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The design space of mechanical metamaterials can be drastically enriched by the employment of non-mechanical interactions between unit cells. Here, the mechanical behavior of planar metamaterials consisting of rotating squares is controlled through the periodic embedment of modified elementary cells with attractive and repulsive configurations of the magnets. The proposed design of mechanical metamaterials produced by three-dimensional printing enables the efficient and quick reprogramming of their mechanical properties through the insertion of the magnets into various locations within the metamaterial. Experimental and numerical studies reveal that under equibiaxial compression various mechanical characteristics, such as buckling strain and post-buckling stiffness, can be finely tuned through the rational placement of the magnets. Moreover, this strategy is shown to be efficient in introducing bistability into the metamaterial with an initially single equilibrium state.

Lattice structures produced by additive manufacturing are increasingly used in lightweight, load-bearing applications, yet their mechanical performance is strongly influenced by geometry, process parameters, and boundary conditions. This study investigates the compressive behavior of body-centered cubic (BCC) 316L stainless steel lattices fabricated by laser powder bed fusion (LPBF). Four relative densities (20%, 40%, 60%, and 80%) were achieved by varying the strut diameter, and specimens were built in both vertical and horizontal orientations. Quasi-static compression tests characterized the elastic modulus, yield strength, energy absorption, and mean force, while finite element simulations reproduced the deformation and hardening behavior. The experimental results showed a direct correlation between density and mechanical properties, with vertically built specimens performing slightly better due to reduced processing defects. Simulations quantified the effect of strut–joint rounding and the need for multi-cell configurations to closely match the experimental curves. Regardless of the boundary conditions, for a density of 20%, simulating a single cell underestimated stiffness because of unconstrained strut buckling. For higher densities and thicker struts, this sensitivity to boundary conditions strongly decreased, indicating the possibility of using a single cell for shorter simulations—a point rarely discussed in the literature. Both experiments and simulations confirmed Gibson–Ashby scaling for elastic modulus and yield strength, while the tangent modulus was highly sensitive to boundary conditions. The combined experimental and numerical results provide a framework for the reliable modeling and design of metallic lattices for energy absorption, biomedical, and lightweight structural applications.

Topological edge modes are excitations that are localized at the materials’ edges and yet are characterized by a topological invariant defined in the bulk. Such bulk–edge correspondence has enabled the creation of robust electronic, electromagnetic, and mechanical transport properties across a wide range of systems, from cold atoms to metamaterials, active matter, and geophysical flows. Recently, the advent of non-Hermitian topological systems—wherein energy is not conserved—has sparked considerable theoretical advances. In particular, novel topological phases that can only exist in non-Hermitian systems have been introduced. However, whether such phases can be experimentally observed, and what their properties are, have remained open questions. Here, we identify and observe a form of bulk–edge correspondence for a particular non-Hermitian topological phase. We find that a change in the bulk non-Hermitian topological invariant leads to a change of topological edge-mode localization together with peculiar purely non-Hermitian properties. Using a quantum-to-classical analogy, we create a mechanical metamaterial with nonreciprocal interactions, in which we observe experimentally the predicted bulk–edge correspondence, demonstrating its robustness. Our results open avenues for the field of non-Hermitian topology and for manipulating waves in unprecedented fashions.

Mechanical instabilities, especially in the form of bistable and multistable mechanisms, have recently garnered a lot of interest as a mode of improving the capabilities and increasing the functionalities of soft robots, structures, and soft mechanical systems in general. Although bistable mechanisms have shown high tunability through the variation of their material and design variables, they lack the option of modifying their attributes dynamically during operation. Here, we propose a facile approach to overcome this limitation by dispersing magnetically active microparticles throughout the structure of bistable elements and using an external magnetic field to tune their responses. We experimentally demonstrate and numerically verify the predictable and deterministic control of the response of different types of bistable elements under varying magnetic fields. Additionally, we show how this approach can be used to induce bistability in intrinsically monostable structures simply by placing them in a controlled magnetic field. Furthermore, we show the application of this strategy in precisely controlling the features (e.g., velocity and direction) of transition waves propagating in a multistable lattice created by cascading a chain of individual bistable elements. Moreover, we can implement active elements like a transistor (gate controlled by magnetic fields) or magnetically reconfigurable functional elements like binary logic gates for processing mechanical signals. This strategy serves to provide programming and tuning capabilities required to allow more extensive utilization of mechanical instabilities in soft systems with potential functions such as soft robotic locomotion, sensing and triggering elements, mechanical computation, and reconfigurable devices.

Topological phononic crystals, alike their electronic counterparts, are characterized by a bulk–edge correspondence where the interior of a material dictates the existence of stable surface or boundary modes. In the mechanical setup, such surface modes can be used for various applications such as wave guiding, vibration isolation, or the design of static properties such as stable floppy modes where parts of a system move freely. Here, we provide a classification scheme of topological phonons based on local symmetries. We import and adapt the classification of noninteracting electron systems and embed it into the mechanical setup. Moreover, we provide an extensive set of examples that illustrate our scheme and can be used to generate models in unexplored symmetry classes. Our work unifies the vast recent literature on topological phonons and paves the way to future applications of topological surface modes in mechanical metamaterials.

