Shell buckling for programmable metafluids.

The pursuit of materials with enhanced functionality has led to the emergence of metamaterials-artificially engineered materials whose properties are determined by their structure rather than composition. Traditionally, the building blocks of metamaterials are arranged in fixed positions within a lattice structure1-19. However, recent research has revealed the potential of mixing disconnected building blocks in a fluidic medium20-27. Inspired by these recent advances, here we show that by mixing highly deformable spherical capsules into an incompressible fluid, we can realize a 'metafluid' with programmable compressibility, optical behaviour and viscosity. First, we experimentally and numerically demonstrate that the buckling of the shells endows the fluid with a highly nonlinear behaviour. Subsequently, we harness this behaviour to develop smart robotic systems, highly tunable logic gates and optical elements with switchable characteristics. Finally, we demonstrate that the collapse of the shells upon buckling leads to a large increase in the suspension viscosity in the laminar regime. As such, the proposed metafluid provides a promising platform for enhancing the functionality of existing fluidic devices by expanding the capabilities of the fluid itself.

Liquid Crystal Elastomer Lattices with Thermally Programmable Deformation via Multi-Material 3D Printing.

An integrated design, modeling, and multi-material 3D printing platform for fabricating liquid crystal elastomer (LCE) lattices in both homogeneous and heterogeneous layouts with spatially programmable nematic director order and local composition is reported. Depending on their compositional topology, these lattices exhibit different reversible shape-morphing transformations upon cycling above and below their respective nematic-to-isotropic transition temperatures. Further, it is shown that there is good agreement between their experimentally observed deformation response and model predictions for all LCE lattice designs evaluated. Lastly, an inverse design model is established and the ability to print LCE lattices with the predicted deformation behavior is demonstrated. This work opens new avenues for creating architected LCE lattices that may find potential application in energy-dissipating structures, microfluidic pumping, mechanical logic, and soft robotics.

3D spatiotemporally scalable in vivo neural probes based on fluorinated elastomers.

Electronic devices for recording neural activity in the nervous system need to be scalable across large spatial and temporal scales while also providing millisecond and single-cell spatiotemporal resolution. However, existing high-resolution neural recording devices cannot achieve simultaneous scalability on both spatial and temporal levels due to a trade-off between sensor density and mechanical flexibility. Here we introduce a three-dimensional (3D) stacking implantable electronic platform, based on perfluorinated dielectric elastomers and tissue-level soft multilayer electrodes, that enables spatiotemporally scalable single-cell neural electrophysiology in the nervous system. Our elastomers exhibit stable dielectric performance for over a year in physiological solutions and are 10,000 times softer than conventional plastic dielectrics. By leveraging these unique characteristics we develop the packaging of lithographed nanometre-thick electrode arrays in a 3D configuration with a cross-sectional density of 7.6 electrodes per 100 µm2. The resulting 3D integrated multilayer soft electrode array retains tissue-level flexibility, reducing chronic immune responses in mouse neural tissues, and demonstrates the ability to reliably track electrical activity in the mouse brain or spinal cord over months without disrupting animal behaviour.

Programming 3D Curves with Discretely Constrained Cylindrical Inflatables.

Programming inflatable systems to deform to desired 3D shapes opens up multifarious applications in robotics, morphing architecture, and interventional medicine. This work elicits complex deformations by attaching discrete strain limiters to cylindrical hyperelastic inflatables. Using this system, a method is presented to solve the inverse problem of programming myriad 3D centerline curves upon inflation. The method entails two steps: first, a reduced-order model generates a conceptual solution giving coarse indications of strain limiter placement on the undeformed cylindrical inflatable. This low-fidelity solution then seeds a finite element simulation nested within an optimization loop to further tune strain limiter parameters. We leverage this framework to achieve functionality through a priori programmed deformations of cylindrical inflatables, including 3D curve matching, self-tying knotting, and manipulation. The results hold broad significance for the emerging computational design of inflatable systems.

Versatile vacuum-powered artificial muscles through replaceable external reinforcements.

