Detailed structural analysis and theoretical calculation show that this material is a mechanical metamaterial exhibiting auxetic behavior. Here, we report a metal-organic framework, self-assembled from a porphyrin linker and a new type of Zn-based secondary building unit, serving as a joint in a hinged cube tessellation. However, incorporating movable building blocks inside solids, thereby enabling us to manipulate mechanical movement at the molecular scale, has been a difficult task. Rational design of mechanical metamaterials at the microscale is becoming popular partly because of the advance in three-dimensional printing technologies. This work demonstrates that the topology of the framework and flexible hinges inside the structure are intimately related to the mechanical properties of the material, providing a guideline for the rational design of mechanically responsive metal-organic frameworks.Ībstract = "Mechanical metamaterials exhibit unusual properties, such as negative Poisson's ratio, which are difficult to achieve in conventional materials. These pyramids can be further subdivided into four tetrahedra each for a total of 24 tetrahedron.Mechanical metamaterials exhibit unusual properties, such as negative Poisson's ratio, which are difficult to achieve in conventional materials. For example, it is possible to split a cube into 6 pyramids with the apex in the center of the cube using the faces of the cube as their bases. ![]() These artifacts make the use and manipulation of complex volumetric primitives cumbersome.Īll of the artifacts discussed can be minimized or avoided by splitting the cube into a larger number of more uniformly distributed tetrahedra. Worse yet, moving one of the vertices shared between two adjacent boxes results in “cracking.” Therefore, one of the two adjacent faces (solid box) is rendered with red (bright) running along one diagonal, while the other (wire frame box) has a similar band running along the opposite diagonal. Yet, due to the asymmetry inherent in the tessellation, the adjacent faces have opposite diagonals as bases for their tessellations. For example, the wire frame box in Figure 2-16 has the same tessellation and vertex coloring as the solid one. This artifact is analogous to creating T-junctions in polygonal tessellations.Ĭonnecting multiple boxes through face adjacency leads to inconsistent (and highly noticeable) interpolation bands. Therefore, the resulting faces will have either a red (bright) or a blue (dark) diagonal band running along the edge of the tetrahedron that divides them. However, the interpolation only occurs within a tetrahedron. One would expect the faces of the cube to be smoothly interpolated between the respective vertices. The vertices of the cube alternate between red (bright) and blue (dark). In the remainder of the book, the term “volume” describes the pairing of geometry and appearance. ![]() ![]() It is the combination of geometry (for example, a sphere) and appearance (for example, voxels representing your data) that compose a volumetric shape. In these examples, the shape's geometry and appearance are clearly decoupled. For example, it is possible to move a circular geometry around inside a (larger) texture image like a magnifying glass, or to texture map an image onto a (smaller) sphere or a bicubic patch capable of squashing and twisting. Having an appearance match the size of a geometry, however, is a special, not a general case. For example, two-dimensional texture maps, which are rectangular arrays of values (pixels), are often mapped onto a single rectangular polygon of equal size. In many cases there is a close relationship between appearance and geometry. For example, a rectangular shape may be described by a quad mesh (geometry) with a two-dimensional texture (appearance) mapped onto it. In traditional three-dimensional graphics, graphical objects, called models or shapes in this document, are commonly described in terms of geometry and appearance.
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