Compression response of nature-inspired metamaterials based on Fibonacci spiral

Abstract

In this study, we present a novel nature-inspired metamaterial with a Poisson's ratio sign-switching capability, offering progressive stiffness and enhanced tunability through symmetrical configurations, with potential applications in adaptive materials and impact damping. The metamaterial's architecture is based on the Fibonacci spiral, a pattern frequently observed in biological species and natural formations, derived from the Fibonacci sequence. To develop the metamaterial, the Fibonacci spiral is first thickened to form a 2D structure and then arranged in a circular pattern to create a novel unit cell. This unit cell is then patterned linearly in two directions to form the initial metamaterial structure. To enhance symmetry and stability, the metamaterial is horizontally and vertically cut, mirrored, and augmented with additional material extensions to prevent slipping during compression loading. The final metamaterial design is fabricated using additive manufacturing techniques and examined through finite element analysis (FEA) and experimental testing. Results demonstrate that the metamaterial exhibits an exponential increase in stiffness under compression and displays semi-auxetic behavior, initially shrinking and subsequently expanding when compressed. The proposed metamaterial also shows high specific energy absorption (SEA), particularly in bilateral symmetric configurations. A parametric study reveals that the metamaterial's geometrical parameters, including extrusion thickness, longitudinal cell count, and transverse cell count, significantly influence its stiffness under compression. The unique properties of this nature-inspired mechanical metamaterial, such as its substantial stiffness increase and Poisson's ratio sign-switching behavior, make it promising for applications requiring controlled deformation and high energy absorption. Potential uses include impact absorption systems, biomedical devices, and adaptive structures, particularly in protective gear and automotive components.