Soft pneumatic artificial muscles are a well actuation scheme in soft robotics due to its key features for robotic machines being safe, lightweight, and conformable. In this work, we present a versatile vacuum-powered artificial muscle (VPAM) with manually tunable output motion. We developed an artificial muscle that consists of a stack of air chambers that can use replaceable external reinforcements. Different modes of operation are achieved by assembling different reinforcements that constrain the output motion of the actuator during actuation. We designed replaceable external reinforcements to produce single motions such as twisting, bending, shearing and rotary. We then conducted a deformation and lifting force characterization for these motions. We demonstrated sophisticated motions and reusability of the artificial muscle in two soft machines with different modes of locomotion. Our results show that our VPAM is reusable and versatile producing a variety and sophisticated output motions if needed. This key feature specially benefits unpredicted workspaces that require a soft actuator that can be adjusted for other tasks. Our scheme has the potential to offer new strategies for locomotion in machines for underwater or terrestrial operation, and wearable devices with different modes of operation.

Inverse Design of Mechanical Metamaterials with Target Nonlinear Response via a Neural Accelerated Evolution Strategy.

Materials with target nonlinear mechanical response can support the design of innovative soft robots, wearable devices, footwear, and energy-absorbing systems, yet it is challenging to realize them. Here, mechanical metamaterials based on hinged quadrilaterals are used as a platform to realize target nonlinear mechanical responses. It is first shown that by changing the shape of the quadrilaterals, the amount of internal rotations induced by the applied compression can be tuned, and a wide range of mechanical responses is achieved. Next, a neural network is introduced that provides a computationally inexpensive relationship between the parameters describing the geometry and the corresponding stress-strain response. Finally, it is shown that by combining the neural network with an evolution strategy, one can efficiently identify geometries resulting in a wide range of target nonlinear mechanical responses and design optimized energy-absorbing systems, soft robots, and morphing structures.

Self-regulated non-reciprocal motions in single-material microstructures.

Living cilia stir, sweep and steer via swirling strokes of complex bending and twisting, paired with distinct reverse arcs1,2. Efforts to mimic such dynamics synthetically rely on multimaterial designs but face limits to programming arbitrary motions or diverse behaviours in one structure3-8. Here we show how diverse, complex, non-reciprocal, stroke-like trajectories emerge in a single-material system through self-regulation. When a micropost composed of photoresponsive liquid crystal elastomer with mesogens aligned oblique to the structure axis is exposed to a static light source, dynamic dances evolve as light initiates a travelling order-to-disorder transition front, transiently turning the structure into a complex evolving bimorph that twists and bends via multilevel opto-chemo-mechanical feedback. As captured by our theoretical model, the travelling front continuously reorients the molecular, geometric and illumination axes relative to each other, yielding pathways composed from series of twisting, bending, photophobic and phototropic motions. Guided by the model, here we choreograph a wide range of trajectories by tailoring parameters, including illumination angle, light intensity, molecular anisotropy, microstructure geometry, temperature and irradiation intervals and duration. We further show how this opto-chemo-mechanical self-regulation serves as a foundation for creating self-organizing deformation patterns in closely spaced microstructure arrays via light-mediated interpost communication, as well as complex motions of jointed microstructures, with broad implications for autonomous multimodal actuators in areas such as soft robotics7,9,10, biomedical devices11,12 and energy transduction materials13, and for fundamental understanding of self-regulated systems14,15.

Curvilinear Kirigami Skins Let Soft Bending Actuators Slither Faster.

The locomotion of soft snake robots is dependent on frictional interactions with the environment. Frictional anisotropy is a morphological characteristic of snakeskin that allows snakes to engage selectively with surfaces and generate propulsive forces. The prototypical slithering gait of most snakes is lateral undulation, which requires a significant lateral resistance that is lacking in artificial skins of existing soft snake robots. We designed a set of kirigami lattices with curvilinearly-arranged cuts to take advantage of in-plane rotations of the 3D structures when wrapped around a soft bending actuator. By changing the initial orientation of the scales, the kirigami skin produces high lateral friction upon engagement with surface asperities, with lateral to cranial anisotropic friction ratios above 4. The proposed design increased the overall velocity of the soft snake robot more than fivefold compared to robots without skin.

A buckling-sheet ring oscillator for electronics-free, multimodal locomotion.

