Ultralight fractal structures from hollow tubes

A material’s architecture can be controlled over an ever increasing set of length scales.

Physical Review Letters 109, 204301 (2012)

D. Rayneau-Kirkhope, Y. Mao, R. Farr

A material’s architecture can be controlled over an ever
increasing set of length scales.

A fractal design is shown to be highly efficient both as a load bearing structure and as a general metamaterial. Through changing the hierarchical order of the structure, the scaling of material required for stability against loading can be manipulated. We show that the transition from solid to hollow beams changes the scaling in a manner analogous to increasing the hierarchical order by one. An example second order solid beam frame is constructed using rapid prototyping techniques. The optimal hierarchical order of the structure is found for different values of loading. Possible fabrication methods and applications are then discussed.