LAUSR

Abstract Design of fractal microstructures holds promise for developing advanced materials with improved mechanical properties and multiple functions. In this paper, a concurrent topology optimization method is proposed to design both two- and three-dimensional, fractal or hierarchical microstructures. The Boolean subtraction operator (BSO) is introduced to guarantee the self-similarity among a hierarchical structure at different levels. This method allows us to generate a diversity of fractal structures which have, for instance, the geometric feature of either clockwise or counterclockwise chirality. By evoking the fractal Menger sponge as the non-designed domain, we have obtained fractal structures in which all internal transversal sections have hybrid fractal morphologies. Though our attention is here focused only on the mechanical properties of materials, the proposed method can also be applied to design fractal structures with optimal optical, acoustic, and electromagnetic properties.