Hierarchical and fractal structured materials: Design, additive manufacturing and mechanical properties

Novel rationally designed structured materials (SMs) exhibit unconventional mechanical properties that cannot be found in common materials. Although most microarchitectures of the developed SMs are based on regular unit cell tessellation design, few studies have explored the potential of fractal geometry as a design tool for creating new SMs. A novel strategy for creating fractal-like aperiodic SMs based on Hilbert self-filling fractal curves synthetization is presented here. Families of continuous Hilbert structured cubes derived from two separate Hilbert curve iterations at three different matching relative densities were obtained, additionally, a method to decompose the Hilbert curve to obtain non-continuous Hilbert structured cubes is proposed. To obtain a broad overview of their mechanical response, samples were manufactured out of thermoplastic polyurethane via fused filament fabrication and tested under compression. An apparent model of elasticity has been proposed to classify their mechanical performance under low and high strain. Results showed that relative stiffness, energy absorption and deformation could be tuned by adjusting parameters of the Hilbert structured cubes. By iterating the Hilbert curve from n = 4 to n = 5, a 51% increase in stiffness was obtained. A significant increment of 82% and 148% on stiffness was observed on non-continuous Hilbert structured cubes for the first and second orders, respectively; besides, energy absorption capabilities and great shape recovery were observed.