Static and dynamic elastic properties of fractal-cut materials

We investigate the static and dynamic (phononic) elastic behavior of fractal-cut materials. These materials are novel in the sense that they deform by rotation of “rigid” units rather than by straining these units, can be fabricated by exploiting a simple cutting paradigm, and have properties that can be manipulated by control of the cut pattern and its hierarchy. We show that variation of fractal-cut level and cut pattern can be exploited to manipulate the symmetry of the elastic constant tensor, the elastic limit of deformation, and, therefore, the elastic response. By studying phonon behavior, we demonstrate how some cut symmetries naturally open acoustic band gaps. Several of the important features of the band structure can be directly related to the static elastic properties. Based upon our phonon calculations, we predict the acoustic transmission spectrum of an example fractal-cut structure and validated it through 3D printing and sound attenuation experiments.