Bending Instability of Rod-Shaped Bacteria

Reversible kink instability drives ultrafast jumping in nematodes and soft robots

Entomopathogenic nematodes (EPNs) exhibit a bending-elastic instability, or kink, before becoming airborne, a feature previously hypothesized but not substantiated to enhance jumping performance. Here, we provide the evidence that this kink is crucial for improving launch performance. We demonstrate that EPNs actively modulate their aspect ratio, forming a liquid-latched α-shaped loop over a slow timescale [Formula: see text] (1 second), and then rapidly open it [Formula: see text] (10 microseconds), achieving heights of 20 body lengths and generating power of ∼104 watts per kilogram. Using a bioinspired physical model [termed the soft jumping model (SoftJM)], we explored the mechanisms and implications of this kink. EPNs control their takeoff direction by adjusting their head position and center of mass, a mechanism verified through phase maps of jump directions in numerical simulations and SoftJM experiments. Our findings reveal that the reversible kink instability at the point of highest curvature on the ventral side enhances energy storage using the nematode's limited muscular force. We investigated the effect of the aspect ratio on kink instability and jumping performance using SoftJM and quantified EPN cuticle stiffness with atomic force microscopy measurements, comparing these findings with those of Caenorhabditis elegans. This investigation led to a stiffness-modified SoftJM design with a carbon fiber backbone, achieving jumps of ∼25 body lengths. Our study reveals how harnessing kink instabilities, a typical failure mode, enables bidirectional jumping in soft robots on complex substrates like sand, offering an approach for designing limbless robots for controlled jumping, locomotion, and even planetary exploration.

Mechanics of pressurized cellular sheets

Everyday experience shows that cellular sheets are stiffened by the presence of a pressurized gas: from bicycle inner tubes to bubble wrap, the presence of an internal pressure increases the stiffness of otherwise floppy structures. The same is true of plants, with turgor pressure (due to the presence of water) taking the place of gas pressure; indeed, in the absence of water, many plants wilt. However, the mechanical basis of this stiffening is somewhat opaque: simple attempts to rationalize it suggest that the stiffness should be independent of the pressure, at odds with everyday experience. Here, we study the mechanics of sheets that are a single-cell thick and show how a pressure-dependent bending stiffness may arise. Our model rationalizes observations of turgor-driven shrinkage in plant cells and also suggests that turgor is unlikely to provide significant structural support in many monolayer leaves, such as those found in mosses. However, for such systems, turgor does provide a way to control leaf shape, in accordance with observations of curling upon drying of moss leaves. Guided by our results, we also present a biomimetic actuator that uncurls upon pressurization.

Mechanics and wrinkling patterns of pressurized bent tubes

Take a drinking straw and bend it from its ends. After sufficient bending, the tube buckles forming a kink, where the curvature is localized in a very small area. This instability, known generally as the Brazier effect, is inherent to thin-walled cylindrical shells, which are particularly ubiquitous in living systems, such as rod-shaped bacteria. However, tubular biological structures are often pressurized, and the knowledge of the mechanical response upon bending in this scenario is limited. In this work, we use a computational model to study the mechanical response and the deformations as a result of bending pressurized tubes. In addition, we develop a model inspired by tension-field theory to analytically describe the mechanical behavior before and after the wrinkling transition. Furthermore, we investigate the development and evolution of wrinkle patterns beyond the instability, showing different wrinkled configurations. We discover the existence of a multiwavelength mode following the purely sinusoidal wrinkles and anticipating the kinked configuration of the tube.

Non-Classical Euler Buckling and Brazier Instability in Cylindrical Liquid Droplets

Crystalline monolayers prevalent in nature and technology possess elusive elastic properties with important implications in fundamental physics, biology, and nanotechnology. Leveraging the recently discovered shape transitions of oil-in-water emulsion droplets, upon which these droplets adopt cylindrical shapes and elongate, we investigate the elastic characteristics of the crystalline monolayers covering their interfaces. To unravel the conditions governing Euler buckling and Brazier kink formation in these cylindrical tubular interfacial crystals, we strain the elongating cylindrical droplets within confining microfluidic wells. Our experiments unveil a nonclassical relation between the Young's modulus and the bending modulus of these crystals. Intriguingly, this relation varies with the radius of the cylindrical crystal, presenting a nonclassical mechanism for tuning of elasticity in nanotechnology applications.

Reversible kink instability drives ultrafast jumping in nematodes and soft robots

Entomopathogenic nematodes (EPNs) exhibit a bending-elastic instability, or kink, before becoming airborne, a feature hypothesized but not proven to enhance jumping performance. Here, we provide the evidence that this kink is crucial for improving launch performance. We demonstrate that EPNs actively modulate their aspect ratio, forming a liquid-latched closed loop over a slow timescale O (1 s), then rapidly open it O (10 µs), achieving heights of 20 body lengths (BL) and generating ∼ 10 4 W/Kg of power. Using jumping nematodes, a bio-inspired Soft Jumping Model (SoftJM), and computational simulations, we explore the mechanisms and implications of this kink. EPNs control their takeoff direction by adjusting their head position and center of mass, a mechanism verified through phase maps of jump directions in simulations and SoftJM experiments. Our findings reveal that the reversible kink instability at the point of highest curvature on the ventral side enhances energy storage using the nematode's limited muscular force. We investigated the impact of aspect ratio on kink instability and jumping performance using SoftJM, and quantified EPN cuticle stiffness with AFM, comparing it with C. elegans . This led to a stiffness-modified SoftJM design with a carbon fiber backbone, achieving jumps of ∼25 BL. Our study reveals how harnessing kink instabilities, a typical failure mode, enables bidirectional jumps in soft robots on complex substrates like sand, offering a novel approach for designing limbless robots for controlled jumping, locomotion, and even planetary exploration.

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.