curved surfaces, however, remains challenging for engineers. These challenges can, for example, be observed in the case of thin-walled structural elements, which are very popular due to their combination of lightness, load transfer efficiency, [11][12][13][14] and low cost. Although an initially flat panel can be reasonably bent in a single direction to adapt the shape of an arch, transforming the panel into a shell dome or a saddle and, thus, changing its Gaussian curvature remains challenging. [15][16][17][18] Several studies have used computer-aided design using conformal geometry, [19,20] origami, [21][22][23][24][25][26][27][28][29][30] kirigami, [31,32] or crumpling [33,34] approaches to create curved objects from flat sheets. However, these approaches rely on very thin sheets and only lead to an approximation of the desired curvature. Other techniques based on non-uniform swelling [35,36] or inflation [37] or liquid crystal phase transition [38] have also been proposed, but these structures are made of soft materials and may not be suitable for large-scale and/or load-bearing structures. "Bending-active system" [39,40] is another approach to create form-finding structures. These form-finding structures rely on the elastic deformation of a combination of several structural elements (e.g., vector-active, surface-active, form-active, etc.) that are initially planar or straight. [40][41][42][43][44] Therefore, individual curved beam, shell, or membrane elements of bending-active systems remain elastically constrained and can carry residual bending stresses. [40] Therefore, patterningThe design of advanced functional devices often requires the use of intrinsically curved geometries that belong to the realm of non-Euclidean geometry and remain a challenge for traditional engineering approaches. Here, it is shown how the simple deflection of thick meta-plates based on hexagonal cellular mesostructures can be used to achieve a wide range of intrinsic (i.e., Gaussian) curvatures, including dome-like and saddle-like shapes. Depending on the unit cell structure, non-auxetic (i.e., positive Poisson ratio) or auxetic (i.e., negative Poisson ratio) plates can be obtained, leading to a negative or positive value of the Gaussian curvature upon bending, respectively. It is found that bending such meta-plates along their longitudinal direction induces a curvature along their transverse direction. Experimentally and numerically, it is shown how the amplitude of this induced curvature is related to the longitudinal bending and the geometry of the meta-plate. The approach proposed here constitutes a general route for the rational design of advanced functional devices with intrinsically curved geometries. To demonstrate the merits of this approach, a scaling relationship is presented, and its validity is demonstrated by applying it to 3D-printed microscale meta-plates. Several applications for adaptive optical devices with adjustable focal length and soft wearable robotics are presented.
By taking into account the hydrodynamic interactions in a one dimensional array of model cilia attached to a no-slip cylinderical surface, we investigate their synchronized motion. We show how the emergence of metachronal waves depends on the initial state of the system and investigate the conditions under which the formation of symplectic and antiplectic waves are possible.
The Poynting effect generically manifests itself as the extension of the material in the direction perpendicular to an applied shear deformation (torsion) and is a material parameter hard to design. Unlike isotropic solids, in designed structures, peculiar couplings between shear and normal deformations can be achieved and exploited for practical applications. Here, a metamaterial is engineered that can be programmed to contract or extend under torsion and undergo nonlinear twist under compression. First, it is shown that the system exhibits a novel type of inverted Poynting effect, where axial compression induces a nonlinear torsion. Then the Poynting modulus of the structure is programmed from initial negative values to zero and positive values via a pre-compression applied prior to torsion. The work opens avenues for programming nonlinear elastic moduli of materials and tuning the couplings between shear and normal responses by rational design. Obtaining inverted and programmable Poynting effects in metamaterials inspires diverse applications from designing machine materials, soft robots, and actuators to engineering biological tissues, implants, and prosthetic devices functioning under compression and torsion.
Mechanical metamaterials can exhibit extraordinary properties with a topological origin, such as localized floppy modes at the boundaries that naturally exist in the quantum Hall effect and topological insulators. The boundary modes can steadily propagate as topological kinks by keeping their localized shape intact, representing a soliton-like nonlinear wave pocket described by the well-known ϕ 4 model. The propagation of such topological kinks is usually self-induced and beyond the scope of programmability. However, we display a shear-driven transformations of topological kinks in a mechanical lattice consisting of a network of bistable units. We show that the structural characteristic of our system results in the emergence of domains with different structural phases in the structure, separated by topological kinks and antikinks in a longitudinally confined system. Then we show that the kinks/antikinks travel in under a shear deformation (torsion) by altering the domain size and structural phase of the system. Depending on the direction and magnitude of shear deformation, different events such as kink/antikink transformation, creation, or annihilation contribute to the structural phase transition of the system. Our observations suggest that our system is potentially a mechanical counterpart to a ferromagnetic system, where our structural units act as mechanical hysteretic elements and shearing plays as an external magnetic field that similarly alters magnetization in ferromagnetic materials. Controllable kink/antikink transformations provide a flexible platform to program the structural phase and evolution of materials, useful for encoding data, information processing, and energy transportation in a mechanical system.
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