from core-shell inflatables. (b) Inflation of a deployable elastic gridshell (scale bar, 25 cm).