Material-Based Design Computation: Tiling Behavior

From natural objects to man-made artifacts, tiling is all around us: it is the act of rationalizing highly complex form by breaking it up into smaller, continuous components. If well pursued, tiled objects can be easily designed and assembled. However, a geometric-centric view of tiling, whereby a predefined form determines the shape, size, and organization of tiles, has victimized the field of digital design. This paper questions the role of tiling as rationalizing method and offers an alternative theoretical framework and technical grounding for tiling behavior: the act of generation-through-tessellation informed by material behavior. The tools developed are implemented in the design of a 3D-printed chaise lounge, using multiple materials. The technical objective is to introduce a quantitative characterization and analysis of property mapping, as it is applied to a tiling algorithm using Voronoi cell tessellation. The network of tessellated Voronoi cells is used as an element in the Voronoi Finite Element Method (V-FEM) that the author developed. Various characterization functions and geometric parameters are generated, and V-FEM is executed for plane-strain analysis of doubly curved surfaces, from which global and local responses are evaluated.