Enhanced Energy Absorption Properties of Sierpinski Triangle-Inspired Multi-Layer High-Fractal Structures

Abstract

The design of hierarchical structures can significantly enhance mechanical properties and energy absorption characteristics, thereby improving the overall performance of engineering structural materials. This paper introduces a novel Multi-Layer, High-Fractal-Order Triangular structure (MLFT) based on the Sierpinski Triangle (ST), arranged in a multi-array configuration and fabricated using a 3D-printed aluminum alloy. The influence of layer number and fractal order on mechanical performance and energy absorption characteristics under quasi-static compression was investigated through theoretical analysis, experimental testing, and numerical simulations using Abaqus. The results reveal that, under in-plane quasi-static compression, the fractal order plays a critical role in determining mechanical properties. The inherent non-uniformity of substructures within higher-order multilayer fractal triangles induces multi-stage deformation, forming an effective secondary stress plateau that significantly enhances max compressive strength 2-3 times. Furthermore, a theoretical analytical model was developed to predict the initial yield load, and its accuracy was validated through simulation data. Regarding energy absorption, MLFTs with a fractal order of 3 exhibited greater specific energy absorption, being 2-3 times greater than that of non-fractal structures with the same layer. Likewise, it demonstrated superior homogeneous plastic deformation characteristics during the whole compression process, with a strain hardening index of 0.56, which is 2.8 times greater than that of aluminum alloy. This study elucidates the crucial role of fractal order in enhancing the mechanical and energy absorption properties of structural materials, with the results offering potential guidance for designing lightweight, high-performance metallic structural materials.

Keywords: Fractal Structure, Energy absorption, mechanical properties, Peak stress, Strain hardening