Harnessing fractal cuts to design robust lattice metamaterials for energy dissipation

Lattice metamaterials exhibit remarkable mechanical properties and novel functionalities, such as high specific stiffness, fracture toughness, tunable vibroacoustic properties, and energy absorption. This study explores a group of lattice metamaterials with fractal cuts that feature energy dissipation via structural sliding friction mechanisms and intrinsic material damping. Lattice metamaterials with three types of fractal cuts patterns were designed and fabricated using additive manufacturing. Three-point bending tests and numerical analysis have been combined to investigate their bending behavior. Experimental results show that the structural bending compliance of the metamaterials can be sharply enhanced by increasing the fractal orders, while at the same time keeping the shape recoverability during cyclic loading. Loss factors associated with the cyclic bending of these metamaterials are almost independent of the fractal order used, which is attributed to the synergistic effect between friction and viscoelasticity. It is further demonstrated via validated finite element models that the sliding friction plays a critical role by investigating the effects of the bending displacement and sample thickness on the flexural behavior. Results suggest that the magnitude of the maximum bending displacement has a negligible effect on the loss factors, and a power scaling law exists between bending stiffness and sample thickness. This study suggests that fractal lattice metamaterials have unique energy dissipation properties, with potential applications in many industrial sectors such as defense, energy, and transportation.