Self-deployable contracting-cord metamaterials with tunable mechanical properties

TL;DR

This work introduces self-deployable contracting-cord metamaterials that achieve continuous post-deployment tunability of stiffness and damping via bead-based particle jamming (CCPJ). A single actuation system threads contracting cords through concavo-convex beads, enabling self-assembly into preprogrammed configurations, with further contraction modulating mechanical properties while preserving structure. Experimental and numerical results show dramatic tunability in bending-dominated configurations, with stiffness exceeding $>35\times$ and damping changes of $>50\%$, driven by geometric nonlinearity from bead cone angles. The approach yields lightweight, reversible, and tunable metamaterials with potential impact in soft robotics, reconfigurable architectures, and space engineering.

Abstract

Recent advances in active materials and fabrication techniques have enabled the production of cyclically self-deployable metamaterials with an expanded functionality space. However, designing metamaterials that possess continuously tunable mechanical properties after self-deployment remains a challenge, notwithstanding its importance. Inspired by push puppets, we introduce an efficient design strategy to create reversibly self-deployable metamaterials with continuously tunable post-deployment stiffness and damping. Our metamaterial comprises contracting actuators threaded through beads with matching conical concavo-convex interfaces in networked chains. The slack network conforms to arbitrary shapes, but when actuated, it self-assembles into a preprogrammed configuration with beads gathered together. Further contraction of the actuators can dynamically tune the assembly's mechanical properties through the beads' particle jamming, while maintaining the overall structure with minimal change. We show that, after deployment, such metamaterials exhibit pronounced tunability in bending-dominated configurations: they can become more than 35 times stiffer and change their damping capability by over 50%. Through systematic analysis, we find that the beads'conical angle can introduce geometric nonlinearity, which has a major effect on the self-deployability and tunability of the metamaterial. Our work provides routes towards reversibly self-deployable, lightweight, and tunable metamaterials, with potential applications in soft robotics, reconfigurable architectures, and space engineering.

Figures (42)

• Figure 1: The concept and prototype of the self-deployable contracting-cord mechanical metamaterials.(A) The metamaterial is inspired by push puppets. (B-D) The self-deployment and mechanical properties tuning process of a fundamental beam of the proposed mechanical metamaterials. (B) Image of an undeployed beam---composed of beads threaded by a contracting string-like actuator---in the soft state. (C) Self-assembly of the beads shown in b, after a contracting tension is applied through the actuator. (D) Image of the jammed beam, becoming a stiff load-bearing structure with further contraction of the actuator. (E) Self-deployment and mechanical property tuning of a $2\times2\times2$ cubic lattice. Top: The lattice changes from a soft unassembled state to a deployed state with tension generated by the embedded actuators. Bottom: After deployment, a lattice with low string tension can capture a dropped ball by dissipating the kinetic energy through extensive damping. However, a ball dropped on the same lattice with high string tension will bounce back due to its increased stiffness. Note that the weights attached to the beam in (C) and (D) are selectively brightened in the images for visualization purposes.
• Figure 2: Characterization of a CCPJ-based beam with variable applied contracting tension.(A) The deformation and von Misses stress distribution of a beam under bending loading and unloading. The beam is composed of 11 concavo-convex beads with a 40$^\circ$ cone angle (CAD model shown in the insert) and the string pretensioned at 50 N. (B) Experimentally measured force-displacement curves at different initial contracting tensions. The coloured lines represent the average values, and the shaded areas represent the standard deviations between three different tests. (C) Bending, tensile, and compressive test apparent modulus as a function of the initial contracting tension. The shaded areas represent the standard deviation between three different tests. (D) Loss factor, representing the damping capability, as a function of the contracting tension, for bending, tensile, and compressive tests. The shaded areas are the standard deviation between three different tests.
• Figure 3: Relating the tunability of mechanical properties to cone angle.(A) The tunability of the apparent bending modulus, $\delta\textsubscript{E}$, as a function of bead cone angle, $\alpha$, as determined by experimental characterization. $\delta\textsubscript{E}$ is defined as the ratio of the apparent bending modulus at 120 N over the modulus at 10 N. (B) The tunability of loss factor, $\delta_{\eta}$, as a function of bead cone angle for bending tests. The shaded areas represent the standard deviation between three different tests. See Methods for a detailed definition of $\delta\textsubscript{E}$ and $\delta_{\eta}$. (C-E) The simulated deformation and von Misses stress distribution of three beams (with beads having 40$^\circ$, 70$^\circ$, and 80$^\circ$ cone angles) under bending indentation up to 1 mm. The strings are pretensioned to 120 N.
• Figure 4: Characterizing self-deployment of an individual beam.(A) Testing schematic. Beads assemble into a vertical beam against gravity, driven by a nylon string under tension induced by dropping a one-kilogram weight. (B) Image of a deployed beam with beads of 40$^{\circ}$ cone angle, showing a high alignment accuracy. (C) Image of an assembled beam with beads of 80$^{\circ}$ cone angle, displaying a large offset, $\Delta x$, between the cap and end beads. (D) A typical deployment failure mode---locking occurs mostly between last two beads. (E) Success rate and alignment accuracy as a function of cone angle. The success rate is calculated as the ratio of successful attempts over 20 trials. The alignment error is defined as the ratio of the outer diameter of the beads over the offset ($\Delta x/D_O$). Error bars represent the deviation between three different tests.
• Figure 5: Characterization of a single metamaterial unit cell.(A) Labeled image of a bending-dominated lattice. Each beam in the lattice was assembled with a pre-tensioned nylon string. Beams were connected into two squares using customized 3D printed joints. Four rigid bars were used to connect these two squares. Two of the rigid bars provide connectors for interfacing with Instron clamps. (B) Measured force-displacement curves at different contracting tensions for the bending-dominated lattice. The coloured lines represent the average values, and the shaded areas represent the standard deviation between three different tests. (C) Image of a stretching-dominated lattice. Two diagonal beams distinguish its structure from the bending-dominated lattice. (D) Measured force-displacement curves at different contracting tensions for the stretching-dominated lattice. The coloured lines represent the average values, and the shaded areas represent the standard deviation between three different tests. (E) Normalized stiffness, $\overline{K}$, of lattices as a function of contracting tension. The stiffness at different contracting tensions is normalized over the stiffness at 0 N tension. The insert shows non-normalized stiffness. (F) Normalized loss factor, $\overline{\eta}$, as a function of contracting tension. The loss factor is normalized over the value at 0 N tension. The insert shows the non-normalized loss factor.