Hierarchical, random and bifurcation tiling with heterogeneity in micro-structures construction via functional composition

This paper proposes new methods and algorithms for the construction of micro-structures that leads to a high degree of precision and water-tight models. That proposed approach involves the tiling of the domain of a deformation map using copies of a tile. The resulting tiling is functionally composed into the deformation map to obtain freeform micro-structures. Such a decoupling of the micro and macro structures allows a simplified control over design parameters. Herein, we present several extensions to this micro-structure construction scheme, comprising bivariate and trivariate tiles, implicit and parametric, including with potential discontinuities. We present support for fractal-like micro-structures, with self-similarity, allow the encoding of volumetric properties and hence heterogeneity, support for shelling and capping boundary operations, random tiling and bifurcation tiling, and support for degree reduction of the result. We verify the robustness of our approach by subjecting some of our heterogeneous micro-structures to isogeometric analysis. Finally, a variety of results from an implementation of our algorithms are also presented.