Locomotion of soft robots typically relies on control of multiple inflatable actuators by electronic computers and hard valves. Soft pneumatic oscillators can reduce the demand on controllers by generating complex movements required for locomotion from a single, constant input pressure, but either have been constrained to low rates of flow of air or have required complex fabrication processes. Here, we describe a pneumatic oscillator fabricated from flexible, but inextensible, sheets that provides high rates of airflow for practical locomotion by combining three instabilities: out-of-plane buckling of the sheets, kinking of tubing attached to the sheets, and a system-level instability resulting from connection of an odd number of pneumatic inverters made from these sheets in a loop. This device, which we call a "buckling-sheet ring oscillator" (BRO), directly generates movement from its own interaction with its surroundings and consists only of readily available materials assembled in a simple process-specifically, stacking acetate sheets, nylon film, and double-sided tape, and attaching an elastomeric tube. A device incorporating a BRO is capable of both translational and rotational motion over varied terrain (even without a tether) and can climb upward against gravity and downward against the buoyant force encountered under water.

Unfolding Textile-Based Pneumatic Actuators for Wearable Applications.

Textile based pneumatic actuators have recently seen increased development for use in wearable applications thanks to their high strength to weight ratio and range of achievable actuation modalities. However, the design of these textile-based actuators is typically an iterative process due to the complexity of predicting the soft and compliant behavior of the textiles. In this work we investigate the actuation mechanics of a range of physical prototypes of unfolding textile-based actuators to understand and develop an intuition for how the geometric parameters of the actuator affect the moment it generates, enabling more deterministic designs in the future. Under benchtop conditions the actuators were characterized at a range of actuator angles and pressures (0 - 136 kPa), and three distinct performance regimes were observed, which we define as Shearing, Creasing, and Flattening. During Flattening, the effects of both the length and radius of the actuator dominate with maximum moments in excess of 80 Nm being generated, while during Creasing the radius dominates with generated moments scaling with the cube of the radius. Low stiffness spring like behavior is observed in the Shearing regime, which occurs as the actuator approaches its unfolded angle. A piecewise analytical model was also developed and compared to the experimental results within each regime. Finally, a prototype actuator was also integrated into a shoulder assisting wearable robot, and on-body characterization of this robot was performed on five healthy individuals to observe the behavior of the actuators in a wearable application. Results from this characterization highlight that these actuators can generate useful on-body moments (10.74 Nm at 90° actuator angle) but that there are significant reductions compared to bench-top performance, in particular when mostly folded and at higher pressures.

Mechanical Valves for On-Board Flow Control of Inflatable Robots.

Inflatable robots are becoming increasingly popular, especially in applications where safe interactions are a priority. However, designing multifunctional robots that can operate with a single pressure input is challenging. A potential solution is to couple inflatables with passive valves that can harness the flow characteristics to create functionality. In this study, simple, easy to fabricate, lightweight, and inexpensive mechanical valves are presented that harness viscous flow and snapping arch principles. The mechanical valves can be fully integrated on-board, enabling the control of the incoming airflow to realize multifunctional robots that operate with a single pressure input, with no need for electronic components, cables, or wires. By means of three robotic demos and guided by a numerical model, the capabilities of the valves are demonstrated and optimal input profiles are identified to achieve prescribed functionalities. The study enriches the array of available mechanical valves for inflatable robots and enables new strategies to realize multifunctional robots with on-board flow control.

Mechanical and hydrodynamic analyses of helical strake-like ridges in a glass sponge.

From the discovery of functionally graded laminated composites, to near-structurally optimized diagonally reinforced square lattice structures, the skeletal system of the predominantly deep-sea sponge Euplectella aspergillum has continued to inspire biologists, materials scientists and mechanical engineers. Building on these previous efforts, in the present study, we develop an integrated finite element and fluid dynamics approach for investigating structure-function relationships in the complex maze-like organization of helical ridges that surround the main skeletal tube of this species. From these investigations, we discover that not only do these ridges provide additional mechanical reinforcement, but perhaps more significantly, provide a critical hydrodynamic benefit by effectively suppressing von Kármán vortex shedding and reducing lift forcing fluctuations over a wide range of biologically relevant flow regimes. By comparing the disordered sponge ridge geometry to other more symmetrical strake-based vortex suppression systems commonly employed in infrastructure applications ranging from antennas to underwater gas and oil pipelines, we find that the unique maze-like ridge organization of E. aspergillum can completely suppress vortex shedding rather than delaying their shedding to a more downstream location, thus highlighting their potential benefit in these engineering contexts.

