| dc.description.abstract | Over the past decades, the benefits of segmentation and fragmentation has started gaining the interest of researchers of engineering design community. Fragmented materials in which the individual segments are held together not using a binder or adhesive, but simply through the geometry of constituting shapes and their arrangement are called topologically interlocking materials. Such materials has proven to have distinctive properties like energy absorption, fracture toughness and structural integrity compared to monolithic solids.
The geometric design space of the existing topologically interlocking shapes has remained limited and we observe that there is no systematic design methodology to design and explore topologically interlocking shapes. We note that this problem is better understood using the conceptual framework of space-filling shapes because it helps us create both water-tight (or void-free shapes) and repeatable shapes (that are easy to mass produce). So the aim of our research was to develop a systematic methodology to design and explore potentially new topologically interlocking shapes that are repeating and fill-space in a water-tight way. We inspire our approach from a novel topological shape called ‘Scutoid’ that are found in skin cells. The presence of this shape minimizes the tissue energy and stabilizes the 3D packing. Scutoids are important to us because they are both watertight and showed some potential for topo-logical interlocking. Scutoids are constructed by a layer-by-layer Voronoi decomposition. We use this fact to generalize and develop an elegant design methodology to design a new class of shapes that did not exist before called ‘Delaunay Lofts’. Specifically, the ‘Topology shift’ or bifurcation that makes Scutoids interesting, happens when a Voronoi edge collapses to a four valency Voronoi vertex and splits back to a Voronoi edge. We show that if we use a quad grid as a reference and define control line segments passing through the quad grid, we automatically obtain the bifurcation. Subsequently, we describe how we can use Wallpaper symmetry groups to create repeatable shapes. However, the algorithmic limitations of Delaunay Lofts restricts free-form exploration of control curves and the shapes fails to show significant topological interlocking capabilities.
To overcome this, we developed an algorithm for Voronoi decomposition with higher dimensional Voronoi sites. Further, we take inspiration from Abeille’s Vault design from 1699 and pro-pose the design of interlocking shapes by finding a visual correspondence with weave symmetry. Then we do a structural analysis and compare the results of three such topologically interlocking assemblies we get using predefined Voronoi sites. The results show that the tiles have a well-defined stress patterns and stress magnitudes are comparable to that of the equivalent monolothic solid. This research also shows a great potential in the areas of 3D printing in-fills, metamaterial designs, packaging and education applications. | |
