Hierarchical and fractal mechanical metamaterials: Design, fabrication and characterization.

Abstract

Mechanical metamaterials have recently gained much attention due to their unique properties, derived from their sophisticated microstructural design. Advances in additive manufacturing technologies allow us to fabricate complex geometries, that were very challenging to produce with conventional manufacturing techniques. In this study, we explore the use of hierarchy and fractal geometry to create new mechanical metamaterials. A methodology to design, fabricate, and characterize new fractal metamaterials based on diverse self-filling curves is presented here. We designed and parametrized a variety of fractal metamaterials, fabricated them using different additive manufacturing techniques and tested them under various load scenarios. The Hilbert curve was used to cut-extrude a solid cube and obtain a fractal honeycomb design. Samples were fabricated with TPU via Fused Filament Fabrication and tested under quasi-static uniaxial compression. The constituent material was firstly characterized under tension and compression showing a strain dependent behavior. Models of the fractal structure with different iteration orders and matching relative densities were tested under in-plane compression at two different orientations. A fractal decomposition technique was developed to enhance the stiffness of the structures. The results showed increase on stiffness for higher iteration orders and higher fractal decomposition at low strain levels. Lower densities and fractal iteration resulted more flexible and better at energy absorption. Various cellular structures and self-filling curve structures were used as reinforcement on a slender beam using different design approaches. The results showed increase on stiffness on the cellular patterns, specially for the reentrant pattern. Fractal reinforcements resulted into more flexible samples that withstand larger deformations before fracture occurs. Numerical simulations showed good accuracy with the experimental tests and delved the unconventional stress distributions on the fractal beams that caused eccentric deformations. Lower iteration orders resulted into increase of flexural stiffness. Brittle behavior was spotted on the cellular reinforcements. I-shaped structures were tested under out-of-plane loads and in-plane compression to study load-conformability and buckling. The tests revealed high influence of the axially aligned beams on the stiffness of the structures. Higher fractal iteration orders resulted into more flexible structures for both cases. Hybrid structures showed enhanced properties, having greater influence of the geometry in the middle. Higher iteration order structures showed better conformability and flexibility. The fractal structures showed different buckling deformation modes, showing failure tunability through fractal reinforcement.