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The predominantly deep-sea hexactinellid sponges are known for their ability to construct remarkably complex skeletons from amorphous hydrated silica. The skeletal system of one such species of sponge, Euplectella aspergillum , consists of a square-grid-like architecture overlaid with a double set of diagonal bracings, creating a chequerboard-like pattern of open and closed cells. Here, using a combination of finite element simulations and mechanical tests on 3D-printed specimens of different lattice geometries, we show that the sponge’s diagonal reinforcement strategy achieves the highest buckling resistance for a given amount of material. Furthermore, using an evolutionary optimization algorithm, we show that our sponge-inspired lattice geometry approaches the optimum material distribution for the design space considered. Our results demonstrate that lessons learned from the study of sponge skeletal systems can be exploited for the realization of square lattice geometries that are geometrically optimized to avoid global structural buckling, with implications for improved material use in modern infrastructural applications. Computational analysis and mechanical testing demonstrate that the skeletal system of a marine sponge has, through the course of evolution, achieved a near-optimal resistance to buckling.

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. This work presents a mechanical metamaterial with 1D array of bistable arches where nonreciprocity and reversibility can be independently programmed. The effects of asymmetry both at the structural and element level on propagation of transition waves are examined.

Kirigami-inspired metamaterials are attracting increasing interest because of their ability to achieve extremely large strains and shape changes via out-of-plane buckling. While in flat kirigami sheets, the ligaments buckle simultaneously as Euler columns, leading to a continuous phase transition; here, we demonstrate that kirigami shells can also support discontinuous phase transitions. Specifically, we show via a combination of experiments, numerical simulations, and theoretical analysis that, in cylindrical kirigami shells, the snapping-induced curvature inversion of the initially bent ligaments results in a pop-up process that first localizes near an imperfection and then, as the deformation is increased, progressively spreads through the structure. Notably, we find that the width of the transition zone as well as the stress at which propagation of the instability is triggered can be controlled by carefully selecting the geometry of the cuts and the curvature of the shell. Our study significantly expands the ability of existing kirigami metamaterials and opens avenues for the design of the next generation of responsive surfaces as demonstrated by the design of a smart skin that significantly enhances the crawling efficiency of a simple linear actuator.

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. Curved elastic shells have unique mechanical behavior and multiple stable configurations, but these properties fade when the shell thickness increases. Here the authors report a strategy to realize bistable doubly curved shells with arbitrary thickness, and how to optimize the dynamic response of one-dimensional connected arrays of such doubly-curved bistable shells.

Soft actuators are the components responsible for producing motion in soft robots. Although soft actuators have allowed for a variety of innovative applications, there is a need for design tools that can help to efficiently and systematically design actuators for particular functions. Mathematical modeling of soft actuators is an area that is still in its infancy but has the potential to provide quantitative insights into the response of the actuators. These insights can be used to guide actuator design, thus accelerating the design process. Here, we study fluid-powered fiber-reinforced actuators, because these have previously been shown to be capable of producing a wide range of motions. We present a design strategy that takes a kinematic trajectory as its input and uses analytical modeling based on nonlinear elasticity and optimization to identify the optimal design parameters for an actuator that will follow this trajectory upon pressurization. We experimentally verify our modeling approach, and finally we demonstrate how the strategy works, by designing actuators that replicate the motion of the index finger and thumb.

Transition waves that sequentially switch bistable elements from one stable configuration to another have received significant interest in recent years not only because of their rich physics but also, for their potential applications, including unidirectional propagation, energy harvesting, and mechanical computation. Here, we exploit the propagation of transition waves in a bistable one-dimensional (1D) linkage as a robust mechanism to realize structures that can be quickly deployed. We first use a combination of experiments and analyses to show that, if the bistable joints are properly designed, transition waves can propagate throughout the entire structure and transform the initial straight configuration into a curved one. We then demonstrate that such bistable linkages can be used as building blocks to realize deployable three-dimensional (3D) structures of arbitrary shape.