Controlling Liquid Crystal Orientations for Programmable Anisotropic Transformations in Cellular Microstructures.

Geometric reconfigurations in cellular structures have recently been exploited to realize adaptive materials with applications in mechanics, optics, and electronics. However, the achievable symmetry breakings and corresponding types of deformation and related functionalities have remained rather limited, mostly due to the fact that the macroscopic geometry of the structures is generally co-aligned with the molecular anisotropy of the constituent material. To address this limitation, cellular microstructures are fabricated out of liquid crystalline elastomers (LCEs) with an arbitrary, user-defined liquid crystal (LC) mesogen orientation encrypted by a weak magnetic field. This platform enables anisotropy to be programmed independently at the molecular and structural levels and the realization of unprecedented director-determined symmetry breakings in cellular materials, which are demonstrated by both finite element analyses and experiments. It is illustrated that the resulting mechanical reconfigurations can be harnessed to program microcellular materials with switchable and direction-dependent frictional properties and further exploit "area-specific" deformation patterns to locally modulate transmitted light and precisely guide object movement. As such, the work provides a clear route to decouple anisotropy at the materials level from the directionality of the macroscopic cellular structure, which may lead to a new generation of smart and adaptive materials and devices.

Programming nonreciprocity and reversibility in multistable mechanical metamaterials.

Nonreciprocity can be passively achieved by harnessing material nonlinearities. In particular, networks of nonlinear bistable elements with asymmetric energy landscapes have recently been shown to support unidirectional transition waves. However, in these systems energy can be transferred only when the elements switch from the higher to the lower energy well, allowing for a one-time signal transmission. Here, we show that in a mechanical metamaterial comprising a 1D array of bistable arches nonreciprocity and reversibility can be independently programmed and are not mutually exclusive. By connecting shallow arches with symmetric energy wells and decreasing energy barriers, we design a reversible mechanical diode that can sustain multiple signal transmissions. Further, by alternating arches with symmetric and asymmetric energy landscapes we realize a nonreciprocal chain that enables propagation of different transition waves in opposite directions.

Microstructural design for mechanical-optical multifunctionality in the exoskeleton of the flower beetle Torynorrhina flammea.

Biological systems have a remarkable capability of synthesizing multifunctional materials that are adapted for specific physiological and ecological needs. When exploring structure-function relationships related to multifunctionality in nature, it can be a challenging task to address performance synergies, trade-offs, and the relative importance of different functions in biological materials, which, in turn, can hinder our ability to successfully develop their synthetic bioinspired counterparts. Here, we investigate such relationships between the mechanical and optical properties in a multifunctional biological material found in the highly protective yet conspicuously colored exoskeleton of the flower beetle, Torynorrhina flammea Combining experimental, computational, and theoretical approaches, we demonstrate that a micropillar-reinforced photonic multilayer in the beetle's exoskeleton simultaneously enhances mechanical robustness and optical appearance, giving rise to optical damage tolerance. Compared with plain multilayer structures, stiffer vertical micropillars increase stiffness and elastic recovery, restrain the formation of shear bands, and enhance delamination resistance. The micropillars also scatter the reflected light at larger polar angles, enhancing the first optical diffraction order, which makes the reflected color visible from a wider range of viewing angles. The synergistic effect of the improved angular reflectivity and damage localization capability contributes to the optical damage tolerance. Our systematic structural analysis of T. flammea's different color polymorphs and parametric optical and mechanical modeling further suggest that the beetle's microarchitecture is optimized toward maximizing the first-order optical diffraction rather than its mechanical stiffness. These findings shed light on material-level design strategies utilized in biological systems for achieving multifunctionality and could thus inform bioinspired material innovations.

Liquid-induced topological transformations of cellular microstructures.

