PSI - Issue 83

Kemal Arslan et al. / Procedia Structural Integrity 83 (2026) 218–228

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Keywords: Menger fractal structure; Hierarchical porous architecture; Additive manufacturing; Crashworthiness; Energy absorption; Finite element modeling

1. Introduction Energy-absorbing structures are essential members in engineering designs where impact mitigation and crashworthiness are critical, particularly in the automotive, aerospace, and defense industries. Such structures are designed to dissipate impact energy efficiently while maintaining controlled deformation and structural integrity. In the automotive sector, thin-walled metallic components, especially aluminum and steel tubes, have been extensively studied and adopted due to their well-understood deformation modes and energy absorption behavior under axial crushing loads. Foundational studies by Abramowicz and Jones (1984a, 1984b) established the fundamentals of the crushing behavior of square and circular tubes, while later studies showed that crash performance can be improved through geometrical modifications, trigger design, inserting filler material or structure, and multi-cell arrangements to overcome the limitations of traditional single-cell tubes, such as unstable collapse and high initial peak force [Guler et al. (2010), K  l  çaslan (2015), Rai et al. (2019), Wang et al. (2022), Zarei and Kröger (2008), Simpson and Kazanc  (2020), Qui et al. (2015), Gong et al. (2021)]. The rapid development of Additive Manufacturing (AM) technologies has further advanced this field by presenting superior geometric flexibility. Unlike conventional manufacturing techniques, AM enables the production of intricate cellular and architected structures that can be tailored across multiple length scales to enhance energy absorption performance. Studies have shown that AM-fabricated structures offer excellent design flexibility and can exhibit improved energy absorption efficiency, particularly in specific energy absorption and deformation control, due to their ability to promote stable progressive deformation [Bandinelli et al. (2024), Wan et al. (2024), Han et al. (2025), Xing et al. (2026)]. Within the class of architected structures, fractal-based geometries, such as Menger sponge-inspired structures, have recently attracted attention for their hierarchical and self-similar nature. Fractal structures can provide unique opportunities by distributing material efficiently across multiple scales, potentially enhancing energy dissipation mechanisms. The Menger sponge, a well-known three-dimensional fractal structure, is generated by repeated subdividing and removing cubic volumes, resulting in a highly porous yet mechanically interconnected architecture. Initial attempts were made to investigate the energy absorption and mechanical performance of Menger fractal cubic structures across different fractal orders and dimensions [Bogahawaththa et al. (2024, 2025)]. These studies indicated that Menger fractal structures exhibit a unique force-displacement response with multi-stage energy absorption mechanisms compared with conventional cellular structures, suggesting improved crashworthiness, and that their mechanical behavior can be tailored by tuning fractal dimensions. Despite these studies thoroughly investigating the energy absorption behavior of Menger fractal structures, they are limited to their cubic forms. Therefore, further research is needed to better understand the energy absorption capabilities of the tubular form of Menger fractal structures, particularly for crash box applications. Based on this motivation, the present study aims to numerically investigate the dynamic crushing behavior of additively manufactured aluminum alloy Menger fractal tubular structures with different fractal orders. The first- and second order Menger geometries were analyzed and compared with a conventional steel tube of equivalent mass using the explicit finite element framework. The findings present preliminary results regarding the potential use of Menger fractals in crashworthiness applications. 2. Materials and Structure Design The Menger Fractal (MF) cube, first described by Karl Menger in 1926, is a self-similar structure formed by recursively subdividing and selectively removing cubic elements. The procedure begins with a solid cube and continues with the removal of smaller cubes, which are the central smaller cube and the six face-centered smaller cubes, from the larger cube, and repeating this removal process for the remaining cubes (Fig. 1a). Therefore, the volume of the Menger cube ( V n ) can be calculated as