No abstract

No abstract

Individual cells and multicellular systems respond to cell-scale curvatures in their environments, guiding migration, orientation, and tissue formation. However, it remains largely unclear how cells collectively explore and pattern complex landscapes with curvature gradients across the Euclidean and non-Euclidean spectra. Here, we show that mathematically designed substrates with controlled curvature variations induce multicellular spatiotemporal organization of preosteoblasts. We quantify curvature-induced patterning and find that cells generally prefer regions with at least one negative principal curvature. However, we also show that the developing tissue can eventually cover unfavorably curved territories, can bridge large portions of the substrates, and is often characterized by collectively aligned stress fibers. We demonstrate that this is partly regulated by cellular contractility and extracellular matrix development, underscoring the mechanical nature of curvature guidance. Our findings offer a geometric perspective on cell-environment interactions that could be harnessed in tissue engineering and regenerative medicine applications.

No abstract

No abstract

Rapid advances in additive manufacturing have kindled widespread interest in the rational design of metamaterials with unique properties over the past decade. However, many applications require multi-physics metamaterials, where multiple properties are simultaneously optimized. This is challenging since different properties, such as mechanical and mass transport properties, typically impose competing requirements on the nano-/micro-/ meso-architecture of metamaterials. Here, a parametric metamaterial design strategy that enables independent tuning of the effective permeability and elastic properties is proposed. Hyperbolic tiling theory is applied to devise simple templates, based on which triply periodic minimal surfaces (TPMS) are partitioned into hard and soft regions. Through computational analyses, it is demonstrated how the decoration of hard, soft, and void phases within the TPMS substantially enhances their permeability-elasticity property space and offers high tunability in the elastic properties and anisotropy at constant permeability. Also shown is that this permeability-elasticity balance is well captured using simple scaling laws. The proposed concept is demonstrated through multi-material additive manufacturing of representative specimens. The approach, which is generalizable to other designs, offers a route towards multi-physics metamaterials that need to simultaneously carry a load and enable mass transport, such as load-bearing heat exchangers or architected tissue-substituting meta-biomaterials.

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.

Two-matrix composites combine fibers with two distinct matrices. This is achieved by impregnating fiber bundles with a high-stiffness matrix and embedding the cured bundles in a flexible matrix. Two-matrix composites have been shown to offer unprecedented combinations of transverse flexibility and longitudinal tensile strength, and could offer improved fiber alignment and manufacturability. Here, we explore this concept further by embedding carbon fiber micropultrusions in flexibilized epoxy matrices and examining the longitudinal compression behavior. Our results on thin-walled rings reveal that the failure mode depends on micropultrusion diameter, with small diameters resulting in micropultrusion kinking and larger diameters in splitting and crushing. Additionally, we find that two-matrix composites can offer higher compression strength than conventional composites with the same flexible matrix, despite a lower fiber volume fraction. The inherent manufacturing advantages and high anisotropy could make two-matrix composites interesting candidates for specific applications, such as morphing wings or additively manufactured composites.