The fundamental topology of cellular structures-the location, number and connectivity of nodes and compartments-can profoundly affect their acoustic1-4, electrical5, chemical6,7, mechanical8-10 and optical11 properties, as well as heat1,12, fluid13,14 and particle transport15. Approaches that harness swelling16-18, electromagnetic actuation19,20 and mechanical instabilities21-23 in cellular materials have enabled a variety of interesting wall deformations and compartment shape alterations, but the resulting structures generally preserve the defining connectivity features of the initial topology. Achieving topological transformation presents a distinct challenge for existing strategies: it requires complex reorganization, repacking, and coordinated bending, stretching and folding, particularly around each node, where elastic resistance is highest owing to connectivity. Here we introduce a two-tiered dynamic strategy that achieves systematic reversible transformations of the fundamental topology of cellular microstructures, which can be applied to a wide range of materials and geometries. Our approach requires only exposing the structure to a selected liquid that is able to first infiltrate and plasticize the material at the molecular scale, and then, upon evaporation, form a network of localized capillary forces at the architectural scale that 'zip' the edges of the softened lattice into a new topological structure, which subsequently restiffens and remains kinetically trapped. Reversibility is induced by applying a mixture of liquids that act separately at the molecular and architectural scales (thus offering modular temporal control over the softening-evaporation-stiffening sequence) to restore the original topology or provide access to intermediate modes. Guided by a generalized theoretical model that connects cellular geometries, material stiffness and capillary forces, we demonstrate programmed reversible topological transformations of various lattice geometries and responsive materials that undergo fast global or localized deformations. We then harness dynamic topologies to develop active surfaces with information encryption, selective particle trapping and bubble release, as well as tunable mechanical, chemical and acoustic properties.

Multistable inflatable origami structures at the metre scale.

From stadium covers to solar sails, we rely on deployability for the design of large-scale structures that can quickly compress to a fraction of their size1-4. Historically, two main strategies have been used to design deployable systems. The first and most frequently used approach involves mechanisms comprising interconnected bar elements, which can synchronously expand and retract5-7, occasionally locking in place through bistable elements8,9. The second strategy makes use of inflatable membranes that morph into target shapes by means of a single pressure input10-12. Neither strategy, however, can be readily used to provide an enclosed domain that is able to lock in place after deployment: the integration of a protective covering in linkage-based constructions is challenging and pneumatic systems require a constant applied pressure to keep their expanded shape13-15. Here we draw inspiration from origami-the Japanese art of paper folding-to design rigid-walled deployable structures that are multistable and inflatable. Guided by geometric analyses and experiments, we create a library of bistable origami shapes that can be deployed through a single fluidic pressure input. We then combine these units to build functional structures at the metre scale, such as arches and emergency shelters, providing a direct route for building large-scale inflatable systems that lock in place after deployment and offer a robust enclosure through their stiff faces.

Harnessing Mechanical Deformation to Reduce Spherical Aberration in Soft Lenses.

Mechanical deformation has recently emerged as a promising platform to realize optical devices with tunable response. While most studies to date have focused on the tuning of the focal length, here we use a combination of experiments and analyses to show that an applied tensile strain can also largely reduce spherical aberration. We first demonstrate the concept for a cylindrical elastomeric lens and then show that it is robust and valid over a range of geometries and material properties. As such, our study suggests that large mechanical deformations may provide a simple route to achieve the complex profiles required to minimize aberration and realize lenses capable of producing images of superior quality.

Universally bistable shells with nonzero Gaussian curvature for two-way transition waves.

Multi-welled energy landscapes arising in shells with nonzero Gaussian curvature typically fade away as their thickness becomes larger because of the increased bending energy required for inversion. Motivated by this limitation, we propose a strategy to realize doubly curved shells that are bistable for any thickness. We then study the nonlinear dynamic response of one-dimensional (1D) arrays of our universally bistable shells when coupled by compressible fluid cavities. We find that the system supports the propagation of bidirectional transition waves whose characteristics can be tuned by varying both geometric parameters as well as the amount of energy supplied to initiate the waves. However, since our bistable shells have equal energy minima, the distance traveled by such waves is limited by dissipation. To overcome this limitation, we identify a strategy to realize thick bistable shells with tunable energy landscape and show that their strategic placement within the 1D array can extend the propagation distance of the supported bidirectional transition waves.