Multistable mechanical metamaterials are a type of mechanical metamaterials with special features, such as reusability, energy storage and absorption capabilities, rapid deformation, and amplified output forces. These metamaterials are usually realized by series and/or parallel of bistable units. They can exhibit multiple stable configurations under external loads and can be switched reversely among each other, thereby realizing the reusability of mechanical metamaterials and offering broad engineering applications. This paper reviews the latest research progress in the design strategy, manufacture and application of multistable mechanical metamaterials. We divide bistable structures into three categories based on their basic element types and provide the criterion of their bistability. Various manufacturing techniques to fabricate these multistable mechanical metamaterials are introduced, including mold casting, cutting, folding and three-dimensional/4D printing. Furthermore, the prospects of multistable mechanical metamaterials for applications in soft driving, mechanical computing, energy absorption and wave controlling are discussed. Finally, this paper highlights possible challenges and opportunities for future investigations. The review aims to provide insights into the research and development of multistable mechanical metamaterials. The design principle and advantages of multistable mechanical metamaterials were introduced. The most advanced manufacture techniques of multistable mechanical metamaterials were reviewed. Multistable mechanical metamaterials have attractive applications, such as wave control, soft actuator and energy absorption. Perspectives and challenges on multistable mechanical metamaterials were provided.

When cyclically driven, certain disordered materials exhibit transient and multiperiodic responses that are difficult to reproduce in synthetic materials. Here, we show that elementary multiperiodic elements with period T = 2 — togglerons—can serve as building blocks for such responses. We experimentally realize metamaterials composed of togglerons with tunable transients and periodic responses-including odd periods. Our approach suggests a hierarchy of increasingly complex elements in frustrated media, and opens a new strategy for rational design of sequential metamaterials.

Crumpling an ordinary thin sheet transforms it into a structure with unusualmechanical behaviors, such as enhanced rigidity, emission of crackling noise, slow relaxations, and memory retention. A central challenge in explaining these behaviors lies in understanding the contribution of the complex geometry of the sheet. Here we combine cyclic driving protocols and three-dimensional (3D) imaging to correlate the global mechanical response and the underlying geometric transformations in unfolded crumpled sheets. We find that their response to cyclic strain is intermittent, hysteretic, and encodes a memory of the largest applied compression. Using 3D imaging we show that these behaviors emerge due to an interplay between localized and interacting geometric instabilities in the sheet. A simple model confirms that these minimal ingredients are sufficient to explain the observed behaviors. Finally,we showthat after training, multiple memories can be encoded, a phenomenon known as return point memory. Our study lays the foundation for understanding the complex mechanics of crumpled sheets and presents an experimental and theoretical framework for the study of memory formation in systems of interacting instabilities.

Dilational materials are stable, three-dimensional isotropic auxetics with an ultimate Poisson's ratio of −1. Inspired by previous theoretical work, we design a feasible blueprint for an artificial material, a metamaterial, which approaches the ideal of a dilational material. The main novelty of our work is that we also fabricate and characterize corresponding metamaterial samples. To reveal all modes in the design, we calculate the phonon band structures. On this basis, using cubic symmetry we can unambiguously retrieve all different non-zero elements of the rank-four effective metamaterial elasticity tensor from which all effective elastic metamaterial properties follow. While the elastic properties and the phase velocity remain anisotropic, the effective Poisson's ratio indeed becomes isotropic and approaches −1 in the limit of small internal connections. This finding is also supported by independent, static continuum-mechanics calculations. In static experiments on macroscopic polymer structures fabricated by three-dimensional printing, we measure Poisson's ratios as low as −0.8 in good agreement with the theory. Microscopic samples are also presented.

Origami structures demonstrate great theoretical potential for creating metamaterials with exotic properties. However, there is a lack of understanding of how imperfections influence the mechanical behaviour of origami-based metamaterials, which, in practice, are inevitable. For conventional materials, imperfection plays a profound role in shaping their behaviour. Thus, this paper investigates the influence of small random geometric imperfections on the nonlinear compressive response of the representative Miura-ori, which serves as the basic pattern for many metamaterial designs. Experiments and numerical simulations are used to demonstrate quantitatively how geometric imperfections hinder the foldability of the Miura-ori, but on the other hand, increase its compressive stiffness. This leads to the discovery that the residual of an origami foldability constraint, given by the Kawasaki theorem, correlates with the increase of stiffness of imperfect origami-based metamaterials. This observation might be generalizable to other flat-foldable patterns, in which we address deviations from the zero residual of the perfect pattern; and to non-flat-foldable patterns, in which we would address deviations from a finite residual.