Effect of fractal dimension on mechanical behaviour and energy absorption of Menger sponge-inspired fractal structures
Madhusha Bogahawaththa, Damith Mohotti, Paul J. Hazell, Hongxu Wang, Kasun Wijesooriya, C.K. Lee
Abstract
The Fractal Dimension (FD) of Menger Fractal Cubes (MFCs) defines their intricate geometry, making them ideal for lightweight structural applications. However, the effect of FD on their structural behaviour is largely unexplored. This study examines AlSi7Mg MFC geometries formed through a recursive process, with densities ranging from 40 to 1958 kg/m³, corresponding to FDs ranging from 2.35 to 2.73. Compression tests and simulations revealed that higher fractal orders increased densification displacement, achieving up to 80 % compressibility , with multi-level extended plateau regions indicating enhanced energy absorption. The fourth-order MFC with an FD of 2.35 and a density of 40 kg/m³ showed a specific energy absorption (SEA) of 6 J/g, demonstrating its potential for weight-efficient, energy-absorbing structures. The outcomes of this study indicate that total energy absorbed increases with an increasing FD, while crush efficiency improves as FD decreases showing better crashworthiness. Moreover, the structures exhibited unique force-displacement responses tailored to their FD. These findings offer valuable insights into optimising thin-walled fractal structures for various engineering applications by adjusting the FD to fine-tune relative density and enhance mechanical performance.