Bending of kerf chiral fractal lattice metamaterials

Dispersion relations govern wave behaviors, and tailoring them is a grand challenge in wave manipulation. We demonstrate the inverse design of phononic dispersion using nonlocal interactions on one-dimensional spring-mass chains. For both single-band and double-band cases, we can achieve any valid dispersion curves with analytical precision. We further employ our method to design phononic crystals with multiple ordinary (roton or maxon) and higher-order (undulation) critical points and investigate their wave packet dynamics. 

Drawing Dispersion Curves: Band Structure Customization via Nonlocal Phononic Crystals

Topological materials can host edge and corner states that are protected from disorder and material imperfections. In particular, the topological edge states of mechanical structures present unmatched opportunities for achieving robust responses in wave guiding, sensing, computation, and filtering. However, determining whether a mechanical structure is topologically nontrivial and features topologically protected modes has hitherto relied on theoretical models. This strong requirement has limited the experimental and practical significance of topological mechanics to laboratory demonstrations. Here, we introduce and validate an experimental method to detect the topologically protected zero modes of mechanical structures without resorting to any modeling step. Our practical method is based on a simple electrostatic analogy: Topological zero modes are akin to electric charges. To detect them, we identify elementary mechanical molecules and measure their chiral polarization, a recently introduced marker of topology in chiral phases. Topological zero modes are then identified as singularities of the polarization field. Our method readily applies to any mechanical structure and effectively detects the edge and corner states of regular and higher-order topological insulators. Our findings extend the reach of chiral topological phases beyond designer materials and allow their direct experimental investigation. 

Model-free characterization of topological edge and corner states in mechanical networks

Stretchable materials that can sustain a large deformation are in high demand, because they find broad applications ranging from stretchable energy storage devices to tunable noise and vibration devices. One main challenge is creating strain‐releasing mechanisms from inherently brittle materials. This work explores a new approach to designing stretchable metamaterials, using a "kerfing" pattern inspired by the ancient Greek Key configuration. The kerfing architecture allows for substantial in‐plane elongation. In‐plane tensile experiments show an ≈8‐times increase in stretchability when the kerfing width is enlarged four times. With higher‐order fractal patterns, the fractal lattice exhibits a stretchability of up to ≈520%, far beyond the inherent deformability of the brittle constituent. Moreover, this design also enables the tunability of various mechanical properties, including stiffness, strength, toughness, and Poisson's ratio. Ashby‐type plots are presented, revealing the relationships between stretchability and other mechanical properties to aid in the design and fabrication of advanced engineering materials. To demonstrate a vital application of the achieved stretchability, elastic wave propagation in the proposed kerfing metamaterials is studied. Simulations indicate that multiple broad phononic bandgaps arise in these structures as the fractal order increases. These bandgaps prove to be adjustable not only through the fractal lattice geometry but also by means of applied mechanical loading. This investigation highlights the potential of fractal‐based layouts as a promising avenue for designing cutting‐edge stretchable metamaterials with customizable mechanical properties and functionalities. 

Greek Key Inspired Fractal Metamaterials with Superior Stretchability for Tunable Wave Propagation


 The confinement of waves within a waveguide can enable directional transmission of signals, which has found wide applications in communication, imaging, and signal isolation. Extending this concept to static systems, where material deformation is piled up along a spatial trajectory, remains elusive due to the sensitivity of localized deformation to structural defects and impurities. Here, we propose a general framework to characterize localized static deformation responses in two dimensional generic static mechanical metamaterials, by exploiting the duality between space in static systems and time in one dimensional non-reciprocal wave systems. An internal time-reverse symmetry is developed by the space-time duality. Upon breaking this symmetry, quasi-static load induced deformation can be guided to travel along a designated path, thereby realizing a stress guide. A combination of time-reverse and inversion symmetries discloses the parity-time symmetry inherent in static systems, which can be leveraged to achieve directional deformation shielding. The tailorable stress guides can find applications in various scenarios, ranging from stress shielding and energy harvesting in structural tasks to information processing in mechanical computing devices.

Stress guides in generic static mechanical metamaterials

The process of kerfing enables planar structures with the ability to undergo dramatic out-of-plane deformation in response to static loads. Starting from flat and stiff sheets, kerfing allows for the formation of a wide variety of unconventional free-form shapes, making the process especially attractive for architectural applications. In this work, we investigate numerically and experimentally the bandgap behavior of densely cut kerfed strips. Our study reveals a rich landscape of bandgaps that is predominantly ascribable to the activation of resonant sub-units within the kerf unit cells. We also document how the extreme deformability of the strips under twisting and bending loads, enhanced by the meandering cut pattern, can serve as a powerful bandgap tuning mechanism.

Bandgap tuning in kerfed metastrips under extreme deformation

/pdf/stress-focusing-and-damage-protection-in-topological-maxwell-3foi366w.pdf

Stress focusing and damage protection in topological Maxwell metamaterials

Recent developments in topological mechanics have demonstrated the ability of Maxwell lattices to effectively focus stress along domain walls between differently polarized domains. The focusing ability can be exploited to protect the lattice bulk from accidental stress concentration - and eventually onset and propagation of fracture - at structural hot spots such as defects and cracks. A recent study has revisited the problem for structural lattices featuring non-ideal hinges, showing that the focusing remains robust, albeit diluted in strength. Realizing that the problem of domain wall localization has been traditionally framed in the context of linear elasticity, in this work we extend the study to the realm of soft structures undergoing nonlinear finite deformation. Through experiments performed on silicone hyperelastic prototypes, we assess and quantify the robustness of the phenomenon against the macroscopic shape changes induced by large deformation, with special attention to deformation levels that alter the topology of the bulk, lifting the topological protection. Furthermore, we identify a simple geometric indicator for this transition. 

pdf/robustness-of-stress-focusing-in-soft-lattices-under-1gjp7lsj0b.pdf

Robustness of stress focusing in soft lattices under topology-switching deformation

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Bandgap tuning in kerfed metastrips under extreme deformation

Stress focusing and damage protection in topological Maxwell metamaterials

Robustness of stress focusing in soft lattices under topology-switching deformation