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Register a new userControlling the Deformation of Metamaterials: Corner Modes via Topology
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Topological metamaterials have invaded the mechanical world, demonstrating acoustic cloaking and waveguiding at finite frequencies and variable, tunable elastic response at zero frequency. Zero frequency topological states have previously relied on the Maxwell condition, namely that the system has equal numbers of degrees of freedom and constraints. Here, we show that otherwise rigid periodic mechanical structures are described by a map with a nontrivial topological degree (a generalization of the winding number introduced by Kane and Lubensky) that creates, directs and protects modes on their boundaries. We introduce a model system consisting of rigid quadrilaterals connected via free hinges at their corners in a checkerboard pattern. This bulk structure generates a topological linear deformation mode exponentially localized in one corner, as investigated numerically and via experimental prototype. Unlike the Maxwell lattices, these structures select a single desired mode, which controls variable stiffness and mechanical amplification that can be incorporated into devices at any scale.
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Topological mechanics can realize soft modes in mechanical metamaterials in which the number of degrees of freedom for particle motion is finely balanced by the constraints provided by interparticle interactions. However, solid objects are generally hyperstatic (or overconstrained). Here, we show how symmetries may be applied to generate topological soft modes even in overconstrained, rigid systems. To do so, we consider non-Hermitian topology based on non-square matrices, and design a hyperstatic material in which low-energy modes protected by topology and symmetry appear at interfaces. Our approach presents a novel way of generating softness in robust scale-free architectures suitable for miniaturization to the nanoscale.
Defects, and in particular topological defects, are architectural motifs that play a crucial role in natural materials. Here we provide a systematic strategy to introduce such defects in mechanical metamaterials. We first present metamaterials that are a mechanical analogue of spin systems with tunable ferromagnetic and antiferromagnetic interactions, then design an exponential number of frustration-free metamaterials, and finally introduce topological defects by rotating a string of building blocks in these metamaterials. We uncover the distinct mechanical signature of topological defects by experiments and simulations, and leverage this to design complex metamaterials in which we can steer deformations and stresses towards parts of the system. Our work presents a new avenue to systematically include spatial complexity, frustration, and topology in mechanical metamaterials.
Multi-step pathways, constituted of a sequence of reconfigurations, are central to a wide variety of natural and man-made systems. Such pathways autonomously execute in self-guided processes such as protein folding and self-assembly, but require external control in macroscopic mechanical systems, provided by, e.g., actuators in robotics or manual folding in origami. Here we introduce shape-changing mechanical metamaterials, that exhibit self-guided multi-step pathways in response to global uniform compression. Their design combines strongly nonlinear mechanical elements with a multimodal architecture that allows for a sequence of topological reconfigurations, i.e., modifications of the topology caused by the formation of internal self-contacts. We realized such metamaterials by digital manufacturing, and show that the pathway and final configuration can be controlled by rational design of the nonlinear mechanical elements. We furthermore demonstrate that self-contacts suppress pathway errors. Finally, we demonstrate how hierarchical architectures allow to extend the number of distinct reconfiguration steps. Our work establishes general principles for designing mechanical pathways, opening new avenues for self-folding media, pluripotent materials, and pliable devices in, e.g., stretchable electronics and soft robotics.
Double-negative acoustic metamaterials (AMMs) offer the promising ability of superlensing for applications in ultrasonography, biomedical sensing and nondestructive evaluation. Here, under the simultaneous increasing or non-increasing mechanisms, we develop a unified topology optimization framework considering the different microstructure symmetries, minimal structural feature sizes and dispersion extents of effective parameters. Then we apply the optimization framework to furnish the heuristic resonance-cavity-based and space-coiling metamaterials with broadband double negativity. Meanwhile, we demonstrate the essences of double negativity derived from the novel artificial multipolar LC and Mie resonances which can be induced by controlling mechanisms in optimization. Furthermore, abundant numerical simulations validate the double negativity, negative refraction, enhancements of evanescent waves and subwavelengh imaging for the optimized AMMs. Finally, we experimentally show the desired broadband subwavelengh imaging using the 3D-printed optimized space-coiling metamaterial. The present methodology and broadband metamaterials provide the ideal strategy of constructing AMMs for subwavelengh imaging technology.
Atomistic simulations are employed to study structural evolution of pore ensembles in binary glasses under periodic shear deformation with varied amplitude. The consideration is given to porous systems in the limit of low porosity. The initial ensembles of pores are comprised of multiple pores with small sizes, which are approximately normally distributed. As periodic loading proceeds, the ensembles evolve into configurations with a few large-scale pores and significantly reduced number of small pores. These structural changes are reflected in the skewed shapes of the pore-size distribution functions and the appearance of a distinct peak at large length scales after hundreds of shear cycles. Moreover, periodic shear causes substantial densification of solid domains in the porous systems. The structural evolution of pore ensembles is found to stem from the formation of shear-band like regions of enhanced particle mobility after a number of transient cycles. The spatial extent of increased mobility depends strongly on the strain amplitude. A scaling theory is developed to qualitatively describe the transformation of the pore initial configurations of small-size voids into larger-scale void agglomerates.
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