Curvature Induced by Deflection in Thick Meta‐Plates

Abstract

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.

Characterization of two-photon-polymerization lithography structures via Raman spectroscopy and nanoindentation

“…The more recently developed photoresist IP-Q was designed by the same manufacturer for larger size applications, e.g., mounts, 3 molds, 4 and structural metamaterials. 5 Currently, a major constraint of TPP in general and specifically IP-Q is that users have limited access to knowledge about material properties. For example, before this work, no degree of conversion (DC) and Young's modulus values for IP-Q have been reported.…”

Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part I

“…Consider, for instance, the tile surrounded by other tiles depicted in figure 9. By writing (2.10) for each vertex of the tile and summing all these equations, several terms cancel out and the resultant equation is ϕ {2,3} n (2,3) + ϕ {3,4} n (3,4) + ϕ {4,5} n (4,5) + ϕ {5,6} n (5,6) + ϕ {6,7} n (6,7) + ϕ {7,2} n (7,2) = 0, somehow representing the null 'circulation' of the relative rotations around a tile (see also figure 9).…”

Unexpected bending behavior of architected 2D lattice materials

“…Further increase in the bending moment tends to suppress the transverse curvature because of the geometrically nonlinear effect, and the plate becomes more cylindrical in nature (12)(13)(14). In light of these results, it has been commonly believed as a rule that the 2D lattices with a positive IPR also behave so, while those with negative IPR adopt synclastic curvature (dome shape) in the same loading condition (8,(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27). Both kinds of curvatures are easily observable in conventional and reentrant 2D hexagonal honeycombs, which have positive and negative IPRs, respectively (15).…”

“…Nonetheless, for the large number of literature we mention here (2,3,23,(29)(30)(31)(32)(33)(34)(35)(36)(37)(38) among others, most of them are concentrated on the in-plane responses. Exploration of the out-of-plane bending is rare (17,21,26,(39)(40)(41)(42)(43)(44)(45), and the underlying mechanisms for anticlastic and synclastic curvatures remain elusive at the structural element level. Here, we combine theory and experiments to explore unidirectional bending of 2D lattice materials with starshaped unit cells consisting of elastic beams of rectangular cross section.…”