Transition fronts, moving through solids and fluids in the form of propagating domain or phase boundaries, have recently been mimicked at the structural level in bistable architectures. What has been limited to simple one-dimensional (1D) examples is here cast into a blueprint for higher dimensions, demonstrated through 2D experiments and described by a continuum mechanical model that draws inspiration from phase transition theory in crystalline solids. Unlike materials, the presented structural analogs admit precise control of the transition wave’s direction, shape, and velocity through spatially tailoring the underlying periodic network architecture (locally varying the shape or stiffness of the fundamental building blocks, and exploiting interactions of transition fronts with lattice defects such as point defects and free surfaces). The outcome is a predictable and programmable strongly nonlinear metamaterial motion with potential for, for example, propulsion in soft robotics, morphing surfaces, reconfigurable devices, mechanical logic, and controlled energy absorption.

We combine experimental, numerical, and analytical tools to design highly nonlinear mechanical metamaterials that exhibit a new phenomenon: gaps in amplitude for elastic vector solitons (i.e., ranges in amplitude where elastic soliton propagation is forbidden). Such gaps are fundamentally different from the spectral gaps in frequency typically observed in linear phononic crystals and acoustic metamaterials and are induced by the lack of strong coupling between the two polarizations of the vector soliton. We show that the amplitude gaps are a robust feature of our system and that their width can be controlled both by varying the structural properties of the units and by breaking the symmetry in the underlying geometry. Moreover, we demonstrate that amplitude gaps provide new opportunities to manipulate highly nonlinear elastic pulses, as demonstrated by the designed soliton splitters and diodes. Here, the authors experimentally observed, numerically simulate, and mathematically analyze the existence of amplitude gaps for elastic vector solitons in highly deformable mechanical metamaterials consisting of rigid units and elastic hinges.

Advances in fabrication technologies are enabling the production of architected materials with unprecedented properties. Most such materials are characterized by a fixed geometry, but in the design of some materials it is possible to incorporate internal mechanisms capable of reconfiguring their spatial architecture, and in this way to enable tunable functionality. Inspired by the structural diversity and foldability of the prismatic geometries that can be constructed using the snapology origami technique, here we introduce a robust design strategy based on space-filling tessellations of polyhedra to create three-dimensional reconfigurable materials comprising a periodic assembly of rigid plates and elastic hinges. Guided by numerical analysis and physical prototypes, we systematically explore the mobility of the designed structures and identify a wide range of qualitatively different deformations and internal rearrangements. Given that the underlying principles are scale-independent, our strategy can be applied to the design of the next generation of reconfigurable structures and materials, ranging from metre-scale transformable architectures to nanometre-scale tunable photonic systems. A robust and scale-independent strategy for the design of reconfigurable architected materials (in which properties are adjusted by altering structure rather than composition) is described, based on space-filling assemblies of polyhedra. Reconfigurable architected materials take shape Architected materials (metamaterials) achieve new properties from the way their structures are engineered, rather than their composition. They usually have only one fixed geometry, although a recent paper from Katia Bertoldi and colleagues describes a reconfigurable three-dimensional (3D) metamaterial. In the present paper, the same group reports a general design strategy that leads to an entire class of reconfigurable metamaterials. The authors begin with space-filling polyhedra, which they separate and generate connecting faces from the edges of one polyhedron to others in the direction normal to the surfaces (these are said to be prismatic). The researchers then create these structures and identify those that are reconfigurable. They develop a numerical algorithm to identify the parameters that allow the structures to be reconfigurable, and use it to predict mobility and deformation modes in all 28 polyhedral tilings of 3D space. The original unit cells of all 13 reconfigurable architectures contain prisms. The authors further increase the number of reconfigurable architectures by reducing the number of extrusions from the polyhedral surfaces, and find that 10% of the structures they studied could be made reconfigurable. Finally, they identify qualitatively different reconfigurations, including shear and uniform expansion, along one or two principal directions, and internal reconfigurations that do not alter the external shape.

Soft structures with rationally designed architectures capable of large, nonlinear deformation present opportunities for unprecedented, highly tunable devices and machines. However, the highly dissipative nature of soft materials intrinsically limits or prevents certain functions, such as the propagation of mechanical signals. Here we present an architected soft system composed of elastomeric bistable beam elements connected by elastomeric linear springs. The dissipative nature of the polymer readily damps linear waves, preventing propagation of any mechanical signal beyond a short distance, as expected. However, the unique architecture of the system enables propagation of stable, nonlinear solitary transition waves with constant, controllable velocity and pulse geometry over arbitrary distances. Because the high damping of the material removes all other linear, small-amplitude excitations, the desired pulse propagates with high fidelity and controllability. This phenomenon can be used to control signals, as demonstrated by the design of soft mechanical diodes and logic gates.