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Materials Science in Additive Manufacturing Energy absorption of Moore’s thin-walled structures

arrangement. Among them, the cross-section profile is one used as infills. In early 2000, hollow foam-filled tubes
of the most critical factors . Various shapes have been were studied analytically and numerically to demonstrate
[13]
explored for the outer layer tubes, including triangle [14,15] , the higher weight-efficiency in energy absorption .
[33]
square [16-18] , pentagon , hexagon , and circle [14,15,21,22] and Compared to tubes without foam-infill, hollow foam-filled
[19]
[20]
more recently different cross-section designs for the infill tubes exhibited higher energy absorption capacity with the
have been proposed and elaborated [23-25] . same mass. Similarly, Dadrasi et al. conducted a study
[34]
When it comes to cross-sectional configurations, nature- to compare the crashworthiness of another fractal-pattern
inspired patterns are often employed due to its multi- inspired thin-walled columns with and without foam-infill.
functional features and outperformed characteristics [26,27] . The previous studies have focused on the out-of-plane
One of the fascinating patterns that could be found in nature crashworthiness of structures as vertical thin-walls are
is the fractal, for instance, the galaxy and seashell. Fractal, known to provide strength and stiffness. Moreover, most of
as defined in mathematics, is a geometry that resembles the structures have integrated fractal patterns with a thin-
itself at various scales . Several studies investigating the walled tube as the outer layer to improve their mechanical
[28]
crashworthiness of fractal-inspired thin-walled structures properties. However, this outer layer tube adds extra
(Figure 1) have provided a new approach to designing weight and cost.
novel lightweight energy absorbers with improved crashing
characteristics [29-32] . In 2018, Zhang et al. investigated Furthermore, fatigue damage also plays an
[23]
[35,36]
the crashworthiness of fractal hierarchical hexagon thin- important role in energy absorption ; therefore,
walled structures that were inspired by spider webs. Fractal cyclic performance is critical for energy absorption in
[37]
configurations, geometrical parameters, and fractal orders engineering applications . An energy absorbing device
have proven to play important roles in energy absorption. with low recoverability after cyclic loading is likely to have
Besides, Wang et al. proposed a thin-walled structure a short lifespan, which could potentially lead to casualties,
[24]
design with cross-sections of Koch snowflakes. Interestingly, structural damages, and extra maintenance cost. However,
the 2 order Koch snowflake design outperformed a wide loading and unloading cyclic compression experiments
nd
range of multi-cell structures with the same mass, thus have not been studied on any fractal-inspired thin-walled
supporting the argument proposed by Zhang et al. . structures. Moore space-filling curves, as another type of
[23]
Numerically and analytically, Huang et al. introduced a fractal structure, are rarely used as the design motif for thin-
[26]
gradient fractal thin-walled structure inspired by bamboos walled structures. Space-filling curves are characterized
to improve the SEA, comparing to conventional square by a unique feature, that is, a finite area would be filled
honeycombs. Again, the 2 order fractal tube yielded the with a curve of infinite length after an infinite number of
nd
best energy absorption per unit mass. iterations. Theoretically, Moore space-filling curves could
fill a limited design space with infinite length of curves.
To improve the energy absorption capacity of fractal- For a given relative density of thin-walled structures, the
inspired thin-walled structures, reinforcements have been cross-section could be filled with infinite space-filling
curves by increasing fractal hierarchy. Thus, thin-walled
A structures with such cross-sectional configurations could
offer great potential for excellent mechanical responses in
the in-plane direction .
[38]
From the design point of view, many studies have been
carried out over the past few decades on different cross-
sectional shapes of thin-walled structures. However, the
B complex geometries of cross-sectional configurations have
yet to be explored due to the limitations of conventional
manufacturing technology . The manufacturing process
[39]
of structures with complex geometries has become easier
than ever using advanced additive manufacturing (3D
printing) techniques [40-42] . The main purpose of the present
work was to study energy absorption for a novel compliant
thin-walled structure. These newly designed infill
patterns were inspired from Moore space-filling curves
Figure 1. Fractal cross-sections employed in thin-walled structure design: with three fractal hierarchies. Three relative densities,
(A) Koch snowflake; (B) Sierpiński curve. that is, 20%, 30%, and 40%, were investigated for each

Volume 2 Issue 1 (2023) 2 https://doi.org/10.36922/msam.53